Notes on Basic Math

Introduction to Notes on Basic Math

In mathematics all calculations made with the basic math operation. The notes on basic math operation names are addition, subtraction, division, multiplication. These functions are mainly used in math and computer. The basic math helps us to find out the result in accurate manner. Here we will see about these four methods notes.

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Addition and Subtraction


The notes of addition and subtraction is as follows.

Addition

Addition is used to adding the numbers. We use the symbol +. The other name is sum, plus, increment, total.

Examples

1) Adding the following two numbers. 20, 30.

Solution

The first number is 20

The second number is 30

So add the two numbers= 20

30 (+)

50

2) What is the total of the following numbers? 120, 30, 170, 40?

Solution

The given numbers are 120, 30, 170, and 40.

Total = 120

30 (+)

170

40

360

Subtraction

It is used to find the difference between two numbers. The symbol is -. The other words is minus, less, Decrease.

Examples

1) What is the difference between the following two numbers? 41, 36.

Solution

The given numbers are 41, 36.

The difference between the two numbers is = 41

36 (-)

5

2) Find out the difference between the following numbers? 46, 57.

Solution

Given numbers are 46 and 57.

The difference is 46

57 (-)

-11

The answer is -11. Because the 1st number 46 is less than 2nd number 57. So the symbol must be put which the number is big. I have recently faced lot of problem while learning Quadratic Equation Formulas, But thank to online resources of math which helped me to learn myself easily on net.


Multiplication and Division


The notes about multiplication and division is as follws.

Multiplication

It is used to product the numbers. the symbol is x. the other name is multiplication, multiply.

Examples

1) Multiply the following numbers. 12, 4.

Solution

The given numbers are 12 and 4.

The multiplication is 12 x 4= 48.

2) What is the multiplication of the following numbers? 13, 2, 6.

Solution

Given numbers are 13, 2 and 6.

The multiplication is 13 x 2 x 6 =13 x 12=156.

Division

It is one of the basic math operations. The symbol is ÷. The other name is division, quosient.This is one of the basic math operation.

Examples

1) Divide the following numbers. 12/4

Solution

The given number is 12. The divisor is 4.

The division is 12/4=3.

2) Divide the following number 20 with 5.

Solution

The division is 20/5=4.

These are the notes of the basic math.

Probabilities Math

Probabilities math

The Probabilities math is the mathematics. This is used to get the expected value of the combination possibles. The Probabilities math is the number of possible outcomes is divided into the total number of outcomes.

Probability =` ("Number of possible outcomes n(a)")/ ("Total number of possibles n(s)")`

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Probabilities math Examples:


Probabilities math – Example 1:

Roll two dice; find the probabilities of Dice are 6 and 1

Sol :  Total Number of possible = n (a) =         {1,1}{1,2}{1,3}{1,4}{1,5}{1,6}

{2,1}{2,2}{2,3}{2,4}{2,5}{2,6}

{3,1}{3,2}{3,3}{3,4}{3,5}{3,6}

{4,1}{4,2}{4,3}{4,4}{4,5}{4,6}

{5,1}{5,2}{5,3}{5,4}{5,5}{5,6}

{6,1}{6,2}{6,3}{6,4}{6,5}{6,6}

n (s) = 36

The number of outcomes n (a) = {6, 1} {1, 6}

n (a) = 2

The probability of getting value = 2/36= 1/18.

Dice Problems:

Probabilities math Example 2:

Roll a single dice; find the probability of get number 4.

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

n (s) = 6

The number of outcomes n (a) = {4}

n (a) = 1

The probability of getting value = 1/6.

Coins Problems:

Probabilities math Example 3:

To toss a coin finds to get one tail of the possible outcomes

Solution:

Step 1:

n (s) = {T, H}=2

Step 2:

Tossing a coin with only one head:

n (a) = {T}=1

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = 1/2.

Convert into a decimal 0.5

The probability of one head is 0.5 or Rounded 50%.

Probabilities math – Example 4:

Throw four coins and find the probability of two tails and two heads.

Solution:

Step 1:

n (s) = {TTTT, TTTH, TTHT, THTT, HTTT, TTHH, THHT, HHTT, THHH, HHHT, HHHT, HHTH, HTHH, THHH, HTTH, HHHH}=16

n (s) = 16

Step 2:

There are 4 tosses with only two tails:

n (a) = { HHTT, TTHH, HTTH, HTTH, }=4

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = 4/16 = 1/4.

Convert into a decimal 0.25

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Practice problems for probabilities math:


Roll two dice; find the probabilities of Dice are not 6 and not 1

Answer:

16/36 (or) 0.4444

2. Roll two dice; find the probabilities of At least one dice isn't 6

Answer:

35/36 (or) 0.9722

Extra Help Math

Introduction to extra math help:

Mathematics is an important tool in many fields, like engineering, medical science and natural science. Tutor vista provides extra helps for student after schooling hour in various subjects like English, math, and science. Tutor vista helps at any time around the clock regardless of place where they are located.  Student can learn extra and do homework from their home after schooling. Tutor explains step by step so that the students can easily understand.   In this article we shall discuss extra help in math problems.

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Extra math help example problem


Example:

Solve the inequality -3< 4(x+2)-3<17 br="">
Solution:

Given inequality is

-3< 4(x+2)-3<17 br="">
Multiplying the factor values for equation

-3<4x br="">
-3<4x br="">
Subtract value 5 on both sides of equation

-3-5<4x br="">
-8<4x br="">
Divide by 4 for all terms

-2
Conclusion:

The solution consists of all real number the interval (-2, 3)

Example:

Seven men 9 hours need to complete a particular job. Calculate how long it takes 10 men to do the job they work at the same rate?

Step 1:

Let the given problem as If 7 men then 9 hours need. If 10 men then how many hour need to complete the job

Step 2:

The inverse proportional relationship:

7 => 9

10 =>7 / 10 x 9

=> 63/10

=>6.3 hours

Answer:

They will take to complete the job in 6.3 hours.

Example:

Solve the x for the equation.

2(2x - 2) + 2x = 4(2x + 2)

Solution:

Multiplying factor 2 with (2x-2) and 4 with (2x+2)

4x - 4 + 2x = 8x + 8

Subtract 2x on both side of equation

4x - 4 +2x-2x= 8x -2x+ 8

4x - 4 = 6x+8

Subtract 6x on both side of the equation

4x-6x-4 = 6x-6x+8

-2x-4=8

-2x=8+4

-2x=12

Simplify the x value

x =12/-2

x = -6

Answer:

x = -6

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Extra math help practice problem


Problem:

Solve the x for the equation.

2(4x - 2) + 2x = 3(2x + 4)

Answer:

x = 4

Problem:

Eight men 10 hours need to complete a particular job. Calculate how long it takes 11 men to do the job they work at the same rate?

Answer:

They will take to complete the job in 7.2 hours.

2nd Grade Math Solve

Introduction to second grade math:

The second grade math defines the basic mathematics for the students of second grade. This involves the basic addition and subtraction with two digits and three digits. It also involves the counting of numbers and number patterns. The second grade syllabus teaches the students about the place values, comparing numbers, patterns, and also teaches about the time and date graph.

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Addition in second grade


Addition in second grade math to solve:

Addition is one of the term which is used in arithmetic operation. In addition we are going to add two elements and give the answer. Addition can be done for numbers with any number of digits. Addition is identified by using the sign ‘+’.

Addition with two digits in second grade math:

Here we are going to add two digit numbers. To solve the two digit addition the example problems are given below.

Problem 1: Solve: 25 +36

Here we are going to add the two digit number 25 and 36.

2 5

3 6

-----

6 1

-----

While solve this sum we add 5 and 6 we get a remainder 1 which is added along with 3 and 2. Hence the answer is 61.

Problem 2: Solve: 61 +76

Here we are going to add the two digit numbers 61 and 76.

6 1

7 6

------

1 3 7

-------

Thus the answer is 137.

Addition with three digits in second grade math:

Here we are going to see about the addition of three digit numbers. The example problems to solve three digit additions are given.

Problem 1: Add 369 and 741.

3 6 9

7 4 1

---------

1 1 1 0

---------

Here when we solve 9 and 1 we get the remainder 1 which is added along with 6 and 4 but it also give remainder 1. Thus this remainder 1 is added along with 7 and 3. Therefore the answer is 1110.

Problem 2: Add 252 and 141.

2 5 2

1 4 1

--------

3 9 3

--------

Therefore the answer is 393.

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Subtraction in second grade


Subtraction in second grade math to solve:

Subtraction is the inverse process of addition which is also a term used in arithmetic operations. Subtraction is identified by using the sign ‘-‘.  In the subtraction there are two parts present minuend and also subtrahend. While subtracting the subtrahend from the minuend it gives the difference.

Subtraction with two digits in second grade math:

Here we are going to subtract the two digit numbers. To solve the subtraction with two digits the example problems are given.

Problem 1: Solve: 68 – 24.

6 8

2 4

------

4 4

------

Therefore the answer is 44.

Problem 2: Solve 82 – 53.

8 2

5 3

------

2 9

------

Her in this problem we cannot subtract 3 from 2 hence we are borrowing a 1 from 8 so 2 becomes 12. By subtracting 3 from 12 we get the answer 9. And by subtracting 7 and 5 we get 2.

Subtraction with three digits in second grade math:

Here we are going to subtract three digit numbers.

Problem 1: Subtract 742 and 431.

7 4 2

4 3 1

--------

3 1 1

--------

Therefore the answer is 311.



Problem 2: Subtract 666 and 321.

6 6 6

3 2 0

--------

3 4 6

--------

Therefore the answer is 346.

Grade 7 Math Fractions

Introduction to grade 7 math fractions:

A fraction is a part of a whole. Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator. The denominator of a fraction is the number that shows how many equivalent parts are in the entire measure. The numerator of a fraction is the number that shows how many equal parts of the, whose are taken.

Numerator
denominator

In a fraction, if the numerator is smaller than the denominator, it is called as proper fraction. Proper fractions are in completely reduced form. If the numerator is bigger than the denominator, these types of fractions are called as improper fractions. If a fraction is constructed by a whole number and a proper fraction is called as mixed fraction.

For example, 2/3 is a proper fraction (2 < 3), 5/3 is an improper fraction (5 > 3), 2 1/3 is a mixed fraction (2 is a whole number, 1/3 is a proper fraction)


Grade 7 math fractions – Mixed fraction and improper fraction:


Grade 7 math fraction - Express mixed number as improper fraction:

Procedure: To express a mixed number as an improper fraction

Multiply the whole number by the denominator.
Add the numerator to obtain the numerator of the improper fraction.
The denominator is the same as that of the original fraction.
Example problems:

Problem 1:

Express 4 ½ as an improper fraction

Solution:

Multiply the whole number by the denominator.

Add the numerator to obtain the numerator for the improper fraction.

= (4 * 2 + 1) / 2 = (8 + 1) / 2

The denominator is the same as that of the original fraction.

= 9 / 2

Grade 7 math fraction - Expressing improper fraction as mixed number:

Procedure: To express an improper fraction as a mixed number

Divide the numerator by the denominator
Example problems:

Express the following improper fractions as mixed numbers

15 / 4 = 3 3/4
43 / 3 = 14 1/3.

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Grade 7 math fractions – Mixed fraction and decimal:


Grade 7 math fraction - Decimal to mixed fraction steps with example:

Problem:

0.56 to mixed fraction

Solution:

Here's convert 0.56 to a mixed fraction, means. Since there are 2 digits in 56, the very last digit is the "100th" decimal place. So we can just say that 0.56 is the same as 56/100.

The fraction 56 /100 is not reduced to lowest terms. We can reduce this fraction to lowest terms by dividing both the numerator and denominator by 4.

Divide by 4, 4 is the Greatest Common Divisor (GCD) of the numbers 56 and 100. So, this fraction reduced to lowest terms is 14 /25 = -1 9/25. So your final answer is: 0.56 can be written as the fraction -1 9/25

Grade 7 math fraction- Mixed fraction to decimal steps with example:

Problem:

2 5/3 to decimal.

Solution:

A mixed number is a whole number and a fraction. In this problem mixed number will be 2 5/7

Change the mixed number into an improper fraction. This is done by multiplying the denominator by the whole number and then adding the numerator (2 * 7) + 5. This will be new numerator.

And the improper fraction with the new numerator on top and existing denominator on the bottom, the new fraction 19 / 7.

Divide the numerator by denominator. Add a decimal point after the whole number and continue to divide by adding zeros after the decimal as needed. Then answer is 2.714, which can be rounded up to 2.7

Answer: So final answer 2.7

All Properties of Math

Introduction to properties of math:

The mathematics is the arithmetic operations of addition, subtraction, multiplication, division, and algebra 1, the algebra is the branch of mathematics which deals with the rules of operations and relations, and the building and concepts occur from them, containing terms, polynomials. Algebra can be used with geometry, combinatorial, and number theory. Let us see all properties of mathematics

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All properties of mathematics:


All Reflexive Property

If somewhat is equal to its matching twin

X = X

All Symmetric Property

If somewhat turn over sides of the equivalent sign

X= y & y = x

All Transitive Property

If two objects are equal to a third object, the two are equal

X= y , z = y and x = z

All Commutative Property

If you inverted the order of addition or multiplication

X + y = y + x

All Associative Property

If you altered a alignment rearranged parenthesis, but kept the whole thing else in the same order

X + ( y + z ) = ( x + y ) + z

All Addition Property

If you added the similar non-zero numbers to equal sides

If x=y then

X + z = y + z

All Multiplication Property

If you multiplied the same nonzero number to both sides you have used this property

If x = y xz = yz

All Additive Identity

If you added 0 to get the same number back

X + 0 = x

All Multiplicative Identity

If you multiplied by 1 to get the same number back

(x)1 = x

All Property of Opposites

If you added opposite number’s and ended with 0

x + (-x) = 0

All Property of Reciprocals

If you multiplied by a reciprocal to get 1

(b)1/b=1.

All Distributive Property

If you multiplied x number into or pulled x number out of parenthesis

X ( y + z ) = xy + xz

Qr + rs = (q + s) r

All Multiplication Property of 0

If you multiplied by 0 and got 0

(a)0 = 0

All Multiplicative Property of (-1)

If you multiplied by (-1) and got the opposite of what you started with

X(-1) = -X

All Comparison Property

If you have stated that xy

All 1st Multiplication Property of Order

If you multiplied an inequality by a positive number and maintained the inequality

x < y, c is +, then xz < yz

All 2nd Multiplication Property of Order

If you multiplied as inequality by a negative number and reversed the inequality

x < y, c is –, then xz > yz

All Cancellation Property of Addition

If you cancelled the similar quantity from both sides of an equation (by subtracting)

x + y = y + z then x = y

All Cancellation Property of Multiplication

If you cancelled the same nonzero quantity from both sides of an equation (by division)

xz = yz so x = y

All Zero Product Property

If a product is zero, so you know that one of the factors has to be zero

xy = 0 if x = 0 or y = 0

All Definition of Division

If you changed a division to multiplication by a reciprocal

`x/y` = (x)1/y

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All Definition of Subtraction

If you have switched from adding a negative to just subtraction, or vice versa

x + (-y) = x - y

All Definition of Exponents

If you have also out of order apart exponents or shaped an exponent by multiplying a number by itself

(x) x = x2

All Substitution Property

If you have substitute one statement with an corresponding one and no other property or definition works

Math Sentence For Kids

Introduction to word problems:

Word problems are sentences describing a mathematical question.  It is an alternative method of expressing different mathematical problems. Word problems are simple sentences mainly used to explain a practical situation where mathematical operations or application is used.

Few important words used in word problems are :

Sum, altogether ------  all stands for  `addition (+)`
Substract, take away, left over -----all  stands for ` minus (-)`
Times, product -------- all stands for `"multiply" ( * )`
A simple way to explain addition or substraction to kids is by forming simple sentences. Kids can relate more easily to simple sentences than mathematical symbol.

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Simple word problems on addition:


Ex 1: Mary had 3 cookies.  John had 5 cookies. How may cookies do they have altogether?

Sol: Step 1:  First we will try to find the word which describes mathematical operation

In this question, word is "altogether", means we have to perform addition

Step 2:  Mary -------- 3 cookies

John --------- 5 cookies

Step 3: Total -------  Add 3 and 5

So,  3 + 5 = 8 cookies

Ex 2: Alice had 2 pencils.  Her mother gave her 3 pencils.  How many pencils do Alice altogether?

Ans: Alice has 5 pencils

Ex 3: In a box, there are 5 candies. If Joe put 8 more candies in the box, then how many candies are there in the box altogether?

Ans:  There will be 13 candies in the box altogether


Simple word problems on subtraction:


Ex 1: Matt had 10 oranges.  He made juices out of 6 organes then how many oranges are left?

Sol: Step 1: First we will try to find the word which describes mathematical operation

In this question, word is "left", means we have to perform subtraction

Step 2:  Matt had 10 oranges

6 oranges were used for taking juice

Step 3:  10 - 6 = 4

Remaining will be 4 oranges

Ex 2: 15 posters were pasted all over the school. If 5 were removed, then how many were left?

Ans:  10 posters

Ex 3: Sally had 8 dolls.  She gave 3 dolls to her cousin.  How many dolls does Sally have left?

Ans: 5 dolls

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Simple word problems on multiplication:


Ex:  Cost of one banana is $ 5. Jack buys 3 bananas. What is the total cost of 3 bananas?

Cost of 3 bananas is $ 15

Ex 2:  What is the product of 5 and 6?

Ans: 30

Ex 3:  Mike's paper boat measures 2 inches. Mike's dad makes a paper boat 4 times bigger than Mike's. What is the measure of dad's boat?

Ans:  Dad's boat is 8 inches.

Solve For X in Math

Introduction:

Solving deals with the variable, the variables are in the form of alphabets, such as x, y, z, m, n. Using this we can create any expressions in the equation form and find the value of variables. This article we will be discussing about solving for x in math. Mostly we use mathematical expression assigned with the variable x only. Basically algebra equations also use the variable x in math. Now we are solving some equation with x variable. Having problem with Dividing Radical Expressions keep reading my upcoming posts, i will try to help you.


Examples problems:


Example 1: Solve for x term in the given equation, 9x + 6 = 5x + 10

Solution:

Step 1: First we write the given expression for solving i.e. arrange the expression in correct form.

9x + 6 = 5x + 10

Step 2: Arrange in order for the constant values to right side; In this case first we have to subtract with 6 on both sides.

(9x + 6) – 6 = (5x + 10) – 6

9x = 5x + 4

Step 3: We have to subtract with 5x on both sides. Then arrange the coefficient of x values to the left side.

9x – 5x = (5x + 4) – 5x

4x = 4

Step 4: If possible, eliminate the coefficient values in the left side by dividing or multiplying. Now, we eliminate the coefficient of x, where the coefficient of x value is 4. So, we divide 4 on both sides.

4x/4 = 4/4

Step 5: Thus, the solution is obtained.

x = 1

Example 2: Solve for x term in the given equation, 8x - 5 = 3x + 25.

Solution:

Step 1: First we write the given expression for solving; arrange the expression in correct form.

8x - 5 = 3x + 25

Step 2: Arrange in order for the constant values to right side; In this case first we have to add with 5 on both sides.

(8x - 5) + 5 = (3x + 25) + 5

8x = 3x + 30

Step 3: We have to subtract with 3x on both sides. Then arrange the coefficient of x values to the left side.

(8x) – 3x = (3x + 30) – 3x

5x = 30

Step 4: If possible, eliminate the coefficient values in the left side by dividing or multiplying. Here, we eliminate the coefficient of x, where the coefficient of x value is 5. So, we divide 5 on both sides.

5x/5 = 30/5

Step 5: Thus, the solution is obtained.

x = 6

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Practice problems:


1. Solve for x in math to given equation, 2x + 2x = 8

Answer is x = 2.

2. Solve for x in math to given equation, 3x + 2 = 5x – 8

Answer is x = 5.

3. Solve for x in math to given equation, 6x - 4 = 2x + 8

Answer is x = 3.

4. Solve for x in math to given equation, 2x - 4 = x + 8

Answer is x = 12.

5. Solve for x in math to given equation, 8x - 14 = 4x + 2

Answer is x = 4.

Answer Key Book for Math

Introduction to answer key book for math :

In this article, we are going to discuss about the answer key book for math, The arithmetic operators are the basics in mathematics which includes addition, subtraction, division and multiplication. The basic arithmetic operators have more advanced operations, which includes square roots of algebraic equation, exponentiation, logarithmic functions, etc. Solution and answering methods or keys for the example problems are explained here.  Answer for the test would be in the form of objective type. Let us see the some examples in answer key book for math. Having problem with Integrals of Inverse Trig Functions keep reading my upcoming posts, i will try to help you.


Example problems in answer key book for math:


Math book problem 1:

A survey showed that `4/5` of a newspaper’s readers had access to a computer during the day. What is `4/5` written as a percent?

75%
80%
65%
90%

Solution: 2) 80 %

Answer key :

`4/5`   written as percent

`4/5` * 100 = `400/5` = 80%

Math book problem 2 :

What is the value for the expression given below?
4 - 23 * 3

-20
-14
18
24

Solution:  1)  -20.

Answer key:

4 - 23 * 3 = 4 - 8 * 3

= 4 - 24

= -20

Math book problem 3 :

Laural's average score on five mathematics tests is 90. What is the sum of the scores of Laural’s five tests?

368
450
474
372

Solution:   2)  450

Answer key :

Laural’s mean score on five mathematics tests is 90

so, here average of all the subject is 95 the total score is 90 * 5 = 450 marks

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Practice problems in answer key book for math:


Problem 1:

In a fancy shop, there are 12 toys, 18 balls, 24 dolls and 5 notebooks. Find the total number of fancy items in the shop?

Problem 2:

John has 24 pens and 3 scales and he gave 19 pens and 1 scale to his friend. calculate the remaining pencils and scales the john has?

Problem 3:

There are 15 boys in a class. The book seller sold 8 books to each boy. Find the total number of books sold by the seller.

Problem 4:

James has 24 fishes. He gave 6 fishes each to his friends. Find the total number of friends he have.

Problem 5:

A survey showed that 5/8 of a newspaper’s readers had access to a mobile in the office. What is 5/8 written as a percent?

problem 6:

Mac’s mean score on Three mathematics tests is 85. What is the sum of the scores of Mac’s Three tests?

Answer keys

i).59 items in the shop

ii).5 pens and 2 scales

iii).120 books

iv).4 friends

v).62.5 percent.

vi).255 total score.

Basic Math Calculator

Introduction to basic math calculator:
In general, calculators are used to perform various operations. Mathematical calculators perform both simple and complex operations. Basic mathematical calculators are used to perform various simple mathematical operations such as addition, subtraction, multiplication, division etc.,

In this article of basic math calculator, we are going to discuss about various simple mathematical operations using calculators. Is this topic Adding Negative Numbers hard for you? Watch out for my coming posts.


Basic Addition and Subtraction Calculator:


Examples for addition calculator:

1) 19 + 27 = ?

Step 1: Enter the numbers 19

Step 2: Press the + sign

Step 3: Enter the numbers 27

Step 4: If we press = sign, the result can be obtained as 46.

2) 712 + 323 = ?

Step 1: Enter the numbers 712

Step 2: Press the + sign

Step 3: Enter the numbers 323

Step 4: If we press = sign, the result can be obtained as 1035.

Examples for subtraction calculator:

1) 120 - 70 = ?

Step 1: Enter the numbers 120

Step 2: Press the - sign

Step 3: Enter the numbers 70

Step 4: If we press = sign, the result can be obtained as 50.

2) 347 - 127 = ?

Step 1: Enter the numbers 347

Step 2: Press the - sign

Step 3: Enter the numbers 127

Step 4: If we press = sign, the result can be obtained as 220.

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Basic Multiplication and Division Calculator:


Examples for multiplication:

1) 10  * 35 = ?

Step 1: Enter the numbers 10

Step 2: Press the  *  sign

Step 3: Enter the numbers 35

Step 4: If we press = sign, the result can be obtained as 350.

2) 72  * 37 = ?

Step 1: Enter the numbers 72

Step 2: Press the  *  sign

Step 3: Enter the numbers 37

Step 4: If we press = sign, the result can be obtained as 2664.

Examples for Division:

1) 120/ 6 = ?

Step 1: Enter the numbers 120

Step 2: Press the  /   sign

Step 3: Enter the number 6

Step 4: If we press = sign, the result can be obtained as 20.

2) 462 / 12 = ?

Step 1: Enter the numbers 462

Step 2: Press the  /  sign

Step 3: Enter the number 12

Step 4: If we press = sign, the result can be obtained as 38.5.

3) 5246 / 242 = ?

Step 1: Enter the numbers 5246

Step 2: Press the  /  sign

Step 3: Enter the numbers 242

Step 4: If we press = sign, the result can be obtained as 21.677.

Fourth Grade Math Terms

Introduction to fourth grade math terms:

Preparation of math terms is an essential one because it provides the foundation for solving various mathematical problems and also for learning basic operations in math.

In this article of fourth grade math terms,various basic math terms related to fourth grade are given.


Fourth grade math terms:


Algebraic equation

It refers to any equation that contains only algebraic expressions and signs of operations.

Area

The Area of a region is the number of square units that it takes to cover the region.

Circle

A circle is the path traced by a point which moves in a plane in such a way that its distance from a fixed point remains constant.

Collinear points

If three or more points lie on th same line, then they are called collinear points.

Complementary  angles

Two angles are said to be complementary if the sum is equal to 90o

Concurrent lines

If two or more straight lines pass through the same point, then they are called concurrent lines. The point through which the lines pass is known as point of concurrency.

Equivalent fractions

Fractions that show the same amount are called equivalent fractions.

Even numbers

The numbers, which are divisible by two are called even numbers

Improper fraction

A fraction whose numerator is equal to or greater than the denominator is called improper fraction.

Integers

All natural numbers , 0 and negatives of natural numbers form integers.

Irrational numbers

A number which cannot be put in the form a/b, where a and b are integers and a is not equal to zero, is called an irrational number.

Like terms

Terms that differ in their numerical coefficients but do not differ in symbol are called like terms. Please express your views of this topic Function Calculator by commenting on blog.


Additional Fourth grade math terms:


Mixed fraction

The sum of a whole number and a proper fraction is called as mixed fraction.

Natural Numbers

To count a given number of objects, we use numbers, which we call counting numbers or natural numbers. The numbers 1,2,3,4... are called natural numbers.

Odd numbers

The numbers, which are not divisible by two, are called odd numbers.

Proper fraction

A fraction whose numerator is less than its denominator is called a proper fraction.

Rational numbers

The numbers of  the form a/b,where a and b are integers and a is not equal to zero, are known as rational numbers.

Supplementary angles

The two angles are said to be Supplementary if the sum is equal to180o.

Unlike terms

Terms may or may not differ in their numerical coefficient are called unlike terms.

Volume

The quantity of matter contained in a solid is called volume.

Whole numbers

All natural numbers together with 0 form whole numbers.

Easy Help for Math Integers

Introduction:

Integers are numbers which doesn't contain decimal and fractions point in them. Integers are numbers in both positive and negative direction (-9, -8, -7, 0, 7, 8, 9). In other words, integers are the whole numbers with both positive and negative sign (where zero has no sign). The numbers like 34.6 ,51/4 cannot be said as integers. Integers are used everywhere in mathematics, Since they are the important elements to form math. Easy help for math integers involves the basic operation of addition and subtraction of integers. I like to share this Adding Integers with you all through my article.


Examples for Integer addition:

Here are few examples for easy help on addition of  math integers,

Example 1:

Find the sum of the integers, 23 and 45.

Solution:

The easy help for adding two integers is as follows,

2     4

(+)4      5

6      9

Example 2:

Find the sum of the integers, 133 and 155.

Solution:

The easy help for adding two integers is as follows,

1     3     4

(+)1     5      5

2      8      9

Example 3:

Find the sum of the integers, 34 and 55.

Solution:

The easy help for adding two integers is as follows,

3     4

(+)5      5

8      9

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Examples for Integer subtraction:


Here are few examples for easy help on subtraction of  math integers,

Example 1:

Find the difference between the integers,  45 and 23

Solution:

The easy help for subtracting two integers is as follows,

4     5

(-)2      3

2      2

Example 2:

Find the difference between the integers, 155 and 133.

Solution:

The easy help for subtracting two integers is as follows,

1     5     5

(-)1     3      3

0      2      2

Example 3:

Find the difference between the integers, 55 and 33.

Solution:

The easy help for subtracting two integers is as follows,

5     5

(-)3     3

2      2

Help with Pre Algebra Math

Introduction help with pre-algebra math:

A pre-algebra math is a study of basic mathematic operations and math’s functions. Mathematics is a one of a language and logic thing of science. This is an essential tool, medicine and the geography fields. In mathematics concept and fundamental concept are arithmetic operations. The basic arithmetic operations for math are addition of a integer values, and subtraction of an integer values, and division of an integer values and multiplication of an integer values.  This type of math problems help to lower grade algebra is deals with pre algebra, math and geometry problems.In this article we shall discuss for help with pre-algebra math.

I like to share this algebra 2 word problems and answers with you all through my article.

Sample problem for help with pre algebra math:

Problem 1:

Solve the given linear equations and find out the x value x – 8 = 10

Solution:

Find out the x value of the given linear equation.

we are move the -8 into the right side, we get
X = 10 + 8

X = 18.

The x value of an equation is 18.

Problem 2:

Find the value of the given numerical values 18 + (10 * 12)

Solution:

We are going to find the value of given data.

In the first we are going to multiply the terms 10 and 12, we get

10 * 12 = 120

In the next step we are going to add the terms 18 and 120, we get

18 + 120 = 138

The value of the given equation is 138.

Problem 3:

Find the co-efficient of linear equation 6x2 + 10y2 = 0

Solution:

find the co-efficient value of the x and y terms.

we are going to find the x co-efficient value.
X co-efficient is 6

In the next step we are going to find the y co-efficient value.

Y co-efficient is 10.

Understanding Laws of Probability is always challenging for me but thanks to all math help websites to help me out.

Practice problem for help with pre algebra math:

Solve the given linear equations and find out the x value x – 2 = 5
Answer: x = 7

Solve the given linear equations and find out the x value x + 2 = 3
Answer: x = 1

Types of Interest in Math

Interest is classified into two types. They are:

Simple interest

Compound interest

Simple interest: Simple interest is money we can earn by primarily investing some amount in bank or somewhere else (the principal). The percentage (the interest) of the principal amount is added to the principal, simple interest will increase our initial investments grow.

Compound interest: The difference between the original principal and the amount at the end of the last time period is known as the compound interest on the original principal period for that.

The important difference between compound and simple interest is  that simple interest is paid only on the principal, whereas compound interest is paid on both the principal and the accumulated interest.


Interest formula


Simple interest formula:

The formula used for calculating the simple interest is

SI = `(PNR)/100`

Where,

P is the Principal,

N is the time period,

R is the rate of interest.

Compound interest formula:

The formula used for calculating the compound interest is

A = P (1 + `r / 100` )n

Where,

P is the Principal

R is the rate of interest

N is the number of years.


Solved Examples


Pro 1: Find the simple interest on an amount of $500 for one year at the rate of 6% per annum.

Sol: The formula is SI = PNR / 100

Principal (P) = $500

Rate of interest(r) = 6 % per annum

N= Interest on 100 dollar for 1 year = $6

Interest on 500 dollar for 1 year =6 / 100 × 500 = $30

Therefore the interest is $30.

Pro 2: Find the amount of and compound interest on $6000 for 3 years at 3% per annum.

Sol: Let p1, p2, p3… represents the principal for the first year, second year, third year and so on. Also let I1, I2, I3… represent interest for the first year, second year, third year and so on.

Understanding Definition of Compound Interest is always challenging for me but thanks to all math help websites to help me out.

The formula is A = P (1 +` r / 100` )n

C.I. = A – P

P = $6000, r = 3%, n = 3 years

A = P (1 + `r / 100` )` ^n ` = 6000 (1 + `3 / 100` )3

= 6000 (`103 / 100)` 3

= 6000 * 103 * 103 * 103 / 100 * 100 * 100

= 6556.36

Therefore

A = $6556.36

P = $6000

C. I. = A – P = 6556.36 – 6000 = 556.36
C. I. = $556.36

Pro 3: Find the amount and compound interest on 5000 dollars for 1.5 years at 8%per annum. Interest being is added to the principal every half year.

Sol: P = 5000dollars, n= 3 (three half years), r = `8/ 2` = 4%

A = P (1+`r / 100)` n = 5000 (1+4) / 100 3

= 5000 (`104 / 100` )3

= `(5000*104*104*104) / (100*100*100)` =5624.32dollars

A = 5624.32

Compound Interest = A – P = 5624.32 – 5000

= 624.32dollars.

Pro 4:  Find the solution of simple interest, where total amount is 80,000, rate is 0.04 for per annum.

Sol: Simple interest = P*N*R.

=80000 *0.04 * 1.

=3200.

The simple interest is 3200.

Pro 5: Find the solution of simple interest, where total amount is 1,00,000, rate is 0.09 for per annum.

Sol: Simple interest = P*N*R.

=1,00,000 *0.09 * 1.

=9000.

The simple interest is 9000.

Math Terms Division

Introduction to math terms division:
In mathematics, especially in elementary arithmetic, division (÷) is the arithmetic operation that is the inverse of multiplication.

Specifically, if c times b equals a, written: C = b x a

where b is not zero, then a divided by b equals c, written: `a/b = c`

For instance, `6/3 = 2`

since  2 x 3 = 6

In the above expression, a is called the dividend, b the divisor and c the quotient. I like to share this Simplify Algebraic Expressions with you all through my article.


Math terms division:


Math term division type -1:

Division of 2 numbers with the same sign should be ‘+’ ve (positive sign) sign.

‘+’ve (Positive number) ÷’+’ve ( positive number) = ‘+’ve ( positive number)
‘-‘ve (Negative number) ÷ ‘-‘ ve (negative number) = =’+’ ve (positive number)
Math term division type - 2:

Division of 2 numbers with different signs should be ‘-’ve negative

‘+’ve (Positive number) ÷(‘-‘ve negative number) = ‘-‘ve (negative number)
‘-‘ve (Negative number) ÷ ‘+’ve (positive number) = ‘-‘ve (negative number)
Examples on math terms division :

Ex : 42 ÷ 7 = 6 (same signs)

(-26) ÷ (-2) = 13 (same signs)

6 ÷ (-2) = -3 (different signs)

(-10) ÷ 10 = -1 (different signs)

Math Terms Division on Dividing Variable:
In this operation division represents dividing the variables based on the presence of values.

Ex: Solve the following division: 54 ÷ p, given that p = -6

Solution:54 ÷ p

Substitute p = -6,

= 54 ÷ (-6)

= -9 (dissimilar signs).

Understanding Sig Fig Rules is always challenging for me but thanks to all math help websites to help me out.

Math Terms Division Of Dividing Decimal:


Math terms division for solving decimal problems:

Math term division of decimals type - 1:To create the decimal divisor as whole number by changing the decimal point to the right side.
Math term divison of decimals type - 2:To change the same decimal point in the dividend to the right side to create as whole number
Math term  division of type - 3:After divide the new dividend or whole number by new divisor or whole number


Ex:Divide the following decimal function:  24.24 ÷ 0.20

Solution:   24.24 ÷ 0.20 = `24.24/0.20`

= `242.4/2`  (Take the decimal divisor as whole number)

= `2424/20`  (Take the decimal dividend as whole number)

= 121.2 (Divide the new dividend by new divisor).

How to Study For Algebra

Algebra is the division of mathematics concerning the revise of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. For example:

x - 6 = 2

x – 6 + 6 = 2 + 6

x + 0 = 8

x = 8 (the answer)

The algebraic statements that explain relationships are expressed using algebraic terms, expressions, or equations. Earlier than we use algebra to find information about these kinds of relationships, it is important to first covers some basic terminology. Please express your views of this topic math answers for pre algebra by commenting on blog.


Algebraic Expressions


An expression is a significant group of numbers, variables, and signs, positive or negative, of operation that must make mathematical with logical sense. Expressions:

• contain any number of algebraic terms

• Use symbols of operation—addition, subtraction, multiplication, with division.

• do not contain an equality sign (=)

Example for an expression is:

–4ax + 5wx^2y

In an expression, the symbols of operation separate it into terms. The symbol also becomes part of the term that it follows. The expression more than contains two terms, the first term is –4ax and the second term is +5wx^2y. The addition sign separates the two terms. For example, in the term given above the plus sign (+) separates the –4ax from 5wx^2y and is also part of the second term. Conditions that do not have a sign listed in front of them are understood to be positive. I have recently faced lot of problem while learning Math Parallel Lines, But thank to online resources of math which helped me to learn myself easily on net.


Terms and Factors


A word in an algebraic expression is an expression concerning letters and/or numbers (called factors), multiplied together.

Example 1:

The algebraic expression

9x

is an example of one single term. It has factors 9 and x.

The 9 is called the coefficient of the expression.

Example 2:

5x + 3y have two conditions.

First term: 5x, has factors 5 and x

Second term: 3y, has factors 3 and y

The 5 and 3 are called the coefficients of the conditions.

Like Terms

"Like terms" are terms that enclose the same variables raised to the same power.

Examples

3x^2 and 7x^2 are like terms.

-8x^2and 5y^2 are not like terms, since the variable is not the similar.

First Quadrant

Definition:

The x- and y- axis divides the coordinate plane into 4 regions. These regions are called the quadrants.

Each quadrant bounded by two half-axes. These are often numbered from first to fourth and denoted by Roman numerals: I (where the signs of the two coordinates are (+,+), II (-,+), III (-,-), and IV (+,-). When the axes are drawn according to the mathematical form, the numbering goes counter-clockwise starting from the upper right ("northeast") quadrant.


Cartesian coordinate system


A Cartesian coordinate system specifies each and every point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length.

Each reference line is called a coordinate axis of the system, and the point where they meet is its origin. The coordinates are also defined as the positions of the perpendicular projections of the point onto the two axes, expressed as a signed distances from the origin.

Cartesian coordinates can be used to point out where you are on a map or graph.

Please express your views of this topic How do I Find the Perimeter of a Rectangle by commenting on blog.


Examples:


Identify the quadrant in which the points (4, 2) and (3, 8) are located.

Choices:

A. first and second quadrants respectively

B. second and third quadrants respectively

C. second and fourth quadrants respectively

D. only the first quadrant

Correct Answer: D

Solution:

Step 1: Start at the origin.

Step 2: Move 4 units to the right from the y-axis.

Step 3: Then move 2 units above the x-axis.

Step 4: The point (4, 2) is in the first quadrant.

Step 5: Move three units to the right from the origin on the x-axis.

Step 6: Then move 8 units above the x-axis.

Step 7: The point (3, 8) is in the first quadrant

Step 8: The points (4, 2) and (3, 8) are only in the first quadrant respectively.

Product Math Term

Introduction for the term Product in math:

The product is an expression which can be obtained by multiplying two or more numbers or expressions. The commutative law of the multiplication is the order of the complex numbers of the product. In matrices the product has a member of order of factors which has the multiplication as shown in them. We have some of the product of multiplication of numbers which can be shown it below.

Is this topic Product Property of Radicals hard for you? Watch out for my coming posts.

Notation for the term Product in Math :


The followings are some of the notations using in product math terms.

Product notations are dot (.), (*), () (), (x)

These all are symbols are using product of two numbers.

The Dot symbol (•)

The Dot symbol is used to find the product of two variables or numbers.

The Star symbol (*)

The star symbol is used to find the products of the numbers.

The Parentheses symbol ( ) ( )

The parentheses symbol is used to find the multiplication of sign numbers and it is a special symbol use only for signed numbers.

The Cross symbol (x)

The cross symbol product is used in between the two numbers. I have recently faced lot of problem while learning Sum to Product Identities, But thank to online resources of math which helped me to learn myself easily on net.


Example problems for Product Math Term:


Ex 1: Multiply 91 by 13.

Sol:

91 and 13(it is nothing but 13 times of 91.

It can written as like

= Two times of 91+1 times of 91

= 1183

= 1183

Ex 2: (a) Solve:

13 x10= 13 times 10=130

(b) Solve:

4 x 4= 4 times 4 = 16

(c) Solve:

4 x 8 =4 times 8 =32

(d) Solve:

1000 * 14 =1000times 15 = 15000

(e) Solve:

(12) .(12)=12 times 12 = 144

Arithmetic Word Problems:

Ex 3: A cost of one bags is 3 dollars. Find the price of 10 bags?

Sol:

Price of 1 bag = 3 dollars

Price of 10 bags = 10 x 3

Price of 10 bags = $30

Ex 4: There are 20 boys and 16 girls in the class. All boys are having individually 2 pen’s find the total no of pen the boys having?

Sol:

Total Number of boys = 20

Total Number of girls = 16

Each boy having 2 pens

Total no of pens= 20 * 2 = 40.

Math Integers

Introduction:

In arithmetic, an integer valued polynomial P (t) is a polynomial taking an integer value P(n) for every integer n. absolutely every polynomial with integer coefficients is integer-valued. There are simple examples to show that the converse is not true: for example the polynomial. I like to share this Polynomial Regression with you all through my article.


t(t + 1)/2

Giving the triangle information takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.

Source Wikipedia


Integer valued polynomial Explanation:

In this integer valued polynomial express the values are real numbers. For every polynomial are integer coefficients.

Here will explain the indegervalued polynomials in the example

The general formula for the integer valued polynomials is given below use this formula and express the inter even numbers

t (t+1)/2

This formula using to evaluate the real number.

For example t=3 we take to express the equation Answer for this problem.   we sub suite the value in above formula to drive the equations.

The triangle numbers takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.

= 3(3+1)/2

=3(4)/2

=12/2

Answer = 6

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Integer valued polynomial examples:


Example1:

To find the value of the given problem?

If t=6 and find the polynomial

Solution:

The triangle numbers takes on integer values whenever t = n is an integer. That is because one out of n and n + 1 must be an even number.

We use the formula and express the given problem

Formula=t(t+1)/2

=6(6+1)

=6(7)

Answer =42

Each polynomial with numeral coefficients is integer-valued.

Example2:

To find the value of the given problem?

If t=8 and find the polynomial

Solution:

We use the formula and express the given problem

Formula=t(t+1)/2

=8(8+1)

=8(9)

Answer  = 72

Math Ordered Pairs

Introduction to ordered pair learning:

Ordered pair learning is a topic in Algebra, which is a subdivision in mathematics. An ordered pair  represents a location (object or point) in the plane. Ordered pairs contains  two terms ‘x’ and ‘y’, represented in the form (x, y), the position of the terms cannot be interchanged unless the they are equal. Ordered pairs are also called as co-ordinates.

Learning to Find ordered pairs:

Depending upon the number of equations given the procedure to find the ordered pairs learning differs.
1. If only one equation is given,
Convert the given equation into a format,
y = a1x +c,
Then substitute different values for ‘x’ and obtain ‘y’
Form ordered pairs learning (x, y), where ‘x’ is the substituted value and ‘y’ is the obtained value.
Therefore different ordered pairs are obtained for various ‘x’ values.

2. If more than one equation is given,
Solve those equations and find out the values of ‘x’ and ‘y’,
Then (x, y) is the ordered pair

Having problem with Hexadecimal Addition keep reading my upcoming posts, i will try to help you.

Learning example problems to find ordered pairs

Problem 1:
Find the ordered pairs of y-2x=1
Solution:
y-2x=1,
Change the above equation into y =1+2x,
Substitute x=0
y =1+2(0),
y =1
Therefore the ordered pair (x, y) is (0, 1).
Substitute x=1
y =1+2(1),
y =3
Therefore the ordered pair (x, y) is (1, 3).
Substitute x=2
y =1+2(2),
y =5
Therefore the ordered pair (x, y) is (2, 5).
Substitute x=3
y =1+2(3),
y =7
Therefore the ordered pair (x, y) is (3, 7).
Substitute x=4
y =1+2(4),
y =9
Therefore the ordered pair (x, y) is (4, 9).

Problem 2:
Find the ordered pair of the equations,
3x+2y=5
4x+6y=3
Solution:
Let's start with 3x+2y = 5 for the variable x.
Move the 2y to the right hand side by subtracting 2y from both sides, like this:
Now, the equation reads:
3x = 5-2y
To isolate the x, we have to divide both sides of the equation by the other variables around the x on the left side of the equation.
The last step is to divide both sides of the equation by 3
The solution to your equation is:
x =5/3-(2/3)y
Next, let's solve 4x+6y = 3 for the variable y.
Move the 4x to the right hand side by subtracting 4x from both sides, like this:
Now, the equation reads:
6y = 3-4x
To isolate the ‘y’, we have to divide both sides of the equation by the other variables around the y on the left side of the equation.
The last step is to divide both sides of the equation by 6,
The solution to your equation is:
y =1/2-(2/3)x
Now, plug the earlier result, x=5/3-(2/3)y, in for x everywhere it occurs in
y=1/2-(2/3)x.
This gives y=1/2-2/3(5/3-(2/3)y). Now all we have to do is solve this for y,to have our first solution.
1/2-2/3*(5/3-(2/3)y) evaluates to ½ - 10/9 + 4y/9
Y - 4y/9 = -11/18
5y/9 =-11/18
The last step is to divide both sides of the equation by 5/9 like this:
y = - 11/18 * 9/5
The solution to the equation is:
y = -11/10
Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=5/3-(2/3)y.
This gives x=5/3-2/3(-11/10).
On, simplifying.
x= 12/5,
So, the ordered pair to given equations are:
(12/5, -11/10)

Math Solver

Introduction to math solver:
Math is the study numbers.Various branches of math are arithmetic,algebra,geometry,trigonometry,calculus,everyday math.

Math solver is a program that is used to calculate the answers to problems in math.The math solver is used to calculate the given math problems. Math solver is mainly used to find a solution with ease and also to work out the accurate solution for the given problem. I like to share this Easy Math Problems with you all through my article.

We generally input the given values to us and within a fraction of a second the math solver gives us the solution that is correct and easy to understand.It is an easy way of doing problems very quickly.Math solver is software that takes the input of data from us , uses the correct formula and gives the output. The math solver program of algebra solves the problems using the various algebraic formulas.The expansion formulas gives us the expansion of expressions while the factorization math solver gives the factors of expressions.Same way the arithmetic math solver to find the interests on investments gives the interest using that particular formula.For geometry also we can draw graphs using math solver that are neat and very clear.


Math Solver:

Mathematics is defined as the science of the study of quality, structure, space, and change. Mathematician gvies out patterns; establish truth by scrupulous deduction from appropriately chosen axioms and definitions”. Using math solver we can solve the given problems. Math solver helps us to solve problems in specific time. The following are the examples involved in math solver. Having problem with Circumference Calculator keep reading my upcoming posts, i will try to help you.


Solving example problems using math solver:

Ex 1: There are 1030 books in the library. We bought 67 more books for the library. How many books are there in the library now?

Given:

There are 1030 books in the library

67 more books is added to library

Therefore we need to add both 1030 and 67

1030 + 67 = 1097

There are 1097 books in the library now.

Ex 2: Margret sold 1392 meatballs on Friday. She sold 1940 more meatballs on Saturday than on Friday. How many meatballs did she sell on Saturday?

Given: Margret sold 1392 meatballs on Friday

She sold 1940 more meatballs on Saturday than on Friday

Therefore we need to add 1392 and 1940,

1392 + 1940 = 333

She sold 3332 meatballs on Saturday.

Ex 3: Kevin sold 1000 balls on Friday. She sold 1500 more balls on Saturday than on Friday. How many balls did she sell on Saturday?

Given: Margret sold 1000 meatballs on Friday

She sold 2000 more meatballs on Saturday than on Friday

Therefore we need to add 1000 and 2000,

1000 + 2000 = 3000

She sold 3000 meatballs on Saturday.

help with math word problems

Introduction to help with math word problem:

Math word problem is a real life problem put in words which has to be converted into mathematical form to solve it. Math word problems has to be solved by logically translating the problem to mathematical form. It requires understanding the mathematical concepts and its applications. I like to share this math tutoring free online with you all through my article.

To help with math word problems - examples

Math word problems help - example 1:

Jack has 21 bananas and 18 grapes . How many pieces of fruits does he have?

Solution:

We know that the sum of 21 and 18 is equal to the total sum of fruit. The total amount of pieces of fruit is unknown, so we will represent that sum with x.

Let x = Total Amount of Fruit from word given

The sum of 21 bananas plus 18 grapes is equal to the total amount of fruit. This can be used to explain the problem into an equation,

21 + 18 = x

By solving the last step equation.

Let x = Total Pieces of Fruit

Initial Equation     21 + 18 = x

After combining like terms 39 = x

The problems answer is then rewritten as a sentence.

There are 39 Total Pieces of Fruit

Math word problems  help - example 2:

Mike is twice as good as workman as Jones and therefore he is able to finish a job in 40 days less than Jones. Working together, they can do it in:

Solution:-

Given Mike is twice as good as work man as Jones.

Therefore the ratio of work done Mike and Jones is 1: 2

If difference of time is 1 days, Jones takes 2 days.

If difference of time is 40 days, Jones takes (2/1 x 40) = 80 days.

So, Mike takes 40 days to do the work.

so mikes one day work =  1/40

Jones one day work =  1/80

Now (mikes + Jones) one day work = ( 1/40 + 1/80 )

The LCM of 40 and 80 is 80.

Now take LCM and add we get

= 2 / 80 + 1/ 80

= (3)/ 80

Work done in one day=3/80

No. of days required to cover 80 portions of work=80/3

Mike and Jones together can do the work in 80 / 3 = 16.66 days. Understanding The Multiplication Table is always challenging for me but thanks to all math help websites to help me out.


More help with math word problems - practices


1. Math word problem help - practice 1:

Peter has 12 shirts and 7 T-shirts. How many of shirts does he have?

Answer: 19 Total number of shirts.

2. Math word problem help - practice 2:

The sum of thrice a number plus 8 is 62. Find the number.

Answer: The number is 18.

2. Math word problem help - practice 3:

Walker is thrice as good as worker as Kim and therefore he is able to finish a job in 40 days less than Kim. When they working  together, how long they can do it in?

Answer: 15 days.

Two Cents

Cents – Introduction:

In many national currencies, the cent is a monetary unit that equals 1/100 of the basic monetary unit. Etymologically, the word cent derives from the Latin word "centum" meaning hundred. Cent also refers to a coin which is worth one cent. In the America and Canada, the 1 cent coin is usually identified by the pet name penny, alluding to the British coin and unit of surname. In Ireland the 1cent coin is occasionally recognized as a penny in position to the Irish penny, worth 1/100 of the Irish pound swap by the euro.

Formula for converting the cents to dollars

1 U.S. cent = 0.01 U.S. dollars

Two Cents – Examples:

Two cents – Example 1:

Find how many dollars in the 2 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

2 cents = 2 * 0.01 dollars = 0.02 dollars

Answer:

2 cents = 0.02 dollars

Two cents – Example 2:

Find how many dollars in the 102 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

102 cents = 102 * 0.01 dollars = 1.02 dollars

Answer:

102 cents = 1.02 dollars

Two cents – Example 3:

Find how many dollars in the 22 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

22 cents = 22 * 0.01 dollars = 0.22 dollars

Answer:

22 cents = 0.22 dollars

More Examples for Two Cents:

Two cents – Example 1:

Find how many dollars in the 32 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

32 cents = 32 * 0.01 dollars = 0.32 dollars

Answer:

32 cents = 0.32 dollars

Two cents – Example 2:

Find how many dollars in the 42 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

42 cents = 42 * 0.01 dollars = 0.42 dollars

Answer:

42 cents = 0.42 dollars

Solve Math Problems Fast

Introduction to solve math problems fast:

In this article we are going to discuss about the solve math problems fast. In the math problems have different types of topics. The level math problems has some of the followings numbers sets, logic, real number systems, functions and their graphs, probability and Statistics and some topics from algebra and geometry. The math  problems is more importance for all topics. Here we will see the example problems for solve math problems fast. Is this topic Conditional Probabilities hard for you? Watch out for my coming posts.

Example Problems for Solve Math Problems Fast:
Solve math problems fast – Example: 1

Solve `\int_1^2\int_1^x xy^2dx dy`

Solution:

`I=\int_1^2 \ [ \int_1^x xy^2 dy \ ]dx`

`\int_1^x xy^2dy=\ [ \frac{xy^3}{3}\ ]_{y=1}^{x}=\frac{x^4}{3}-\frac{x}{3}`

Therefore,`I=\int_1^2 \ [ \frac{x^4}{3}-\frac{x}{3} \ ]dx`

` =\int_1^2\frac{x^4}{3}dx-\int_1^2\frac{x}{3}dx`

`=\ [ \frac{x^5}{15} \ ] _1^2- \ [ \frac{x^2}{6} \ ]_1^2`

`=\ [ \frac{32}{15}-\frac{1}{15} \ ]-\ [\frac{4}{6}-\frac{1}{6}\ ]`

` =\frac{31}{15}-\frac{3}{6}`

` =\frac{31}{15}-\frac{1}{2}`

`=\frac{62-15}{30}=\frac{47}{30}`

Solve math problems fast – Example: 2

Determine the unit vector perpendicular to both the vectors `2\bar{i}+\bar{j}+3\bar{k},\bar{i}-2\bar{j}+\bar{k}`

Solution:

Let a,b be the given vectors `2\bar{i}+\bar{j}+3\bar{k},\bar{i}-2\bar{j}+\bar{k}`

`\bar{a}\times\bar{b} =` `[[i,j,k],[2,1,3],[1,-2,1]]`

which is equal to `\bar{i}(1+6)-\bar{j}(2-3)+\bar{k}(-4-1)=7\bar{i}+\bar{j}-5\bar{k}`

Therefore unit vector perpendicular to both the vectors is `\pm\frac{\bar{a}\times\bar{b}}{|a||b|}=\pm\frac{7\bar{i}+\bar{j}-5\bar{k}}{\sqrt{49+1+25}}=\pm\frac{1}{5\sqrt{3}}(7\bar{i}+\bar{j}-5\bar{k})`

Solve math problems fast – Example: 3

Evaluate `\nabla^2(\frac{x}{r^2})`

Solution:

`\nabla^2(\frac{x}{r^2})=\sum \frac{\partial^2}{\partial x^2}[\frac{x}{r^2}] --(1)`

Now,`\frac{\partial}{\partial x}(\frac{x}{r^2})=\frac{1}{r^2}-\frac{2x}{r^3}\frac{\partial r}{\partial x}=\frac{1}{r^2}-\frac{2x}{r^3}[\frac{x}{r}]=\frac{1}{r^2}-\frac{2x^2}{r^4} --(2) [ r^2=x^2+y^2+z^2 and \frac{\partial r}{\partial x}=\frac{x}{r}]`

Therefore,`\frac{\partial^2}{\partial r^2}=\frac{\partial}{\partial x}[\frac{\partial}{\partial x}(\frac{x}{r^2})]=\frac{\partial}{\partial x}[\frac{1}{r^2}-\frac{2x^2}{r^4}],` by using (2)

`=-\frac{2}{r^3}\frac{\partial r}{\partial x}-[\frac{4x}{r^4}-\frac{8x^2}{r^5}\frac{\partial r}{\partial x}]=-\frac{2}{r^3}(\frac{x}{r})-\frac{4x}{r^4}+\frac{8x^2}{r^5}\frac{x}{r}`

Therefore,`\frac{\partial^2}{\partial x^2}[\frac{x}{r^2}]=\frac{8x^3}{r^6}-\frac{6x}{r^4} --(3)`

Now,`\frac{\partial}{\partial y}(\frac{x}{r^2})=-\frac{2x}{r^3}(\frac{y}{r})`

`\frac{\partial^2}{\partial y^2}=\frac{\partial}{\partial y}[-\frac{2xy}{r^4}]`

`=-2x[\frac{1}{r^4}-\frac{4y}{r^5}\frac{\partial r}{\partial y}]=-2x[\frac{1}{r^4}-\frac{4y^2}{r^6}]=\frac{8xy^2}{r^6}-\frac{2x}{r^4} --(4)`

Similarly,`\frac{\partial^2}{\partial z^2}[\frac{x}{r^2}]=\frac{8xz^2}{r^6}-\frac{2x}{r^4} --(5)`

Adding (3),(4),(5), we have

`\sum \frac{\partial^2}{\partial x^2}=\frac{8x}{r^6}[x^2+y^2+z^2]-\frac{10x}{r^4}=-\frac{2x}{r^4}`

`or \nabla^2[\frac{x}{r^2}]=-\frac{2x}{r^4},` by using (1)


I have recently faced lot of problem while learning Sum of Uniform Random Variables, But thank to online resources of math which helped me to learn myself easily on net.

Practice Problems for Solve Math Problems Fast:

1. Find a vector of the magnitude 3 and that which is the perpendicular to both of the vectors `3\bar{i}+\bar{j}-4\bar{k},6\bar{i}+5\bar{j}-2\bar{k}`

`Answer: \pm (2\bar{i}-2\bar{j}+\bar{k})`

2. Solve `\int_1^2\int_3^4 \frac{1}{(x+y)^2}dx dy`

`Answer: log\frac{25}{24}`

Revise Maths

Introduction to Revise maths:
In this article we are discussing about basic maths revise exam problems in which tutor helps the students to get the solutions. Basic maths revise exam problems can solve problems with step by step solutions for all problems. The maths basic problems involved topics such that algebra, geometry, polynomials, trigonometry, data handling and calculus. Let us solve some basic maths revise exam problem with step by step solutions and practice problems are given below. I like to share this Practice Math Problems with you all through my article.

Revise Maths – Example Problems:

Example 1:

John purchased 2 kg 351g apples, 3 kg 800 g mangoes and 1 kg 450 g bananas. What is the total weight of fruits purchased?

Solution:

Weight of apples:        2kg 351 g

Weight of mangoes:    3 kg 800 g

Weight of bananas:    (+) 1 kg 450 g

Total weight: 7k 601 g

Thus, jack purchased 7 kg 601 g fruits.

Example 2:

Find the volume of cuboids of length (l) 5 cm, breadth (b) 2.5 cm and height (h) 3.2 cm

Solution:

Here, length = 5cm

Breadth = 2.5 cm

And height = 3.2 cm

We know that v = l x b h

Hence, v= 5 x 2.5 x 3.2 cu.cm

= 40cu.cm

Example 3:

Find the volume of cubical box of side 5.2 cm.

Solution:

Length of the side of the cube = 5.2 cm

We know that the volume V of the cube = l x l x l

= 5.2 x 5.2 x 5.2cm3

=140.608cm3


Understanding hard math problems for 8th graders is always challenging for me but thanks to all math help websites to help me out.

Revise Maths – Practice Problems:
Problem 1: John purchased 3 m 25 cm cloth for the suit, 2 m 80 cm for the shirt and 2m 20 cm for the trouser. Find the total length (l) of the cloth purchased.

Problem 2: Find the volume of cuboids of (l) length 5 cm, breadth (b) 5 cm and height (h) 2 cm

Problem 3: Find the volume of cubical box of side 3 cm.

Revise maths – answer key:

Problem 1: 8 m 25 cm

Problem 2: 50cm3

Problem 3: 27cm3

Postulate Math

Introduction to postulate math:

In general, math postulates are nothing but the math statements, which are assumed as real without any proofs. Math postulates help to understand various concepts involved in the field of mathematics and also useful for the preparation of exam   In this article postulate math, we are going to study few math postulates which will be helpful for the students. Please express your views of this topic Difference of Cubes Formula by commenting on blog.

Math Postulates:
If the two straight lines cross each other, they cross at only one point.

In general, if perpendicular lines cross, four right angles will be formed.

Consider that equal quantities are added to equal quantities, and then their sums will be equal. Likewise, if similar quantities are subtracted to similar quantities, their differences will be equal.

A square is nothing but a parallelogram having four congruent sides and also four right angles.

A rectangle is nothing but a parallelogram having four right angles.

If same quantities are multiplied by same quantities, the products will be equal.

If the two geometric shapes are said to be congruent, then their area must be same.

The addition of the areas of its non-overlapping parts is referred as the area of section.

The addition of the lengths of any two sides of a triangle will be bigger than the length of the third side.

Is this topic Covariance Statistics hard for you? Watch out for my coming posts.

Additional Math Postulates:

All right angles are said to be congruent according to the Euclid’s postulate.

The addition of interior angles of any triangle will always measure 180 degrees.

Trapezoid is nothing but a quadrilateral, which has single pair of parallel sides.

In general, each and every segment has a single midpoint.

The quotients will be equal if same quantities are divided by equal nonzero quantities.

In general, a line segment can be extended for an indefinite period along a line.

The intersection of planes will be a line, if two planes intersect

If two triangles have equal angles to one another, then the two triangles are similar.

Definition of Slides in Math

Introduction for Math Slides:

Math slides is a transformation which has a plane figure or move across a line. Moving a shape without rotating or flipping is known as slides (translation). A math slides is also known as translation. If any student wants to know about the definition of math slides, they can refer the below examples with definitions Let us see some of the definition and examples for math slides. I like to share this Properties of Exponents with you all through my article.

Definition of Slides in Math – Explanations:

These are the explanations of slides in math with definition and example figure.

Slides are one of the transformations which can translate the image from original direction A, B, C, D and E to other direction as shown.

This means, they can translate the same image to other side A', B', C', D', and E' as shown.

The image of the angle, length and size are not change in them.

The image of the figure translation is its mirror of the image or their translation plane.

Every point in the translation is same distance from the center of the line as shown.

This center line is known as the mirror line.

It has the same size and length from the original image.

The translating image in the opposite side will be always same as the original image as shown in the example figure.

Each point of translation can be marked in them to shows the image length and their sides.

We can show the translation from one place to another in the following example figure.


Please express your views of this topic solved sample papers for class 12 by commenting on blog.

Definition of Slides in Math – Example Figure:

These are the example figure for the definition of slides (translation) in math.

Slides in Math:

The example figure below shows the slides in math with the shape of an object.

Elementary Column Operations

Introduction on elementary column operations:

According to the term elementary Column operation are found to be one of the parts in matrix. Elementary is found be defined as Elementary matrix is found to be defined as a simple matrix where it represented in different identity matrix form. Elementary column operation is the operation that is done by post or right multiplication. I like to share this Complex Fractions with you all through my article.

Rules Based on Elementary Column Operations:

Rule 1: To find the sum given, of elementary column operator, the identity matrix operation is applied.

Rule 2: The post multiplication has to be done for carry out elementary column operations.

Rule 3: The column operator is created from multiplying “column * column"

Representation of Column in Matrix:

The column is represented in matrix as :  `[[a],[b],[c]]`

Example Problems Based on Elementary Column Operations:

Example 1:

Elementary column operation on the term “A”, where the identity used in matrix   `A= [[1,6], [4,1], [0,1]]` and identy matrix `x = [[1,0], [0 ,1]]`

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`A= [[1,6], [4,1], [0,1]]`

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `A= [[1,6], [4,1], [0,1]]`

Step 3: The operation in matrix is done by [row *column]

`X= [[1,0], [0,1]]`

The first and second column is interchanged and the result is,

`X1= [[0,1], [1,0]].`

Now, the found X1 is calculated with given “A”

`A= [[1,6], [4,1], [0,1]]`

`X1= [[0,1], [1,0]]`

`A*X1` for calculation elementary column operation on

`A*X1`

` [[1,6], [4,1], [0,1]] * [[0,1], [1,0]]`

` [[1*0+6*1 , 1*1+6*0],[4*0+1*1 , 4*1+1*0],[0*0+1*1, 0*1+1*0]]`

`[[0+6, 1+0], [0+1,4+1], [0+1, 0+0]]`

`[[6,1],[1,4],[1,0]]`

Hence ,the elmentary column operation for the given value `A=[[6,1],[1,4],[1,0]]`

Example 2:Based on elementary column operations

Elementary column operation on the term “D”, where `D= [[1,2],[1,1],[0,0]] ` the identity used in matrix   `"x= [[1,0],[0,1]] `

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`"D= [[1,2], [1,1],[0,0]], `

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `D=[[1,2],[1,1],[0,0]]`

Step 3: The operation in matrix is done by [row *column]

`X= [[1,0], [0,1]]`

The first and second column is interchanged and the result is,

`"X1= [[0,1],[1,0]]`

Now, the found X1 is calculated with given “A”

`D= [[1,2], [1,1], [0,0]]`

`X1= [[0,1], [1,0]]`

`D*X1` for calculation elementary column operation on

`D*X1`

`[[1,2], [1,1], [0,0]]*[[0,1], [1,0]]`

`[[1*0+2*1 , 1*1+2*0],[1*0+1*1 , 1*1+1*0],[0*0+0*1, 0*1+0*0]]`

`[[0+2, 1+0], [0+1,1+0], [0+0, 0+0]]`

`[[2,1],[1,1],[0,0]]`

Hence ,the elementary column operation for the given value `D=[[2,1],[1,1],[0,0]]`

Understanding free help with math word problems is always challenging for me but thanks to all math help websites to help me out.

Problems to be Solved Based Elementary Column Operations:

Elementary column operation on the term “S”, where  `S ` =  `[[6,2],[2,1],[9,4]]` the identity used in matrix `X` =  `[[1,0],[0,1]] `
Answer: The elementary column operation of  `S` =`[[2,6],[1,2],[4,9]]`

Elementary column operation on the term “Z”, where `Z` =`[[2,1],[3,2],[6,3]]`   the identity used in matrix  `X` = `[[1,0],[0,1]] `

Answer: The elementary column operation of    `Z` =`[[1,2],[2,3],[3,6]]`

Elementary Math Estimation

Introduction to elementary math estimation:

In elementary number theory, integers are studied without use of techniques from other mathematical fields. Questions of divisibility, use of the Euclidean algorithm to compute greatest common divisors, integer factorizations into prime numbers, investigation of perfect numbers and congruence’s belong here. Several important discoveries of this field are Fermat's little theorem, Euler's theorem, the Chinese remainder theorem and the law of quadratic reciprocity. (Source: Wikipedia)

Types of Elementary Math Estimation:

There are four types of basic theory are mainly used in the elementary number theory; these types are classified according to the representation of the number. It will be shown as below,

Addition
Subtraction
Multiplying
Division
In elementary math to estimation it very easy to learning to study. And solve it easy. There are four steps are used in the elementary estimation of the math problems they are solved in the example problems in given below.

Example Problem for Elementary Math

Example 1:

Estimation the example of adding two numbers 163 and 13

Solution:

Let us write the given problem as 163 + 13.

Add the number 163 and 13 we get the sum as,

163 + 13 =176

Therefore, the solution for adding 163 + 13 is 176.

Example 2:

There are 56 peoples travelling in a bus. 17 of them left from the bus in one stopping. Estimation how many people will be left in the bus?

Solution:

Total number of peoples = 56

Number of peoples left from the bus in one stopping = 17

Number of peoples left in the bus = 56 - 17

= 39

Example 3

Estimation the multiplying two numbers 31 and 27

Solution:

The given two numbers 31 and 27

We need to find the product of two numbers

By multiplying 31 and 27

We get 837

So the answer is 837

Problem 4:

Estimation to divide 400 / 4

Solution:

100(quotient)

----

4)  400

400 -

---------

0(remainder)

---------

Practice Example Problem for Elementary Math

1. Estimation of adding 33 and 70

Key: 103

2. Estimation of Subtract 119 and 9

Key: 110

3. Estimation of Multiplying 29 by 20

Key: 580

4. Estimation of Divided 68 by 7

Key: 9.71

Sixth Grade Math Word Problems

Introduction to Sixth Grade math word problems:

Word problem is one of the best ways to turn up children’s towards solving, thinking and analyzing problems. Word problems will enhance this kind of attitude from the childhood stage itself. Sixth grade level includes real numbers,decimal,fraction,charts, graphs, money and basic mathematics like addition,subtraction,multiplication,division .Sixth Grade math word  problems is very essential for the children’s whose age lies between 8-13years old .It will be so fitful ,let us enjoy it, Let us deal about worked problems. Having problem with What is a Trinomial keep reading my upcoming posts, i will try to help you.

Example 1-sixth Grade Math Word Problems

One cat can kill a 10 rat. Then a  how many number of cat can kill  1000 rat?

Given:

1 cat=10 rat

?=1000 rat

Solution:

Step 1:

To find out the no of cat needed to kill a 1000 rat, we have to divide the total no of rat by the no of rat can be killed by single cat.

Step 2:

Division operation is used

The no of cat needed to kill a1000 rat=`1000/10=100 ` cat

Example 2 -Sixth Grade math word problems

One child makes a building with 250 bricks. How many no of bricks needed to make a 5 building?

Given:

1 Building needed=250 bricks

5 Building needed=?

Solution:

Step 1:

To find out the no of bricks needed to make a 5 building, we have to multiply the no of bricks needed to make a one building with 5

Step 2:

Use multiplication

No of bricks needed for to make 5 Building=`5xx25` =1250 bricks

No of bricks needed is 1250 bricks

Please express your views of this topic how to subtract fractions with unlike denominators by commenting on blog.

Example 3 - Sixth Grade Math Word Problems

A man travels 3 km per hour .So after 5 hour the distance traveled by him?

Given:

Man covered a distance per hour=3 km

Solution:

Step 1:

To find out the distance covered by him, we have to multiply the distance covered in 1 hour with 5

Step 2:

Use Multiplication

The total distance covered in 5hour=`5xx3=15km`

Example 4 - Sixth Grade math word problems

A child has 100 Chocolates and the dog grabbed 20% of it, from the child. How much number of chocolates dog has?

Given:

The number of chocolates Child has at first=100

Grabbed by the dog=20%

Solution:

Step 1:

To find out the 20% of chocolates, multiply the given percent with number of chocolates

=20%of100

Step 2:

Consider % as 1/100

` =(20/100)xx100`

=20

Finally, the dog has 20 chocolates

Univariate Data

Introduction to uni variate data:

Univariate means to equation, expression, polynomial or function of exactly one variable. This term is commonly used in statistics, mean, arithmetic mean to differentiate a distribution of one variable from the distribution of many other variables. Although it could be applied in many other ways as well. Since it is the simpler way to distribute the values. Correspondingly, the “multivariate time series” refers us to the changing values over the time of several quantities. I like to share this Two Way Table with you all through my article.

Properties of Univariate Analysis:

Univariate analysis is been used primarily in descriptive purposes to represent the quantitative analysis and the statistical analysis. It is the easiest method to identify the attributes and the single variable.

Univariate analysis contrasts with the bivariate analysis because it cannot analyse two variables simultaneously – or do multivariate analysis – the analysis of the multiple variables are been done simultaneously.

Univariate analysis is been commonly used in many fields like the scientific research, medical field and in simple hand calculations. Please express your views of this topic free math help online now by commenting on blog.

Data Set (univariate Data):

In our day to day life there may be many simple values that we go across. In those simple values twe can come across problems with only one variable and also with a single column of the data set, these are represented as a list. Mathematically, in the univariate data set there cannot be any repetition (i.e) because it cannot repeat multiple times. In general the order of the univariate data set does not be considered, but collection of those values may be considered to be a multi set rather than the (ordered) list.

Generally, the values might be of any of the kinds described as a level of the measurement. For every variable, the values will be normally of the same kind or similar.  Uni variate data can be as real numbers or the integers. For example, representation of a building's height using the meters. This could also be represented as a nominal data. However, there could also be "missing values", and those values need to be indicated in some representation.