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.

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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

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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)