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