Math made easy algebra rules

Author: Matthew David

Math made easy algebra rules

Introduction to math made easy algebra rules:

Algebra is defined as one of the basis of mathematics.  Mainly algebra is used to study about the rules and the properties. There are many other operations are related to the algebra. In the pure mathematics, algebra is defined be one of the main branches. Algebra can uses the various symbols, letters and numbers.

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. To teach the algebra in the easy way, we have to educate the four basic operations in algebra such as addition, subtraction, multiplication and division. The most important terms of algebra, variables, constant, coefficients, exponents, terms and expressions are used to teach algebra in the easy way. When we want to teach algebra in the easy way, we are using the symbols and alphabets instead of unknown values to make a statement. Hence, the easy way to teach algebra regards the leads of Arithmetic.

Explanation for the math made easy algebra rules

There are many rules are followed in the algebra which made easy to study. They are given below the following,

    Commutative property used for the addition operation.

Rule: p + q = q + p

    Commutative property used for the multiplication operation.

Rule: p * q = q * p

    Associative property used for the addition operation.

Rule: (p + q) + r = p + (q + r)

    Associative property used for the multiplication operation.

Rule: (p * q) * r = p * (q * r)

    Distributive property used for addition operation over the multiplication operation.

Rule: 1.p * (q + r) = p * q + p * r
         2. (p + q) * r = p * r + q * r

    The reciprocal for an non-zero number b is given by `1/p`

Rule: p*( `1/p` ) = 1

    The additive inverse process of the number b is given by –b.

Rule: p + (- p) = 0

    The additive identity used is 0.

Rule: p + 0 = 0 + p = p

    The multiplicative identity used is 1.

Rule: p * 1 = 1 * p = p

Example problem for math made easy algebra rules

Commutative property used for the addition operation:

Problem 1: Use the given value in the commutative rule, p = 5, q = 6

Solution:

Rule: p + q = q + p

By substituting the values , we get,

5 + 6 = 6 + 5

11 = 11

Commutative property used for the multiplication operation:

Problem 2: Use the given value in the commutative multiplication rule, p = 5, q = 6

Solution:

Rule: p * q = q * p

By substituting the values , we get,

5 * 6 = 6 * 5

30 = 30

Associative property used for the addition operation:

Problem 3: Use the given value in the associative rule, p = 5, q = 6, r = 2

Solution:

Rule: (p + q) + r = p + (q + r)

By substituting the values , we get,

( 5 + 6 ) + 2 = 6 + (  5 + 2 )

( 11 ) + 2 = 6  + ( 7 )

13 = 13

Example 1:

Solve the equation for x, 3(5x) = 45.

Solution:

3(5x) = 45 (3 is multiplied within the parenthesis)

3 * 5x = 45

15x = 45 (divide both sides by 15)

`(15x) / 15 = 45 / 15`

x = 3

Example 2:

Solve the equation for x, 2(2x-5) = 50.

Solution:

2(2x-5) = 50 (2 will be multiplied within the parenthesis)

(2 * 2x) – (2 * 5) = 50

4x – 10 = 50 (add both sides by 10)

4x  - 10 + 10 = 50 + 10

4x = 60 (divide both side by 4)

`(4x)/4 = 60/4`

x = 15

Example 3:

Solve the equation for x, `(5x-5) / 3` = 10.

Solution:

`(5x-5) / 3` = 10 (multiply both sides by 3)

`(5x-5) / 3`  * 3 = 10 *3

5x – 5 = 30 (add both sides by -5)

5x – 5 + 5 = 30 + 5

5x = 35 (divide both sides by 5)

`(5x) / 5= 35 / 5`

x = 7

Example 4:

Solve the equation 5x + 5 = x + 55 for x.

Solution:

5x + 5 = x + 55 (add both sides by -5)

5x + 5 – 5 = x + 55 - 5

5x = x + 50 (add both sides by -x)

5x – x = x – x + 50

4x = 50 (divide both sides by 4)

`(4x) / 4 = 50 / 4`

x = 12.5

Example 5:

Solve the equation 2x – 5 = 45 for x.

Solution:

2x – 5 = 45 (add both sides by 5)

2x – 5 + 5 = 45 + 5.

2x = 50 (divide both sides by 2)

`(2x) / 2 = 50 / 2`

x = 25

Practice problem for math made easy algebra rules

Problem 1:

Solve the equation for x, 15x + 5 = 65.

The answer is x = 4

Problem 2:

Solve the equation for x, 6x – 1 = 35

The answer is x = 6

Problem 3:

Solve the equation for x, 6x + 4 = 28

The answer is x = 4

Problem 4:

Solve the equation for x, 3x - 5 = 35 - x

The answer is x = 10

Problem 5:

Solve the equation for x, 4x + 2 = 34 + 2x

The answer is x = 16

Problem 6: Use the given value in the commutative rule for addition, p = 10, q =20

Answer: 30

Problem 7: Use the given value in the associative rule for addition, p = 2, q = 4, r =6

Answer: 12

Article Source: http://www.articlesbase.com/k-12-education-articles/math-made-easy-algebra-rules-6619362.html

About the Author

Between, if you have problem on these topics Consecutive Exterior Angles Theorem, please browse expert math related websites for more help on math problem solver and different math topic.