Tuesday, December 18, 2012

Inverse Property of Addition and Multiplication

Introduction to inverse property of addition and multiplication:

For solving the expression in mathematics, the inverse properties of addition and multiplication are useful. The result of inverse property for addition is 0 and the result of inverse property for multiplication is 1. The inverse property requires a number and its inverse.

Example: Inverse of a term +a is –a for addition `1/a` for multiplication.

Explanation of Inverse Property of Addition and Multiplication:

Statement of inverse property of addition:

Inverse property of addition states that when a number or variable is added to its inverse number or variable, the result of this addition becomes zero. For addition the inverse of a given number or variable is obtained by changing the sign of given number or variable.

Example:

Consider a variable ‘t’. An inverse term of ‘t’ is –t. Addition of new opposite equal terms gives 0.

t + (-t) = t – t =0

Inverse property of multiplication:

Inverse property of multiplication states that when a number or variable is multiplied by its inverse, the result becomes one. For multiplication the inverse of a number or variable is the reciprocal of a given number or variable. Looking out for more help on Mathematical Expressions in algebra by visiting listed websites.

Example:

Consider a variable is ‘t’. The inverse of this variable is t-1 which is `1/t`.

t × `1/t`  = 1

Example Problems to Inverse Property of Addition and Multiplication:

Example: 1

Which is the inverse element of 61 for addition?

a) +61

b) -(-61)

c) `1/61`

d) -61

Solution:

Given number is 61.

Inverse property result is 0.

61 + x = 0

61 is subtracted on both sides.

61 + x – 61 = 0 – 61

x = -61

Answer: d

Example: 2

Which of the following is the inverse element of 9 for multiplication?

a) 9-1

b) `(1/9)^-1`

c) +9

d) -9

Solution:

Inverse property of multiplication result is 1.

9  X x = 1

9 is divided on both sides.

`(9x)/9` = `1/9`  = 9-1

Answer: a

Practice Problems to Inverse Property of Addition and Multiplication:

Problem: 1

What is the inverse element of `7/8` for addition?

Answer: `-7/8`

Problem: 2

What is the inverse element of 100 for multiplication?

Answer: `1/100`

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