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`
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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