INVERSE PROPERTIES
Definition Of Inverse Operation
Inverse Properties state that when a number is combined with its inverse, it is equal to its identity.
More About Inverse Operation
There are two types of inverses of a number: Additive Inverse and Multiplicative Inverse.
`- a` is said to be additive inverse of `a` if a + (- a) = 0.
`1/a` is said to be multiplicative Inverse of `a` if 
.
Video Examples: Inverse Property of Multiplication
Example of Inverse Operation
The additive inverse of 54 is - 54 because if a is a real number, then the additive inverse of a is - also that a + (- a) = 0.
Solved Example on Inverse Operation
Ques: Find the multiplicative inverse of 7.
Choices:
A. - 7
B. 7
C.1/7
D. √7
Correct Answer: C
Solution:
Step 1: Multiplicative inverse of a number is the reciprocal of the number.
Step 2: Reciprocal of 7 is 1/7.
Step 3: 7 × 1/7 = 1.
Step 4: So, the multiplicative inverse of 7 is 1/7.
Quick Summary
- Additive inverse: a + (-a) = 0
- Multiplicative inverse: a * (1/a) = 1
- Additive inverse changes the sign of the number.
- Multiplicative inverse is the reciprocal of the number.
🍎 Teacher Insights
Use real-world examples to illustrate inverse operations. For instance, adding and then subtracting the same amount, or multiplying and then dividing by the same number.🎓 Prerequisites
- Basic arithmetic operations
- Understanding of variables
Check Your Knowledge
Q1: What is the multiplicative inverse of 7?
Q2: What is the additive inverse of 54?
Frequently Asked Questions
Q: What is the additive inverse of a number?
A: The additive inverse of a number 'a' is '-a', such that a + (-a) = 0.
Q: What is the multiplicative inverse of a number?
A: The multiplicative inverse of a number 'a' is '1/a', such that a * (1/a) = 1. Note that 'a' cannot be zero.