Inverse Property of Multiplication
| Site: | Saylor Academy |
| Course: | RWM101: Foundations of Real World Math copy 1 |
| Book: | Inverse Property of Multiplication |
| Printed by: | Guest user |
| Date: | Tuesday, May 13, 2025, 11:23 PM |
Description
buttons.Use the Inverse Properties of Addition and Multiplication
Read this section to see examples of how to apply the inverse property of addition. Focus on the examples in the boxes. Note that in the first multiplication example box, we can use the inverse property for fractions and whole numbers.
What number multiplied by \( \frac {2}{3}\) gives multiplicative identity, \(1\)? In other words, two-thirds times what results in \(1\)?
| \( \frac {2}{3} \cdot \text{____} =1 \) |
We know \(\frac{2}{3} \cdot \frac{3}{2}=1\) |
What number multiplied by \(2\) gives the multiplicative identity, \(1\)? In other words two times what results in \(1\)?
| \( 2 \cdot \text{____} =1 \) |
We know \(2 \cdot \frac{1}{2}=1\) |
Notice that in each case, the missing number was the reciprocal of the number.
We call \( \frac {1}{a}\) the multiplicative inverse of \( a(a≠0)\). The reciprocal of a number is its multiplicative inverse. A number and its reciprocal multiply to \( 1\), which is the multiplicative identity.
INVERSE PROPERTIES
Inverse Property of Addition for any real number \( a,\)
\( a+(−a)=0 \)
\( -a \text { is the additive inverse of a.} \)
Inverse Property of Multiplication for any real number \( a ≠ 0,\)
\( a \cdot \frac {1}{a} = 1 \)
\( \frac {1}{a} \text { is the multiplicative inverse of a.} \)
Source: Rice University, https://openstax.org/books/prealgebra/pages/7-4-properties-of-identity-inverses-and-zero
This work is licensed under a Creative Commons Attribution 4.0 License.
Examples and Exercises
EXAMPLE 7.35
Find the multiplicative inverse:
(a) \( 9 \)
(b) \( -\frac {1}{9} \)
(c) \(0.9 \)
TRY IT 7.69
(a) \(5\)
(b) \(-\frac{1}{7}\)
(c) \(0.3\)
TRY IT 7.70
(a) \(18\)
(b) \(-\frac{4}{5}\)
(c) \(0.6\)
Answers
Exercise 7.35
To find the multiplicative inverse, we find the reciprocal.
(a) The multiplicative inverse of \( 9 \) is its reciprocal, \( \frac {1}{9} \).
(b) The multiplicative inverse of \( − \frac {1}{9} \) is its reciprocal, \( -9 \).
(c) To find the multiplicative inverse of \( 0.9 \) we first convert \( 0.9 \) to a fraction, \( \frac {9}{10} \). Then we find the reciprocal, \( \frac {10}{9} \).
TRY IT 7.69
(a) \(\frac{1}{5}\)
(b) \(-7\)
(c) \(\frac{10}{3}\)
TRY IT 7.70
(a) \(\frac{1}{18}\)
(b) \(-\frac{5}{4}\)
(c) \(\frac{5}{3}\)