Problem: Finding the Multiplicative Inverse
The task is to find the
multiplicative inverse of each given number. The multiplicative inverse of a number \( x \) is a number \( y \) such that:
\[
x \cdot y = 1
\]
In other words, the multiplicative inverse of a number is its reciprocal. For a fraction \( \frac{a}{b} \), the multiplicative inverse is \( \frac{b}{a} \). For an integer \( n \), the multiplicative inverse is \( \frac{1}{n} \).
Let's solve each problem step by step.
---
Problem 5: \( \frac{2}{9} \)
The multiplicative inverse of \( \frac{2}{9} \) is obtained by swapping the numerator and the denominator:
\[
\text{Multiplicative inverse of } \frac{2}{9} = \frac{9}{2}
\]
Solution for Problem 5:
\[
\boxed{\frac{9}{2}}
\]
---
Problem 7: \( 5 \)
The multiplicative inverse of an integer \( n \) is \( \frac{1}{n} \). For \( 5 \):
\[
\text{Multiplicative inverse of } 5 = \frac{1}{5}
\]
Solution for Problem 7:
\[
\boxed{\frac{1}{5}}
\]
---
Problem 9: \( 14 \)
Similarly, for the integer \( 14 \):
\[
\text{Multiplicative inverse of } 14 = \frac{1}{14}
\]
Solution for Problem 9:
\[
\boxed{\frac{1}{14}}
\]
---
Problem 16: \( \frac{10}{3} \)
The multiplicative inverse of \( \frac{10}{3} \) is obtained by swapping the numerator and the denominator:
\[
\text{Multiplicative inverse of } \frac{10}{3} = \frac{3}{10}
\]
Solution for Problem 16:
\[
\boxed{\frac{3}{10}}
\]
---
Problem 18: \( \frac{1}{13} \)
The multiplicative inverse of \( \frac{1}{13} \) is obtained by swapping the numerator and the denominator:
\[
\text{Multiplicative inverse of } \frac{1}{13} = \frac{13}{1} = 13
\]
Solution for Problem 18:
\[
\boxed{13}
\]
---
Problem 20: \( \frac{18}{5} \)
The multiplicative inverse of \( \frac{18}{5} \) is obtained by swapping the numerator and the denominator:
\[
\text{Multiplicative inverse of } \frac{18}{5} = \frac{5}{18}
\]
Solution for Problem 20:
\[
\boxed{\frac{5}{18}}
\]
---
Problem 22: \( 0.5 \)
First, convert \( 0.5 \) to a fraction. Since \( 0.5 = \frac{1}{2} \), the multiplicative inverse is:
\[
\text{Multiplicative inverse of } \frac{1}{2} = \frac{2}{1} = 2
\]
Solution for Problem 22:
\[
\boxed{2}
\]
---
Final Answers:
\[
\boxed{
\begin{aligned}
5) & \quad \frac{9}{2} \\
7) & \quad \frac{1}{5} \\
9) & \quad \frac{1}{14} \\
16) & \quad \frac{3}{10} \\
18) & \quad 13 \\
20) & \quad \frac{5}{18} \\
22) & \quad 2
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of multiplicative inverse worksheet.
