Question
The multiplicative inverse of \( 2 \frac{3}{8} \) is (Type a fraction.)
Ask by Mann Burgess. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The multiplicative inverse of \( 2 \frac{3}{8} \) is \( \frac{8}{19} \).
Solution
The multiplicative inverse of \( 2 \frac{3}{8} \) is calculated as follows:
1. Convert the mixed number to an improper fraction:
\[
2 \frac{3}{8} = 2 + \frac{3}{8} = \frac{16}{8} + \frac{3}{8} = \frac{19}{8}
\]
2. The multiplicative inverse of a number is \( \frac{1}{\text{number}} \). Therefore:
\[
\text{Multiplicative inverse of } \frac{19}{8} = \frac{1}{\frac{19}{8}} = \frac{8}{19}
\]
\(\boxed{\dfrac{8}{19}}\)
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Simplify this solution The Deep Dive
To find the multiplicative inverse of \( 2 \frac{3}{8} \), first convert the mixed number into an improper fraction. This gives us \( \frac{19}{8} \). The multiplicative inverse is simply the reciprocal of this fraction. Therefore, the multiplicative inverse of \( 2 \frac{3}{8} \) is \( \frac{8}{19} \). Remember, the multiplicative inverse of any number \( x \) is \( \frac{1}{x} \), so you can always flip the fraction to find it! Just make sure to handle improper fractions carefully to avoid any mix-ups!
