Park Chandler
12/13/2023 · Middle School
What is the reciprocal of \( 1 \frac{3}{4} \) ?
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Tutor-Verified Answer
Step-by-step Solution
To find the reciprocal of \( 1 \frac{3}{4} \), we first need to convert the mixed number into an improper fraction.
1. Convert \( 1 \frac{3}{4} \) to an improper fraction:
\[
1 \frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{4 + 3}{4} = \frac{7}{4}
\]
2. Now, we find the reciprocal of \( \frac{7}{4} \). The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \). Therefore, the reciprocal of \( \frac{7}{4} \) is:
\[
\frac{4}{7}
\]
Thus, the reciprocal of \( 1 \frac{3}{4} \) is \( \frac{4}{7} \).
Quick Answer
The reciprocal of \( 1 \frac{3}{4} \) is \( \frac{4}{7} \).
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