Chandler Pritchard
09/02/2023 · Middle School
Find the quotient \( 4 \div \frac{3}{8} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find the quotient \( 4 \div \frac{3}{8} \), we can rewrite the division of a number by a fraction as multiplication by the reciprocal of that fraction.
The reciprocal of \( \frac{3}{8} \) is \( \frac{8}{3} \). Therefore, we can rewrite the expression as:
\[
4 \div \frac{3}{8} = 4 \times \frac{8}{3}
\]
Next, we can express \( 4 \) as a fraction:
\[
4 = \frac{4}{1}
\]
Now we can multiply the two fractions:
\[
\frac{4}{1} \times \frac{8}{3} = \frac{4 \times 8}{1 \times 3} = \frac{32}{3}
\]
Thus, the quotient \( 4 \div \frac{3}{8} \) is:
\[
\frac{32}{3}
\]
To express this as a mixed number, we can divide \( 32 \) by \( 3 \):
\[
32 \div 3 = 10 \quad \text{(with a remainder of 2)}
\]
So, we can write:
\[
\frac{32}{3} = 10 \frac{2}{3}
\]
Therefore, the final answer is:
\[
\frac{32}{3} \quad \text{or} \quad 10 \frac{2}{3}
\]
Quick Answer
The quotient \( 4 \div \frac{3}{8} \) is \( \frac{32}{3} \) or \( 10 \frac{2}{3} \).
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