Question
Dividing Fractions Test Pree (Do in boxes) Which expression is equivalent to \( 2 \frac{3}{5} \div \frac{7}{9} ? \)
Ask by Powell Wilson. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
An equivalent expression is \( \frac{13}{5} \times \frac{9}{7} \).
Solution
Step 1: Convert the mixed number to an improper fraction.
2 3/5 = (2 × 5 + 3)/5 = 13/5
Step 2: Change division to multiplication by taking the reciprocal of the divisor.
(13/5) ÷ (7/9) = (13/5) × (9/7)
So, an equivalent expression is:
(13/5) × (9/7)
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Simplify this solution Extra Insights
To divide the mixed number \( 2 \frac{3}{5} \) by the fraction \( \frac{7}{9} \), first convert the mixed number into an improper fraction. This gives us: \[ 2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5} \] Now, instead of dividing by \( \frac{7}{9} \), we multiply by its reciprocal: \[ \frac{13}{5} \div \frac{7}{9} = \frac{13}{5} \times \frac{9}{7} \] Now multiply the numerators and the denominators: \[ \frac{13 \times 9}{5 \times 7} = \frac{117}{35} \] So, the expression equivalent to \( 2 \frac{3}{5} \div \frac{7}{9} \) is \( \frac{117}{35} \).
