Question

Your friend finds the quotient of 3 1 — 2 and 1 2 — 3 . Is your friend correct? Explain your reasoning. 31 — 2 ÷ 12 — 3 = 31 — 2 × 13 — 2 = 7 — 2 × 5 — 2 =— 7 × 5 2 × 2 = 35 — 4 , or 83 —

Answer 1

Explanation:

It seems there might be some confusion in the way the calculations are being carried out. Let's break down the steps and correct any errors:

The initial expression is: \( \frac{3\frac{1}{2}}{1\frac{2}{3}} \)

1. Convert the mixed numbers to improper fractions:

\( \frac{7}{2} \div \frac{5}{3} \)

2. Invert the divisor (second fraction) and multiply:

\( \frac{7}{2} \times \frac{3}{5} \)

3. Multiply the numerators and denominators separately:

\( \frac{7 \times 3}{2 \times 5} = \frac{21}{10} \)

So, the correct quotient is \( \frac{21}{10} \), which cannot be simplified any further as a fraction. It's not equal to \( \frac{35}{4} \) or \( \frac{83}{4} \). The errors occurred when multiplying the mixed numbers and fractions and when simplifying the fractions.