Question

problems 1–4
use any strategy to calculate each quotient.
$2\frac{1}{2} \div \frac{5}{8}$
$\frac{4}{3} \div \frac{5}{2}$
$3\frac{1}{2} \div \frac{1}{3}$
$3 \div \frac{2}{3}$

Explanation:

Problem 1: \( 2\frac{1}{2} \div \frac{5}{8} \)

Step 1: Convert mixed number to improper fraction

\( 2\frac{1}{2} = \frac{2\times2 + 1}{2} = \frac{5}{2} \)

Step 2: Divide by multiplying by reciprocal

\( \frac{5}{2} \div \frac{5}{8} = \frac{5}{2} \times \frac{8}{5} \)

Step 3: Simplify the fractions

Cancel out the common factor 5: \( \frac{1}{2} \times \frac{8}{1} = \frac{8}{2} = 4 \)

Step 1: Multiply by reciprocal of divisor

\( \frac{4}{3} \div \frac{5}{2} = \frac{4}{3} \times \frac{2}{5} \)

Step 2: Multiply numerators and denominators

\( \frac{4\times2}{3\times5} = \frac{8}{15} \)

Step 1: Convert mixed number to improper fraction

\( 3\frac{1}{2} = \frac{3\times2 + 1}{2} = \frac{7}{2} \)

Step 2: Divide by multiplying by reciprocal

\( \frac{7}{2} \div \frac{1}{3} = \frac{7}{2} \times 3 = \frac{21}{2} = 10\frac{1}{2} \)

Answer:

\( 4 \)

Problem 2: \( \frac{4}{3} \div \frac{5}{2} \)