Question

1. $2\frac{5}{8} \times 2\frac{3}{5} =$
2. $2\frac{1}{3} \times 3\frac{1}{4} =$
3. $3\frac{1}{4} \times 1\frac{1}{8} =$

Explanation:

Problem 12: \( 2\frac{5}{8} \times 2\frac{3}{5} \)

Step1: Convert mixed numbers to improper fractions

\( 2\frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{21}{8} \)
\( 2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5} \)

Step2: Multiply the improper fractions

\( \frac{21}{8} \times \frac{13}{5} = \frac{21 \times 13}{8 \times 5} = \frac{273}{40} \)

Step3: Convert back to mixed number (optional)

\( \frac{273}{40} = 6\frac{33}{40} \)

Step1: Convert mixed numbers to improper fractions

\( 2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \)
\( 3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \)

Step2: Multiply the improper fractions

\( \frac{7}{3} \times \frac{13}{4} = \frac{7 \times 13}{3 \times 4} = \frac{91}{12} \)

Step3: Convert back to mixed number (optional)

\( \frac{91}{12} = 7\frac{7}{12} \)

Step1: Convert mixed numbers to improper fractions

\( 3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \)
\( 1\frac{1}{8} = \frac{1 \times 8 + 1}{8} = \frac{9}{8} \)

Step2: Multiply the improper fractions

\( \frac{13}{4} \times \frac{9}{8} = \frac{13 \times 9}{4 \times 8} = \frac{117}{32} \)

Step3: Convert back to mixed number (optional)

\( \frac{117}{32} = 3\frac{21}{32} \)

Answer:

\( 6\frac{33}{40} \) (or \( \frac{273}{40} \))

Problem 15: \( 2\frac{1}{3} \times 3\frac{1}{4} \)