Question

multiply these fractions. cancel and simplify if necessary.

1. $1\frac{1}{2} \times 1\frac{3}{4} =$
2. $2\frac{1}{3} \times 5\frac{2}{5} =$
3. $4\frac{1}{3} \times 1\frac{7}{8} =$
4. $\frac{1}{2} \times 2\frac{1}{8} =$
5. $3\frac{1}{4} \times \frac{7}{8} =$
6. $5\frac{5}{7} \times \frac{14}{15} =$
7. $7 \times 1\frac{3}{8} =$
8. $2\frac{4}{5} \times 5 =$
9. $6\frac{2}{3} \times 9 =$
10. $1\frac{8}{9} \times 1\frac{5}{6} =$
11. $7\frac{1}{7} \times 8\frac{2}{5} =$
12. $1\frac{1}{7} \times 9\frac{1}{3} =$

Explanation:

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

Step 1: Convert mixed numbers to improper fractions

\( 1\frac{1}{2} = \frac{1\times2 + 1}{2} = \frac{3}{2} \)
\( 1\frac{3}{4} = \frac{1\times4 + 3}{4} = \frac{7}{4} \)

Step 2: Multiply the improper fractions

\( \frac{3}{2} \times \frac{7}{4} = \frac{3\times7}{2\times4} = \frac{21}{8} \)

Step 3: Convert back to mixed number (if needed)

\( \frac{21}{8} = 2\frac{5}{8} \)

Step 1: Convert mixed numbers to improper fractions

\( 2\frac{1}{3} = \frac{2\times3 + 1}{3} = \frac{7}{3} \)
\( 5\frac{2}{5} = \frac{5\times5 + 2}{5} = \frac{27}{5} \)

Step 2: Multiply the improper fractions

\( \frac{7}{3} \times \frac{27}{5} = \frac{7\times27}{3\times5} \)
Simplify by canceling 3 and 27: \( \frac{7\times9}{5} = \frac{63}{5} \)

Step 3: Convert back to mixed number

\( \frac{63}{5} = 12\frac{3}{5} \)

Step 1: Convert mixed numbers to improper fractions

\( 4\frac{1}{3} = \frac{4\times3 + 1}{3} = \frac{13}{3} \)
\( 1\frac{7}{8} = \frac{1\times8 + 7}{8} = \frac{15}{8} \)

Step 2: Multiply the improper fractions

\( \frac{13}{3} \times \frac{15}{8} = \frac{13\times15}{3\times8} \)
Simplify by canceling 3 and 15: \( \frac{13\times5}{8} = \frac{65}{8} \)

Step 3: Convert back to mixed number

\( \frac{65}{8} = 8\frac{1}{8} \)

Answer:

\( 2\frac{5}{8} \)

Problem 2: \( 2\frac{1}{3} \times 5\frac{2}{5} \)