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 a 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.

\(\frac{7}{3} \times \frac{27}{5}=\frac{7\times27}{3\times5}=\frac{189}{15}\)

Step 3: Simplify the fraction.

\(\frac{189}{15}=\frac{63}{5}=12\frac{3}{5}\)

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.

\(\frac{13}{3} \times \frac{15}{8}=\frac{13\times15}{3\times8}=\frac{195}{24}\)

Step 3: Simplify the fraction.

\(\frac{195}{24}=\frac{65}{8}=8\frac{1}{8}\)

Answer:

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

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