Find the product of the following fractions: (a) 2/7 7/9 (b) 5/8 3/7 (c) 4/15 9/16 (d) 4 3/5 (e) 7 3/5 (f) 17/12 6. Also, find the product of: (a) 8/15 20 (b) 5/9 15 (c) 3 1/8 *

Here are the solutions to the problems.

2. Find the product.

• (a) $\frac{2}{7} \times \frac{7}{9}$

  $$\frac{2}{7} \times \frac{7}{9} = \frac{2 \times 7}{7 \times 9} = \frac{2}{9}$$ $$\boxed{\frac{2}{9}}$$

• (b) $\frac{5}{8} \times \frac{3}{7}$

  $$\frac{5}{8} \times \frac{3}{7} = \frac{5 \times 3}{8 \times 7} = \frac{15}{56}$$ $$\boxed{\frac{15}{56}}$$

• (c) $\frac{4}{15} \times \frac{9}{16}$

  $$\frac{4}{15} \times \frac{9}{16} = \frac{4 \times 9}{15 \times 16} = \frac{1 \times 3}{5 \times 4} = \frac{3}{20}$$ $$\boxed{\frac{3}{20}}$$

• (d) $4 \times \frac{3}{5}$

  $$4 \times \frac{3}{5} = \frac{4 \times 3}{5} = \frac{12}{5}$$ $$\boxed{\frac{12}{5}}$$

• (e) $7 \times \frac{3}{5}$

  $$7 \times \frac{3}{5} = \frac{7 \times 3}{5} = \frac{21}{5}$$ $$\boxed{\frac{21}{5}}$$

• (f) $\frac{17}{12} \times 6$}

  $$\frac{17}{12} \times 6 = \frac{17 \times 6}{12} = \frac{17}{2}$$ $$\boxed{\frac{17}{2}}$$

3. Find the product.

• (a) $\frac{8}{15} \times 20$

  $$\frac{8}{15} \times 20 = \frac{8 \times 20}{15} = \frac{8 \times 4}{3} = \frac{32}{3}$$ $$\boxed{\frac{32}{3}}$$

• (b) $\frac{5}{9} \times 15$

  $$\frac{5}{9} \times 15 = \frac{5 \times 15}{9} = \frac{5 \times 5}{3} = \frac{25}{3}$$ $$\boxed{\frac{25}{3}}$$

• (c) $3 \frac{1}{8} \times 16$

  Step 1: Convert the mixed number to an improper fraction.

  $$3\frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{24+1}{8} = \frac{25}{8}$$

  Step 2: Multiply.

  $$\frac{25}{8} \times 16 = \frac{25 \times 16}{8} = 25 \times 2 = 50$$ $$\boxed{50}$$

• (d) $3 \frac{6}{7} \times 4 \frac{2}{3}$

  Step 1: Convert mixed numbers to improper fractions.

  $$3\frac{6}{7} = \frac{3 \times 7 + 6}{7} = \frac{21+6}{7} = \frac{27}{7}$$ $$4\frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12+2}{3} = \frac{14}{3}$$

  Step 2: Multiply.

  $$\frac{27}{7} \times \frac{14}{3} = \frac{27 \times 14}{7 \times 3} = \frac{9 \times 2}{1 \times 1} = 18$$ $$\boxed{18}$$

• (e) $5 \frac{5}{6} \times 1 \frac{5}{7}$

  Step 1: Convert mixed numbers to improper fractions.

  $$5\frac{5}{6} = \frac{5 \times 6 + 5}{6} = \frac{30+5}{6} = \frac{35}{6}$$ $$1\frac{5}{7} = \frac{1 \times 7 + 5}{7} = \frac{7+5}{7} = \frac{12}{7}$$

  Step 2: Multiply.

  $$\frac{35}{6} \times \frac{12}{7} = \frac{35 \times 12}{6 \times 7} = \frac{5 \times 2}{1 \times 1} = 10$$ $$\boxed{10}$$

• (f) $4 \frac{1}{8} \times 2 \frac{10}{11}$

  Step 1: Convert mixed numbers to improper fractions.

  $$4\frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{32+1}{8} = \frac{33}{8}$$ $$2\frac{10}{11} = \frac{2 \times 11 + 10}{11} = \frac{22+10}{11} = \frac{32}{11}$$

  Step 2: Multiply.

  $$\frac{33}{8} \times \frac{32}{11} = \frac{33 \times 32}{8 \times 11} = \frac{3 \times 4}{1 \times 1} = 12$$ $$\boxed{12}$$

4. Find the product.

• (a) $1 \frac{3}{5} \times 2 \frac{2}{3}$

  Step 1: Convert mixed numbers to improper fractions.

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

  Step 2: Multiply.

  $$\frac{8}{5} \times \frac{8}{3} = \frac{64}{15}$$ $$\boxed{\frac{64}{15}}$$

• (b) $12 \frac{1}{2} \times 6 \frac{1}{4}$

  Step 1: Convert mixed numbers to improper fractions.

  $$12\frac{1}{2} = \frac{12 \times 2 + 1}{2} = \frac{25}{2}$$ $$6\frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{25}{4}$$

  Step 2: Multiply.

  $$\frac{25}{2} \times \frac{25}{4} = \frac{625}{8}$$ $$\boxed{\frac{625}{8}}$$

• (c) $\frac{5}{8} \times 1000$

  $$\frac{5}{8} \times 1000 = \frac{5 \times 1000}{8} = 5 \times 125 = 625$$ $$\boxed{625}$$

• (d) $2 \frac{4}{15} \times 1 \frac{12}{17}$

  Step 1: Convert mixed numbers to improper fractions.

  $$2\frac{4}{15} = \frac{2 \times 15 + 4}{15} = \frac{30+4}{15} = \frac{34}{15}$$ $$1\frac{12}{17} = \frac{1 \times 17 + 12}{17} = \frac{17+12}{17} = \frac{29}{17}$$

  Step 2: Multiply.

  $$\frac{34}{15} \times \frac{29}{17} = \frac{2 \times 17}{15} \times \frac{29}{17} = \frac{2 \times 29}{15} = \frac{58}{15}$$ $$\boxed{\frac{58}{15}}$$

• (e) $\frac{12}{25} \times \frac{15}{28} \times \frac{35}{36}$

  $$\frac{12}{25} \times \frac{15}{28} \times \frac{35}{36} = \frac{12 \times 15 \times 35}{25 \times 28 \times 36}$$ $$= \frac{(12 \times 3) \times (5 \times 7)}{(5 \times 5) \times (4 \times 7) \times (3 \times 12)}$$ $$= \frac{1}{5 \times 4} = \frac{1}{20}$$ $$\boxed{\frac{1}{20}}$$

• (f) $\frac{10}{27} \times \frac{28}{65} \times \frac{39}{56}$

  $$\frac{10}{27} \times \frac{28}{65} \times \frac{39}{56} = \frac{10 \times 28 \times 39}{27 \times 65 \times 56}$$ $$= \frac{(2 \times 5) \times (28) \times (3 \times 13)}{(3 \times 9) \times (5 \times 13) \times (2 \times 28)}$$ $$= \frac{1}{9}$$ $$\boxed{\frac{1}{9}}$$

5. Find the product.

• (a) $1 \frac{1}{7} \times 1 \frac{1}{22} \times 1 \frac{1}{15}$

  Step 1: Convert mixed numbers to improper fractions.

  $$1\frac{1}{7} = \frac{1 \times 7 + 1}{7} = \frac{8}{7}$$ $$1\frac{1}{22} = \frac{1 \times 22 + 1}{22} = \frac{23}{22}$$ $$1\frac{1}{15} = \frac{1 \times 15 + 1}{15} = \frac{16}{15}$$

  Step 2: Multiply.

  $$\frac{8}{7} \times \frac{23}{22} \times \frac{16}{15} = \frac{8 \times 23 \times 16}{7 \times 22 \times 15} = \frac{8 \times 23 \times 16}{7 \times (2 \times 11) \times 15}$$ $$= \frac{4 \times 23 \times 16}{7 \times 11 \times 15} = \frac{1472}{1155}$$ $$\boxed{\frac{1472}{1155}}$$

• (b) $3 \frac{1}{16} \times 7 \frac{3}{7} \times \frac{25}{39}$

  Step 1: Convert mixed numbers to improper fractions.

  $$3\frac{1}{16} = \frac{3 \times 16 + 1}{16} = \frac{48+1}{16} = \frac{49}{16}$$ $$$$