(3) Work these out mentally. $$ \begin{array}{lll} ext { a } \frac{1}{2} \div \frac{2}{3} & ext { b } \frac{1}{4} \div \frac{3}{5} & ext { c } \frac{3}{7} \div \frac{1}{2} \ ext { d } \frac{5}{9} \div \frac{6}{7} & ext { e } \frac{2}{5} \div \frac{5}{9} & ext { f } \frac{1}{10} \div \frac{3}{7} \ 4 & ext { Work these out mentally. Write each answer as a mixed number. } \ \begin{array}{lll} ext { a } \frac{1}{2} \div \frac{1}{3} & ext { b } \frac{3}{5} \div \frac{4}{7} & ext { c } \frac{1}{3} \div \frac{2}{7} \ ext { d } \frac{7}{9} \div \frac{1}{2} & ext { e } \frac{5}{6} \div \frac{2}{11} & ext { f } \frac{4}{7} \div \frac{3}{13} \ ext { 5. Work these out mentally. Cancel each answer to its simplest form. } \ \begin{array}{lll} ext { a } \frac{5}{8} \div \frac{1}{2} & ext { b } \frac{4}{13} \div \frac{3}{13} & ext { c } \frac{5}{8} \div \frac{5}{12} \ ext { d } \frac{1}{3} \div \frac{5}{9} & ext { e } \frac{1}{4} \div \frac{1}{12} & ext { f } \frac{7}{9} \div \frac{1}{6}\end{array}\end{array}\end{array} $$

Question

(3) Work these out mentally. $$ \begin{array}{lll}	ext { a } \frac{1}{2} \div \frac{2}{3} & 	ext { b } \frac{1}{4} \div \frac{3}{5} & 	ext { c } \frac{3}{7} \div \frac{1}{2} \ 	ext { d } \frac{5}{9} \div \frac{6}{7} & 	ext { e } \frac{2}{5} \div \frac{5}{9} & 	ext { f } \frac{1}{10} \div \frac{3}{7} \ 4 & 	ext { Work these out mentally. Write each answer as a mixed number. } \ \begin{array}{lll}	ext { a } \frac{1}{2} \div \frac{1}{3} & 	ext { b } \frac{3}{5} \div \frac{4}{7} & 	ext { c } \frac{1}{3} \div \frac{2}{7} \ 	ext { d } \frac{7}{9} \div \frac{1}{2} & 	ext { e } \frac{5}{6} \div \frac{2}{11} & 	ext { f } \frac{4}{7} \div \frac{3}{13} \ 	ext { 5. Work these out mentally. Cancel each answer to its simplest form. } \ \begin{array}{lll}	ext { a } \frac{5}{8} \div \frac{1}{2} & 	ext { b } \frac{4}{13} \div \frac{3}{13} & 	ext { c } \frac{5}{8} \div \frac{5}{12} \ 	ext { d } \frac{1}{3} \div \frac{5}{9} & 	ext { e } \frac{1}{4} \div \frac{1}{12} & 	ext { f } \frac{7}{9} \div \frac{1}{6}\end{array}\end{array}\end{array}> $$

UpStudy AI · Accepted Answer

Let's solve each division problem step by step. When dividing fractions, we multiply by the reciprocal of the divisor.

### Part 1: 
1. **a** $$ \frac{1}{2} \div \frac{2}{3} $$
   - Reciprocal of $$ \frac{2}{3} $$ is $$ \frac{3}{2} $$.
   - Calculation: $$ \frac{1}{2} 	imes \frac{3}{2} = \frac{3}{4} $$.

2. **b** $$ \frac{1}{4} \div \frac{3}{5} $$
   - Reciprocal of $$ \frac{3}{5} $$ is $$ \frac{5}{3} $$.
   - Calculation: $$ \frac{1}{4} 	imes \frac{5}{3} = \frac{5}{12} $$.

3. **c** $$ \frac{3}{7} \div \frac{1}{2} $$
   - Reciprocal of $$ \frac{1}{2} $$ is $$ 2 $$.
   - Calculation: $$ \frac{3}{7} 	imes 2 = \frac{6}{7} $$.

4. **d** $$ \frac{5}{9} \div \frac{6}{7} $$
   - Reciprocal of $$ \frac{6}{7} $$ is $$ \frac{7}{6} $$.
   - Calculation: $$ \frac{5}{9} 	imes \frac{7}{6} = \frac{35}{54} $$.

5. **e** $$ \frac{2}{5} \div \frac{5}{9} $$
   - Reciprocal of $$ \frac{5}{9} $$ is $$ \frac{9}{5} $$.
   - Calculation: $$ \frac{2}{5} 	imes \frac{9}{5} = \frac{18}{25} $$.

6. **f** $$ \frac{1}{10} \div \frac{3}{7} $$
   - Reciprocal of $$ \frac{3}{7} $$ is $$ \frac{7}{3} $$.
   - Calculation: $$ \frac{1}{10} 	imes \frac{7}{3} = \frac{7}{30} $$.

### Part 2:
1. **a** $$ \frac{1}{2} \div \frac{1}{3} $$
   - Reciprocal of $$ \frac{1}{3} $$ is $$ 3 $$.
   - Calculation: $$ \frac{1}{2} 	imes 3 = \frac{3}{2} = 1 \frac{1}{2} $$.

2. **b** $$ \frac{3}{5} \div \frac{4}{7} $$
   - Reciprocal of $$ \frac{4}{7} $$ is $$ \frac{7}{4} $$.
   - Calculation: $$ \frac{3}{5} 	imes \frac{7}{4} = \frac{21}{20} = 1 \frac{1}{20} $$.

3. **c** $$ \frac{1}{3} \div \frac{2}{7} $$
   - Reciprocal of $$ \frac{2}{7} $$ is $$ \frac{7}{2} $$.
   - Calculation: $$ \frac{1}{3} 	imes \frac{7}{2} = \frac{7}{6} = 1 \frac{1}{6} $$.

4. **d** $$ \frac{7}{9} \div \frac{1}{2} $$
   - Reciprocal of $$ \frac{1}{2} $$ is $$ 2 $$.
   - Calculation: $$ \frac{7}{9} 	imes 2 = \frac{14}{9} = 1 \frac{5}{9} $$.

5. **e** $$ \frac{5}{6} \div \frac{2}{11} $$
   - Reciprocal of $$ \frac{2}{11} $$ is $$ \frac{11}{2} $$.
   - Calculation: $$ \frac{5}{6} 	imes \frac{11}{2} = \frac{55}{12} = 4 \frac{7}{12} $$.

6. **f** $$ \frac{4}{7} \div \frac{3}{13} $$
   - Reciprocal of $$ \frac{3}{13} $$ is $$ \frac{13}{3} $$.
   - Calculation: $$ \frac{4}{7} 	imes \frac{13}{3} = \frac{52}{21} = 2 \frac{10}{21} $$.

### Part 3:
1. **a** $$ \frac{5}{8} \div \frac{1}{2} $$
   - Reciprocal of $$ \frac{1}{2} $$ is $$ 2 $$.
   - Calculation: $$ \frac{5}{8} 	imes 2 = \frac{10}{8} = \frac{5}{4} = 1 \frac{1}{4} $$.

2. **b** $$ \frac{4}{13} \div \frac{3}{13} $$
   - Reciprocal of $$ \frac{3}{13} $$ is $$ \frac{13}{3} $$.
   - Calculation: $$ \frac{4}{13} 	imes \frac{13}{3} = \frac{4}{3} = 1 \frac{1}{3} $$.

3. **c** $$ \frac{5}{8} \div \frac{5}{12} $$
   - Reciprocal of $$ \frac{5}{12} $$ is $$ \frac{12}{5} $$.
   - Calculation: $$ \frac{5}{8} 	imes \frac{12}{5} = \frac{12}{8} = \frac{3}{2} = 1 \frac{1}{2} $$.

4. **d** $$ \frac{1}{3} \div \frac{5}{9} $$
   - Reciprocal of $$ \frac{5}{9} $$ is $$ \frac{9}{5} $$.
   - Calculation: $$ \frac{1}{3} 	imes \frac{9}{5} = \frac{9}{15} = \frac{3}{5} $$.

5. **e** $$ \frac{1}{4} \div \frac{1}{12} $$
   - Reciprocal of $$ \frac{1}{12} $$ is $$ 12 $$.
   - Calculation: $$ \frac{1}{4} 	imes 12 = 3 $$.

6. **f** $$ \frac{7}{9} \div \frac{1}{6} $$
  
Here are the simplified answers for each division problem: 1. **a** $$ \frac{1}{2} \div \frac{2}{3} = \frac{3}{4} $$ 2. **b** $$ \frac{1}{4} \div \frac{3}{5} = \frac{5}{12} $$ 3. **c** $$ \frac{3}{7} \div \frac{1}{2} = \frac{6}{7} $$ 4. **d** $$ \frac{5}{9} \div \frac{6}{7} = \frac{35}{54} $$ 5. **e** $$ \frac{2}{5} \div \frac{5}{9} = \frac{18}{25} $$ 6. **f** $$ \frac{1}{10} \div \frac{3}{7} = \frac{7}{30} $$ 7. **a** $$ \frac{1}{2} \div \frac{1}{3} = 1 \frac{1}{2} $$ 8. **b** $$ \frac{3}{5} \div \frac{4}{7} = 1 \frac{1}{20} $$ 9. **c** $$ \frac{1}{3} \div \frac{2}{7} = 1 \frac{1}{6} $$ 10. **d** $$ \frac{7}{9} \div \frac{1}{2} = 1 \frac{5}{9} $$ 11. **e** $$ \frac{5}{6} \div \frac{2}{11} = 4 \frac{7}{12} $$ 12. **f** $$ \frac{4}{7} \div \frac{3}{13} = 2 \frac{10}{21} $$ 13. **a** $$ \frac{5}{8} \div \frac{1}{2} = 1 \frac{1}{4} $$ 14. **b** $$ \frac{4}{13} \div \frac{3}{13} = 1 \frac{1}{3} $$ 15. **c** $$ \frac{5}{8} \div \frac{5}{12} = 1 \frac{1}{2} $$ 16. **d** $$ \frac{1}{3} \div \frac{5}{9} = \frac{3}{5} $$ 17. **e** $$ \frac{1}{4} \div \frac{1}{12} = 3 $$ 18. **f** $$ \frac{7}{9} \div \frac{1}{6} = \frac{14}{3} = 4 \frac{2}{3} $$

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