Question
(3) Work these out mentally. \( \begin{array}{lll}\text { a } \frac{1}{2} \div \frac{2}{3} & \text { b } \frac{1}{4} \div \frac{3}{5} & \text { c } \frac{3}{7} \div \frac{1}{2} \\ \text { d } \frac{5}{9} \div \frac{6}{7} & \text { e } \frac{2}{5} \div \frac{5}{9} & \text { f } \frac{1}{10} \div \frac{3}{7} \\ 4 & \text { Work these out mentally. Write each answer as a mixed number. } \\ \begin{array}{lll}\text { a } \frac{1}{2} \div \frac{1}{3} & \text { b } \frac{3}{5} \div \frac{4}{7} & \text { c } \frac{1}{3} \div \frac{2}{7} \\ \text { d } \frac{7}{9} \div \frac{1}{2} & \text { e } \frac{5}{6} \div \frac{2}{11} & \text { f } \frac{4}{7} \div \frac{3}{13} \\ \text { 5. Work these out mentally. Cancel each answer to its simplest form. } \\ \begin{array}{lll}\text { a } \frac{5}{8} \div \frac{1}{2} & \text { b } \frac{4}{13} \div \frac{3}{13} & \text { c } \frac{5}{8} \div \frac{5}{12} \\ \text { d } \frac{1}{3} \div \frac{5}{9} & \text { e } \frac{1}{4} \div \frac{1}{12} & \text { f } \frac{7}{9} \div \frac{1}{6}\end{array}\end{array}\end{array}> \)
Ask by Warren Horton. in Bermuda
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
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** \( \frac{7}{9} \div \frac{1}{6} = \frac{14}{3} = 4 \frac{2}{3} \)
Solution
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: \( \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \).
2. **b** \( \frac{1}{4} \div \frac{3}{5} \)
- Reciprocal of \( \frac{3}{5} \) is \( \frac{5}{3} \).
- Calculation: \( \frac{1}{4} \times \frac{5}{3} = \frac{5}{12} \).
3. **c** \( \frac{3}{7} \div \frac{1}{2} \)
- Reciprocal of \( \frac{1}{2} \) is \( 2 \).
- Calculation: \( \frac{3}{7} \times 2 = \frac{6}{7} \).
4. **d** \( \frac{5}{9} \div \frac{6}{7} \)
- Reciprocal of \( \frac{6}{7} \) is \( \frac{7}{6} \).
- Calculation: \( \frac{5}{9} \times \frac{7}{6} = \frac{35}{54} \).
5. **e** \( \frac{2}{5} \div \frac{5}{9} \)
- Reciprocal of \( \frac{5}{9} \) is \( \frac{9}{5} \).
- Calculation: \( \frac{2}{5} \times \frac{9}{5} = \frac{18}{25} \).
6. **f** \( \frac{1}{10} \div \frac{3}{7} \)
- Reciprocal of \( \frac{3}{7} \) is \( \frac{7}{3} \).
- Calculation: \( \frac{1}{10} \times \frac{7}{3} = \frac{7}{30} \).
### Part 2:
1. **a** \( \frac{1}{2} \div \frac{1}{3} \)
- Reciprocal of \( \frac{1}{3} \) is \( 3 \).
- Calculation: \( \frac{1}{2} \times 3 = \frac{3}{2} = 1 \frac{1}{2} \).
2. **b** \( \frac{3}{5} \div \frac{4}{7} \)
- Reciprocal of \( \frac{4}{7} \) is \( \frac{7}{4} \).
- Calculation: \( \frac{3}{5} \times \frac{7}{4} = \frac{21}{20} = 1 \frac{1}{20} \).
3. **c** \( \frac{1}{3} \div \frac{2}{7} \)
- Reciprocal of \( \frac{2}{7} \) is \( \frac{7}{2} \).
- Calculation: \( \frac{1}{3} \times \frac{7}{2} = \frac{7}{6} = 1 \frac{1}{6} \).
4. **d** \( \frac{7}{9} \div \frac{1}{2} \)
- Reciprocal of \( \frac{1}{2} \) is \( 2 \).
- Calculation: \( \frac{7}{9} \times 2 = \frac{14}{9} = 1 \frac{5}{9} \).
5. **e** \( \frac{5}{6} \div \frac{2}{11} \)
- Reciprocal of \( \frac{2}{11} \) is \( \frac{11}{2} \).
- Calculation: \( \frac{5}{6} \times \frac{11}{2} = \frac{55}{12} = 4 \frac{7}{12} \).
6. **f** \( \frac{4}{7} \div \frac{3}{13} \)
- Reciprocal of \( \frac{3}{13} \) is \( \frac{13}{3} \).
- Calculation: \( \frac{4}{7} \times \frac{13}{3} = \frac{52}{21} = 2 \frac{10}{21} \).
### Part 3:
1. **a** \( \frac{5}{8} \div \frac{1}{2} \)
- Reciprocal of \( \frac{1}{2} \) is \( 2 \).
- Calculation: \( \frac{5}{8} \times 2 = \frac{10}{8} = \frac{5}{4} = 1 \frac{1}{4} \).
2. **b** \( \frac{4}{13} \div \frac{3}{13} \)
- Reciprocal of \( \frac{3}{13} \) is \( \frac{13}{3} \).
- Calculation: \( \frac{4}{13} \times \frac{13}{3} = \frac{4}{3} = 1 \frac{1}{3} \).
3. **c** \( \frac{5}{8} \div \frac{5}{12} \)
- Reciprocal of \( \frac{5}{12} \) is \( \frac{12}{5} \).
- Calculation: \( \frac{5}{8} \times \frac{12}{5} = \frac{12}{8} = \frac{3}{2} = 1 \frac{1}{2} \).
4. **d** \( \frac{1}{3} \div \frac{5}{9} \)
- Reciprocal of \( \frac{5}{9} \) is \( \frac{9}{5} \).
- Calculation: \( \frac{1}{3} \times \frac{9}{5} = \frac{9}{15} = \frac{3}{5} \).
5. **e** \( \frac{1}{4} \div \frac{1}{12} \)
- Reciprocal of \( \frac{1}{12} \) is \( 12 \).
- Calculation: \( \frac{1}{4} \times 12 = 3 \).
6. **f** \( \frac{7}{9} \div \frac{1}{6} \)
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Mind Expander
Let’s dive into the world of fractions! When dividing fractions, remember that you multiply by the reciprocal. So, for example, \( \frac{1}{2} \div \frac{2}{3} \) becomes \( \frac{1}{2} \times \frac{3}{2} \), which equals \( \frac{3}{4} \). Voila, magical math transformations! Now, when you work out the second part, like \( \frac{1}{2} \div \frac{1}{3} \), just flip and multiply! This gives you \( \frac{1}{2} \times \frac{3}{1} = \frac{3}{2} \), which is \( 1 \frac{1}{2} \) as a mixed number. Keep those fraction tricks up your sleeve!