Year 6 Maths: Dividing a Fraction by a Fraction

Hello Year 6! Today, we are going to learn how to divide a fraction by another fraction. This might sound tricky at first, but I promise it will become easier once you understand the steps. Let’s dive in!

What is a Fraction?

A fraction represents a part of a whole. For example, if you have a pizza and you eat 1 out of 4 slices, we say you ate the fraction

$$\frac{1}{4}$$ of the pizza.

Dividing Fractions: The Key Rule

When you divide a fraction by another fraction, we use a simple rule. Instead of dividing, we will multiply by the reciprocal of the second fraction.

What is a Reciprocal?

The reciprocal of a fraction is what you get when you flip it. For example:

• The reciprocal of $$\frac{1}{2}$$ is $$\frac{2}{1}$$ (or just 2).
• The reciprocal of $$\frac{3}{4}$$ is $$\frac{4}{3}$$ .

Steps to Divide a Fraction by a Fraction

1. Keep the first fraction the same.
2. Change the division sign to multiplication.
3. Flip the second fraction to find its reciprocal.
4. Multiply the first fraction by the reciprocal of the second fraction.

Example

Let’s see an example!

Example 1: Divide

$$\frac{1}{2}$$ by $$\frac{1}{4}$$ .

1. Keep the first fraction: $$\frac{1}{2}$$ .
2. Change the division sign to multiplication: $$\frac{1}{2} \div \frac{1}{4}$$ becomes $$\frac{1}{2} \times$$ .
3. Find the reciprocal of $$\frac{1}{4}$$ , which is $$\frac{4}{1}$$ .
4. Now, multiply: $$\frac{1}{2} \times \frac{4}{1} = \frac{1 \times 4}{2 \times 1} = \frac{4}{2} = 2$$ .

So,

$$\frac{1}{2} \div \frac{1}{4} = 2$$ .

Another Example

Example 2: Divide

$$\frac{3}{5}$$ by $$\frac{2}{3}$$ .

1. Keep $$\frac{3}{5}$$ .
2. Change to multiplication: $$\frac{3}{5} \div \frac{2}{3}$$ becomes $$\frac{3}{5} \times$$ .
3. Find the reciprocal of $$\frac{2}{3}$$ , which is $$\frac{3}{2}$$ .
4. Multiply: $$\frac{3}{5} \times \frac{3}{2} = \frac{3 \times 3}{5 \times 2} = \frac{9}{10}$$ .

So,

$$\frac{3}{5} \div \frac{2}{3} = \frac{9}{10}$$ .

Tips and Tricks

• Always remember: Keep, Change, Flip.
• Write down each step. This will help you not to make mistakes.
• Practice with different fractions to get the hang of it!

Questions to Practice

Easy Level Questions

1. $$\frac{1}{2} \div \frac{1}{3}$$
2. $$\frac{3}{4} \div \frac{1}{2}$$
3. $$\frac{2}{5} \div \frac{1}{5}$$
4. $$\frac{5}{6} \div \frac{1}{2}$$
5. $$\frac{1}{4} \div \frac{1}{2}$$
6. $$\frac{2}{3} \div \frac{1}{3}$$
7. $$\frac{3}{5} \div \frac{1}{1}$$
8. $$\frac{1}{1} \div \frac{1}{4}$$
9. $$\frac{4}{5} \div \frac{1}{5}$$
10. $$\frac{2}{2} \div \frac{1}{2}$$
11. $$\frac{1}{3} \div \frac{1}{6}$$
12. $$\frac{1}{5} \div \frac{1}{5}$$
13. $$\frac{2}{8} \div \frac{1}{4}$$
14. $$\frac{3}{6} \div \frac{1}{3}$$
15. $$\frac{4}{8} \div \frac{1}{2}$$
16. $$\frac{5}{10} \div \frac{1}{2}$$
17. $$\frac{6}{12} \div \frac{1}{2}$$
18. $$\frac{2}{4} \div \frac{1}{2}$$
19. $$\frac{1}{2} \div \frac{1}{4}$$
20. $$\frac{3}{7} \div \frac{1}{7}$$

Medium Level Questions

1. $$\frac{4}{5} \div \frac{2}{3}$$
2. $$\frac{1}{2} \div \frac{3}{4}$$
3. $$\frac{5}{6} \div \frac{3}{5}$$
4. $$\frac{3}{4} \div \frac{2}{5}$$
5. $$\frac{7}{8} \div \frac{3}{4}$$
6. $$\frac{2}{3} \div \frac{1}{2}$$
7. $$\frac{3}{8} \div \frac{1}{4}$$
8. $$\frac{5}{9} \div \frac{2}{3}$$
9. $$\frac{2}{5} \div \frac{3}{5}$$
10. $$\frac{1}{3} \div \frac{2}{7}$$
11. $$\frac{5}{12} \div \frac{1}{3}$$
12. $$\frac{4}{7} \div \frac{2}{5}$$
13. $$\frac{3}{10} \div \frac{3}{5}$$
14. $$\frac{6}{11} \div \frac{2}{11}$$
15. $$\frac{2}{9} \div \frac{1}{3}$$
16. $$\frac{4}{6} \div \frac{2}{3}$$
17. $$\frac{3}{4} \div \frac{5}{6}$$
18. $$\frac{8}{9} \div \frac{2}{3}$$
19. $$\frac{5}{10} \div \frac{3}{4}$$
20. $$\frac{9}{10} \div \frac{3}{5}$$

Hard Level Questions

1. $$\frac{5}{6} \div \frac{3}{8}$$
2. $$\frac{7}{10} \div \frac{2}{5}$$
3. $$\frac{3}{4} \div \frac{5}{8}$$
4. $$\frac{9}{10} \div \frac{4}{5}$$
5. $$\frac{11}{12} \div \frac{5}{6}$$
6. $$\frac{8}{15} \div \frac{4}{9}$$
7. $$\frac{6}{7} \div \frac{3}{14}$$
8. $$\frac{5}{8} \div \frac{2}{3}$$
9. $$\frac{2}{11} \div \frac{4}{5}$$
10. $$\frac{1}{2} \div \frac{5}{8}$$
11. $$\frac{4}{5} \div \frac{3}{7}$$
12. $$\frac{2}{3} \div \frac{5}{6}$$
13. $$\frac{3}{4} \div \frac{1}{2}$$
14. $$\frac{7}{12} \div \frac{2}{3}$$
15. $$\frac{9}{16} \div \frac{3}{8}$$
16. $$\frac{10}{11} \div \frac{5}{6}$$
17. $$\frac{4}{9} \div \frac{2}{5}$$
18. $$\frac{1}{3} \div \frac{2}{5}$$
19. $$\frac{3}{5} \div \frac{4}{7}$$
20. $$\frac{9}{14} \div \frac{3}{2}$$

Answers with Explanations

Easy Level Answers

1. $$\frac{1}{2} \div \frac{1}{3} = \frac{3}{2} = 1.5$$
2. $$\frac{3}{4} \div \frac{1}{2} = \frac{3}{2} = 1.5$$
3. $$\frac{2}{5} \div \frac{1}{5} = 2$$
4. $$\frac{5}{6} \div \frac{1}{2} = \frac{5}{3} = 1.67$$
5. $$\frac{1}{4} \div \frac{1}{2} = \frac{1}{2}$$
6. $$\frac{2}{3} \div \frac{1}{3} = 2$$
7. $$\frac{3}{5} \div \frac{1}{1} = \frac{3}{5}$$
8. $$\frac{1}{1} \div \frac{1}{4} = 4$$
9. $$\frac{4}{5} \div \frac{1}{5} = 4$$
10. $$\frac{2}{2} \div \frac{1}{2} = 2$$
11. $$\frac{1}{3} \div \frac{1}{6} = 2$$
12. $$\frac{1}{5} \div \frac{1}{5} = 1$$
13. $$\frac{2}{8} \div \frac{1}{4} = 1$$
14. $$\frac{3}{6} \div \frac{1}{3} = 1.5$$
15. $$\frac{4}{8} \div \frac{1}{2} = 1$$
16. $$\frac{5}{10} \div \frac{1}{2} = 1$$
17. $$\frac{6}{12} \div \frac{1}{2} = 1$$
18. $$\frac{2}{4} \div \frac{1}{2} = 1$$
19. $$\frac{1}{2} \div \frac{1}{4} = 2$$
20. $$\frac{3}{7} \div \frac{1}{7} = 3$$

Medium Level Answers

1. $$\frac{4}{5} \div \frac{2}{3} = \frac{6}{5} = 1.2$$
2. $$\frac{1}{2} \div \frac{3}{4} = \frac{2}{3}$$
3. $$\frac{5}{6} \div \frac{3}{5} = \frac{25}{18} = 1.39$$
4. $$\frac{3}{4} \div \frac{2}{5} = \frac{15}{8} = 1.875$$
5. $$\frac{7}{8} \div \frac{3}{4} = \frac{7}{6} = 1.17$$
6. $$\frac{2}{3} \div \frac{1}{2} = \frac{4}{3} = 1.33$$
7. $$\frac{3}{8} \div \frac{1}{4} = \frac{3}{2} = 1.5$$
8. $$\frac{5}{9} \div \frac{2}{3} = \frac{15}{18} = \frac{5}{6} = 0.83$$
9. $$\frac{2}{5} \div \frac{3}{5} = \frac{2}{3}$$
10. $$\frac{1}{3} \div \frac{2}{7} = \frac{7}{6} = 1.17$$
11. $$\frac{5}{12} \div \frac{1}{3} = \frac{5}{4} = 1.25$$
12. $$\frac{4}{7} \div \frac{2}{5} = \frac{20}{14} = \frac{10}{7} = 1.43$$
13. $$\frac{3}{10} \div \frac{3}{5} = \frac{1}{2}$$
14. $$\frac{6}{11} \div \frac{2}{11} = 3$$
15. $$\frac{2}{9} \div \frac{1}{3} = \frac{2}{3}$$
16. $$\frac{4}{6} \div \frac{2}{3} = 1$$
17. $$\frac{3}{4} \div \frac{5}{6} = \frac{18}{20} = \frac{9}{10} = 0.9$$
18. $$\frac{8}{9} \div \frac{2}{3} = \frac{12}{9} = \frac{4}{3} = 1.33$$
19. $$\frac{5}{10} \div \frac{3}{4} = \frac{5}{7.5} = \frac{2}{3}$$
20. $$\frac{9}{10} \div \frac{3}{5} = \frac{15}{10} = \frac{3}{2} = 1.5$$

Hard Level Answers

1. $$\frac{5}{6} \div \frac{3}{8} = \frac{40}{18} = \frac{20}{9} = 2.22$$
2. $$\frac{7}{10} \div \frac{2}{5} = \frac{35}{20} = \frac{7}{4} = 1.75$$
3. $$\frac{3}{4} \div \frac{5}{8} = \frac{24}{20} = \frac{6}{5} = 1.2$$
4. $$\frac{9}{10} \div \frac{4}{5} = \frac{45}{40} = \frac{9}{8} = 1.125$$
5. $$\frac{11}{12} \div \frac{5}{6} = \frac{66}{60} = \frac{11}{10} = 1.1$$
6. $$\frac{8}{15} \div \frac{4}{9} = \frac{72}{60} = \frac{12}{10} = \frac{6}{5} = 1.2$$
7. $$\frac{6}{7} \div \frac{3}{14} = \frac{84}{21} = 4$$
8. $$\frac{5}{8} \div \frac{2}{3} = \frac{15}{16}$$
9. $$\frac{2}{11} \div \frac{4}{5} = \frac{10}{44} = \frac{5}{22} = 0.227$$
10. $$\frac{1}{2} \div \frac{5}{8} = \frac{8}{10} = \frac{4}{5} = 0.8$$
11. $$\frac{4}{5} \div \frac{3}{7} = \frac{28}{15} = 1.87$$
12. $$\frac{2}{3} \div \frac{5}{6} = \frac{12}{15} = \frac{4}{5} = 0.8$$
13. $$\frac{3}{4} \div \frac{1}{2} = \frac{3}{2} = 1.5$$
14. $$\frac{7}{12} \div \frac{2}{3} = \frac{21}{24} = \frac{7}{8} = 0.875$$
15. $$\frac{9}{16} \div \frac{3}{8} = \frac{72}{48} = \frac{3}{2} = 1.5$$
16. $$\frac{10}{11} \div \frac{5}{6} = \frac{60}{55} = \frac{12}{11} = 1.09$$
17. $$\frac{4}{9} \div \frac{2}{5} = \frac{20}{18} = \frac{10}{9} = 1.11$$
18. $$\frac{1}{3} \div \frac{2}{5} = \frac{5}{6} = 0.83$$
19. $$\frac{3}{5} \div \frac{4}{7} = \frac{21}{20} = 1.05$$
20. $$\frac{