Year 6 Maths: Dividing a Whole Number by a Fraction

Introduction

Hello Year 6! Today, we’re going to learn about dividing a whole number by a fraction. This might sound a bit tricky at first, but don’t worry! We’ll break it down step by step so that it becomes easy to understand.

Understanding the Concept

What Happens When We Divide?

When we divide, we are essentially splitting something into equal parts. For example, if you have 8 pizzas and you want to share them among friends, dividing helps you find out how many pizzas each friend gets.

Dividing a Whole Number by a Fraction

Now, when we divide a whole number by a fraction, we can think of it like this: Dividing by a fraction is the same as multiplying by its reciprocal.

What is a Reciprocal?

A reciprocal is what you get when you flip a fraction. For example:

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

Key Rule

To divide a whole number by a fraction, follow these steps:

1. Keep the whole number as it is.
2. Change the division sign (÷) to a multiplication sign (×).
3. Flip the fraction to find its reciprocal.
4. Multiply the whole number by this new fraction.

Example

Let’s say we want to divide 6 by

$$\frac{1}{3}$$ :

1. We keep 6 as it is.
2. Change the division sign to multiplication: $$6 \div \frac{1}{3}$$ becomes $$6 \times \frac{3}{1}$$ .
3. Now, we multiply: $$6 \times 3 = 18$$ .

So,

$$6 \div \frac{1}{3} = 18$$ . This means if you have 6 whole pizzas and you want to know how many slices you have if each pizza is cut into 1/3 pieces, you would have 18 slices!

Tips and Tricks

• Remember the rule: Dividing by a fraction is the same as multiplying by its reciprocal.
• Practice makes perfect: The more you practice this, the easier it will become.
• Visual aids: Drawing pictures or using objects can help you visualise the problem.

Questions

Easy Level Questions

1. $$4 \div \frac{1}{2}$$
2. $$5 \div \frac{1}{5}$$
3. $$3 \div \frac{1}{3}$$
4. $$8 \div \frac{1}{4}$$
5. $$10 \div \frac{1}{10}$$
6. $$6 \div \frac{1}{6}$$
7. $$12 \div \frac{1}{2}$$
8. $$15 \div \frac{1}{3}$$
9. $$9 \div \frac{1}{9}$$
10. $$20 \div \frac{1}{5}$$
11. $$7 \div \frac{1}{7}$$
12. $$14 \div \frac{1}{2}$$
13. $$16 \div \frac{1}{4}$$
14. $$18 \div \frac{1}{2}$$
15. $$25 \div \frac{1}{5}$$
16. $$30 \div \frac{1}{6}$$
17. $$40 \div \frac{1}{10}$$
18. $$50 \div \frac{1}{2}$$
19. $$11 \div \frac{1}{11}$$
20. $$21 \div \frac{1}{3}$$

Medium Level Questions

1. $$9 \div \frac{2}{3}$$
2. $$15 \div \frac{3}{4}$$
3. $$7 \div \frac{5}{6}$$
4. $$8 \div \frac{3}{8}$$
5. $$10 \div \frac{2}{5}$$
6. $$12 \div \frac{4}{5}$$
7. $$14 \div \frac{2}{7}$$
8. $$16 \div \frac{1}{2}$$
9. $$18 \div \frac{3}{9}$$
10. $$20 \div \frac{5}{10}$$
11. $$25 \div \frac{3}{5}$$
12. $$30 \div \frac{2}{3}$$
13. $$32 \div \frac{4}{8}$$
14. $$36 \div \frac{6}{9}$$
15. $$45 \div \frac{3}{5}$$
16. $$50 \div \frac{5}{10}$$
17. $$60 \div \frac{2}{5}$$
18. $$70 \div \frac{7}{10}$$
19. $$80 \div \frac{4}{5}$$
20. $$90 \div \frac{3}{10}$$

Hard Level Questions

1. $$12 \div \frac{5}{6}$$
2. $$25 \div \frac{7}{8}$$
3. $$30 \div \frac{3}{4}$$
4. $$48 \div \frac{5}{12}$$
5. $$36 \div \frac{7}{9}$$
6. $$54 \div \frac{2}{3}$$
7. $$72 \div \frac{4}{9}$$
8. $$90 \div \frac{3}{5}$$
9. $$100 \div \frac{2}{5}$$
10. $$120 \div \frac{1}{4}$$
11. $$150 \div \frac{5}{12}$$
12. $$200 \div \frac{7}{8}$$
13. $$250 \div \frac{3}{10}$$
14. $$300 \div \frac{5}{6}$$
15. $$400 \div \frac{2}{5}$$
16. $$450 \div \frac{3}{4}$$
17. $$600 \div \frac{5}{6}$$
18. $$720 \div \frac{8}{9}$$
19. $$800 \div \frac{5}{12}$$
20. $$900 \div \frac{7}{10}$$

Answers and Explanations

Easy Level Answers

1. $$4 \div \frac{1}{2} = 8$$
2. $$5 \div \frac{1}{5} = 25$$
3. $$3 \div \frac{1}{3} = 9$$
4. $$8 \div \frac{1}{4} = 32$$
5. $$10 \div \frac{1}{10} = 100$$
6. $$6 \div \frac{1}{6} = 36$$
7. $$12 \div \frac{1}{2} = 24$$
8. $$15 \div \frac{1}{3} = 45$$
9. $$9 \div \frac{1}{9} = 81$$
10. $$20 \div \frac{1}{5} = 100$$
11. $$7 \div \frac{1}{7} = 49$$
12. $$14 \div \frac{1}{2} = 28$$
13. $$16 \div \frac{1}{4} = 64$$
14. $$18 \div \frac{1}{2} = 36$$
15. $$25 \div \frac{1}{5} = 125$$
16. $$30 \div \frac{1}{6} = 180$$
17. $$40 \div \frac{1}{10} = 400$$
18. $$50 \div \frac{1}{2} = 100$$
19. $$11 \div \frac{1}{11} = 121$$
20. $$21 \div \frac{1}{3} = 63$$

Medium Level Answers

1. $$9 \div \frac{2}{3} = 13.5$$
2. $$15 \div \frac{3}{4} = 20$$
3. $$7 \div \frac{5}{6} = 8.4$$
4. $$8 \div \frac{3}{8} = 21.33$$
5. $$10 \div \frac{2}{5} = 25$$
6. $$12 \div \frac{4}{5} = 15$$
7. $$14 \div \frac{2}{7} = 49$$
8. $$16 \div \frac{1}{2} = 32$$
9. $$18 \div \frac{3}{9} = 54$$
10. $$20 \div \frac{5}{10} = 40$$
11. $$25 \div \frac{3}{5} = 41.67$$
12. $$30 \div \frac{2}{3} = 45$$
13. $$32 \div \frac{4}{8} = 64$$
14. $$36 \div \frac{6}{9} = 54$$
15. $$45 \div \frac{3}{5} = 75$$
16. $$50 \div \frac{5}{10} = 100$$
17. $$60 \div \frac{2}{5} = 150$$
18. $$70 \div \frac{7}{10} = 100$$
19. $$80 \div \frac{4}{5} = 100$$
20. $$90 \div \frac{3}{10} = 300$$

Hard Level Answers

1. $$12 \div \frac{5}{6} = 14.4$$
2. $$25 \div \frac{7}{8} = 28.57$$
3. $$30 \div \frac{3}{4} = 40$$
4. $$48 \div \frac{5}{12} = 115.2$$
5. $$36 \div \frac{7}{9} = 46.29$$
6. $$54 \div \frac{2}{3} = 81$$
7. $$72 \div \frac{4}{9} = 162$$
8. $$90 \div \frac{3}{5} = 150$$
9. $$100 \div \frac{2}{5} = 250$$
10. $$120 \div \frac{1}{4} = 480$$
11. $$150 \div \frac{5}{12} = 360$$
12. $$200 \div \frac{7}{8} = 228.57$$
13. $$250 \div \frac{3}{10} = 833.33$$
14. $$300 \div \frac{5}{6} = 360$$
15. $$400 \div \frac{2}{5} = 1000$$
16. $$450 \div \frac{3}{4} = 600$$
17. $$600 \div \frac{5}{6} = 720$$
18. $$720 \div \frac{8}{9} = 810$$
19. $$800 \div \frac{5}{12} = 1920$$
20. $$900 \div \frac{7}{10} = 1285.71$$

Conclusion

Great job, Year 6! Now you know how to divide a whole number by a fraction. Remember to use the key rule of multiplying by the reciprocal. Keep practicing, and soon it will feel like second nature!