Year 6 Maths: Multiplying a Fraction by a Whole Number

Hello Year 6! Today, we’re going to learn about multiplying a fraction by a whole number. This is an important skill that you will use in many areas of maths and everyday life. Let’s break it down step by step.

Understanding Fractions

A fraction consists of two parts: the numerator (the top number) and the denominator (the bottom number). For example, in the fraction $$\frac{3}{4}$$, 3 is the numerator and 4 is the denominator.

Multiplying a Fraction by a Whole Number

When you multiply a fraction by a whole number, you are finding a part of that whole number. Here’s a simple way to do it:

Steps to Multiply a Fraction by a Whole Number

1. Multiply the numerator of the fraction by the whole number.
2. Keep the denominator the same.
3. This gives you a new fraction.

Example

Let’s say we want to multiply $$\frac{2}{5}$$ by 3.

1. Multiply the numerator (2) by the whole number (3):$$2 \times 3 = 6$$
2. Keep the denominator (5) the same:$$\frac{6}{5}$$

So, $$\frac{2}{5} \times 3 = \frac{6}{5}$$.

Key Rules

• Always multiply the numerator.
• The denominator remains unchanged.
• You can simplify the fraction if needed.

Tips and Tricks

• Visualise It: Sometimes drawing a picture can help. For example, if you have $$\frac{2}{5}$$ and want to multiply it by 3, you can think of it as having 3 groups of 2 out of 5 parts.
• Simplify: If your answer is an improper fraction (the numerator is bigger than the denominator), you can convert it to a mixed number.

Example of Simplifying

If you have $$\frac{8}{4}$$, it simplifies to 2, because 8 divided by 4 equals 2.

Practice Questions

Now it’s your turn to practice! Below are sets of questions for you to try.

Easy Level Questions

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

Medium Level Questions

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

Hard Level Questions

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

Answers

Easy Level Answers

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

Medium Level Answers

1. $$\frac{20}{6}$$ or $$\frac{10}{3}$$
2. $$\frac{12}{5}$$
3. $$\frac{15}{7}$$
4. $$\frac{12}{9}$$ or $$\frac{4}{3}$$
5. $$\frac{24}{10}$$ or $$\frac{12}{5}$$
6. $$\frac{14}{8}$$ or $$\frac{7}{4}$$
7. $$\frac{8}{3}$$
8. $$\frac{5}{2}$$
9. $$\frac{15}{4}$$
10. $$\frac{10}{7}$$
11. $$\frac{12}{8}$$ or $$\frac{3}{2}$$
12. $$2$$
13. $$\frac{20}{10}$$ or $$2$$
14. $$\frac{6}{9}$$ or $$\frac{2}{3}$$
15. $$\frac{10}{3}$$
16. $$\frac{12}{5}$$
17. $$\frac{3}{2}$$
18. $$\frac{24}{7}$$
19. $$5$$
20. $$\frac{12}{8}$$ or $$\frac{3}{2}$$

Hard Level Answers

1. $$\frac{35}{12}$$
2. $$\frac{54}{10}$$ or $$\frac{27}{5}$$
3. $$\frac{33}{15}$$ or $$\frac{11}{5}$$
4. $$\frac{52}{20}$$ or $$\frac{13}{5}$$
5. $$\frac{35}{9}$$
6. $$\frac{72}{11}$$
7. $$\frac{24}{14}$$ or $$\frac{12}{7}$$
8. $$\frac{30}{13}$$
9. $$\frac{60}{16}$$ or $$\frac{15}{4}$$
10. $$\frac{24}{5}$$
11. $$\frac{35}{8}$$
12. $$\frac{36}{11}$$
13. $$\frac{18}{15}$$ or $$\frac{6}{5}$$
14. $$\frac{20}{9}$$
15. $$\frac{80}{15}$$ or $$\frac{16}{3}$$
16. $$\frac{30}{12}$$ or $$\frac{5}{2}$$
17. $$\frac{16}{17}$$
18. $$\frac{27}{14}$$
19. $$\frac{15}{10}$$ or $$\frac{3}{2}$$
20. $$\frac{44}{18}$$ or $$\frac{22}{9}$$

I hope this helps you understand how to multiply fractions by whole numbers! Keep practicing, and remember that if you have any questions, you can always ask!