Year 4 Maths: Calculating with Fractions

Understanding Fractions

Hello, Year 4! Today, we’re going to learn about fractions. Fractions are parts of a whole. For example, if you have a pizza and you cut it into 4 equal slices, each slice is a fraction of the pizza. If you eat 1 slice, you have eaten $$\frac{1}{4}$$ of the pizza.

What is a Fraction?

A fraction has two parts:

• The top number is called the numerator. It tells us how many parts we have.
• The bottom number is called the denominator. It tells us how many equal parts the whole is divided into.

For example, in the fraction $$\frac{2}{5}$$:

• 2 is the numerator (we have 2 parts)
• 5 is the denominator (the whole is divided into 5 parts)

Adding Fractions

Same Denominator

When the denominators are the same, adding fractions is easy! You just add the numerators.

Example:

$$\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}$$

Different Denominator

When the denominators are different, you need to make them the same first. You can find a common denominator.

Example:

$$\frac{1}{3} + \frac{1}{6}$$

1. The common denominator of 3 and 6 is 6.
2. Convert $$\frac{1}{3}$$ to $$\frac{2}{6}$$ (because 1 × 2 = 2 and 3 × 2 = 6).
3. Now add: $$\frac{2}{6} + \frac{1}{6} = \frac{3}{6}$$
4. Simplify $$\frac{3}{6}$$ to $$\frac{1}{2}$$.

Subtracting Fractions

Subtracting fractions works the same way as adding.

Same Denominator

Example:

$$\frac{3}{5} – \frac{1}{5} = \frac{3 – 1}{5} = \frac{2}{5}$$

Different Denominator

Use the same method as with addition.

Example:

$$\frac{2}{5} – \frac{1}{10}$$

1. Common denominator is 10.
2. Convert $$\frac{2}{5}$$ to $$\frac{4}{10}$$.
3. Now subtract: $$\frac{4}{10} – \frac{1}{10} = \frac{3}{10}$$.

Multiplying Fractions

Multiplying fractions is simple! You just multiply the numerators together and the denominators together.

Example:

$$\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}$$

Dividing Fractions

To divide fractions, you multiply by the reciprocal (flip the second fraction).

Example:

$$\frac{1}{2} \div \frac{3}{4}$$

1. Flip the second fraction: $$\frac{1}{2} \times \frac{4}{3}$$
2. Multiply: $$\frac{1 \times 4}{2 \times 3} = \frac{4}{6}$$
3. Simplify if possible: $$\frac{2}{3}$$.

Tips and Tricks

1. Always simplify your fractions if you can.
2. When adding or subtracting, always check if the denominators are the same.
3. For multiplication, just multiply straight across.
4. For division, remember to flip the second fraction!

Questions

Easy Level (20 Questions)

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

Medium Level (20 Questions)

1. What is $$\frac{1}{3} + \frac{1}{6}$$?
2. What is $$\frac{2}{5} + \frac{1}{10}$$?
3. What is $$\frac{3}{4} – \frac{1}{2}$$?
4. What is $$\frac{5}{6} – \frac{1}{3}$$?
5. What is $$\frac{1}{2} + \frac{1}{4}$$?
6. What is $$\frac{3}{8} + \frac{1}{4}$$?
7. What is $$\frac{1}{2} – \frac{1}{3}$$?
8. What is $$\frac{4}{5} – \frac{1}{5}$$?
9. What is $$\frac{2}{3} + \frac{1}{6}$$?
10. What is $$\frac{3}{5} – \frac{2}{10}$$?
11. What is $$\frac{5}{8} – \frac{1}{4}$$?
12. What is $$\frac{1}{2} + \frac{1}{8}$$?
13. What is $$\frac{2}{5} + \frac{3}{10}$$?
14. What is $$\frac{3}{6} – \frac{1}{3}$$?
15. What is $$\frac{1}{5} + \frac{2}{5}$$?
16. What is $$\frac{2}{7} + \frac{3}{21}$$?
17. What is $$\frac{3}{10} + \frac{1}{5}$$?
18. What is $$\frac{4}{12} – \frac{1}{4}$$?
19. What is $$\frac{2}{8} + \frac{3}{4}$$?
20. What is $$\frac{7}{10} – \frac{2}{5}$$?

Hard Level (20 Questions)

1. What is $$\frac{3}{4} + \frac{1}{6}$$?
2. What is $$\frac{5}{12} – \frac{1}{4}$$?
3. What is $$\frac{7}{10} + \frac{3}{5}$$?
4. What is $$\frac{1}{3} + \frac{1}{5}$$?
5. What is $$\frac{2}{9} – \frac{1}{3}$$?
6. What is $$\frac{5}{8} + \frac{1}{2}$$?
7. What is $$\frac{7}{12} – \frac{1}{3}$$?
8. What is $$\frac{4}{5} + \frac{1}{10}$$?
9. What is $$\frac{3}{8} + \frac{1}{3}$$?
10. What is $$\frac{5}{6} – \frac{1}{2}$$?
11. What is $$\frac{2}{5} + \frac{1}{15}$$?
12. What is $$\frac{5}{9} – \frac{2}{3}$$?
13. What is $$\frac{1}{2} + \frac{2}{9}$$?
14. What is $$\frac{3}{10} – \frac{1}{5}$$?
15. What is $$\frac{4}{7} + \frac{2}{21}$$?
16. What is $$\frac{7}{8} – \frac{3}{16}$$?
17. What is $$\frac{2}{3} + \frac{1}{4}$$?
18. What is $$\frac{4}{9} – \frac{1}{3}$$?
19. What is $$\frac{8}{12} – \frac{2}{4}$$?
20. What is $$\frac{3}{5} + \frac{2}{15}$$?

Answers

Easy Level Answers

1. $$\frac{1}{2}$$
2. $$\frac{2}{4}$$ or $$\frac{1}{2}$$
3. $$\frac{2}{3}$$
4. $$\frac{3}{5}$$
5. $$\frac{1}{8}$$
6. $$\frac{2}{6}$$ or $$\frac{1}{3}$$
7. $$\frac{4}{4}$$ or $$1$$
8. $$\frac{1}{3}$$
9. $$\frac{3}{5}$$
10. $$\frac{2}{8}$$ or $$\frac{1}{4}$$
11. $$\frac{5}{10}$$ or $$\frac{1}{2}$$
12. $$\frac{2}{4}$$ or $$\frac{1}{2}$$
13. $$\frac{4}{5}$$
14. $$0$$ or $$\frac{0}{1}$$
15. $$\frac{5}{6}$$
16. $$\frac{1}{4}$$
17. $$\frac{2}{9}$$
18. $$\frac{5}{10}$$ or $$\frac{1}{2}$$
19. $$\frac{2}{5}$$
20. $$\frac{2}{7}$$

Medium Level Answers

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

Hard Level Answers

1. $$\frac{11}{12}$$
2. $$\frac{1}{3}$$
3. $$\frac{7}{10}$$
4. $$\frac{8}{15}$$
5. $$\frac{1}{9}$$
6. $$\frac{7}{8}$$
7. $$\frac{5}{12}$$
8. $$\frac{1}{2}$$
9. $$\frac{31}{240}$$
10. $$\frac{1}{3}$$
11. $$\frac{7}{15}$$
12. $$\frac{1}{15}$$
13. $$\frac{25}{18}$$
14. $$\frac{1}{10}$$
15. $$\frac{10}{21}$$
16. $$\frac{5}{16}$$
17. $$\frac{11}{12}$$
18. $$\frac{1}{9}$$
19. $$\frac{0}{1}$$
20. $$\frac{13}{15}$$