Year 6 Maths: Adding Fractions

Introduction to Adding Fractions

Hello Year 6! Today, we’re going to learn about adding fractions. Fractions are parts of a whole, and sometimes we need to add them together. Don’t worry; it’s easier than it sounds!

Understanding Fractions

Before we dive into adding fractions, let’s remember what a fraction is. 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

• The numerator is 3 (we have 3 parts).
• The denominator is 4 (the whole is divided into 4 equal parts).

Adding Fractions: Key Rules

When adding fractions, there are a few important rules to remember:

1. Same Denominators: If the fractions you are adding have the same denominator, just add the numerators and keep the denominator the same.
   • Example: $$\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4}$$
2. Different Denominators: If the fractions have different denominators, you need to find a common denominator before adding.
   • Example: To add $$\frac{1}{3}$$ and $$\frac{1}{4}$$ :
     • The common denominator of 3 and 4 is 12.
     • Convert the fractions:
       • $$\frac{1}{3} = \frac{4}{12}$$ (because $$1 \times 4 = 4$$ and $$3 \times 4 = 12$$ )
       • $$\frac{1}{4} = \frac{3}{12}$$ (because $$1 \times 3 = 3$$ and $$4 \times 3 = 12$$ )
     • Now add them: $$\frac{4}{12} + \frac{3}{12} = \frac{4+3}{12} = \frac{7}{12}$$
3. Simplifying: Sometimes after adding, you might need to simplify the fraction (make it smaller).
   • Example: $$\frac{4}{8}$$ can be simplified to $$\frac{1}{2}$$ .

Tips and Tricks

• Always check if the fractions have the same denominator first.
• Use a number line to visualize the fractions if you’re feeling stuck.
• Practice makes perfect! The more you work with fractions, the easier it gets.

Questions

Easy Level (1 mark each)

1. What is $$\frac{1}{2} + \frac{1}{2}$$ ?
2. What is $$\frac{2}{5} + \frac{1}{5}$$ ?
3. What is $$\frac{3}{8} + \frac{2}{8}$$ ?
4. What is $$\frac{4}{10} + \frac{5}{10}$$ ?
5. What is $$\frac{1}{3} + \frac{1}{3}$$ ?
6. What is $$\frac{3}{6} + \frac{2}{6}$$ ?
7. What is $$\frac{5}{12} + \frac{2}{12}$$ ?
8. What is $$\frac{1}{4} + \frac{1}{4}$$ ?
9. What is $$\frac{2}{9} + \frac{3}{9}$$ ?
10. What is $$\frac{1}{6} + \frac{4}{6}$$ ?

Medium Level (2 marks each)

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

Hard Level (3 marks each)

21. What is $$\frac{1}{3} + \frac{1}{2}$$ ?
22. What is $$\frac{5}{6} + \frac{1}{3}$$ ?
23. What is $$\frac{2}{5} + \frac{3}{10}$$ ?
24. What is $$\frac{4}{9} + \frac{2}{3}$$ ?
25. What is $$\frac{1}{4} + \frac{3}{8}$$ ?
26. What is $$\frac{2}{7} + \frac{1}{14}$$ ?
27. What is $$\frac{5}{12} + \frac{1}{4}$$ ?
28. What is $$\frac{1}{5} + \frac{3}{10}$$ ?
29. What is $$\frac{2}{3} + \frac{5}{9}$$ ?
30. What is $$\frac{3}{8} + \frac{1}{2}$$ ?

Answers

Easy Level Answers

1. $$\frac{2}{2} = 1$$
2. $$\frac{3}{5}$$
3. $$\frac{5}{8}$$
4. $$\frac{9}{10}$$
5. $$\frac{2}{3}$$
6. $$\frac{5}{6}$$
7. $$\frac{7}{12}$$
8. $$\frac{2}{4} = \frac{1}{2}$$
9. $$\frac{5}{9}$$
10. $$\frac{5}{6}$$

Medium Level Answers

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

Hard Level Answers

21. $$\frac{5}{6}$$
22. $$\frac{7}{6} = \frac{1}{6}$$
23. $$\frac{7}{10}$$
24. $$\frac{10}{9} = \frac{1}{9}$$
25. $$\frac{5}{8}$$
26. $$\frac{3}{14}$$
27. $$\frac{8}{12} = \frac{2}{3}$$
28. $$\frac{5}{10} = \frac{1}{2}$$
29. $$\frac{7}{9}$$
30. $$\frac{7}{8}$$

Great job today, Year 6! Keep practising adding fractions, and soon it will become second nature.