Adding and Subtracting Fractions

What You Will Learn

• Add fractions with the same denominator.
• Subtract fractions with the same denominator.
• Find a common denominator for unlike fractions.
• Simplify a fraction answer when possible.
• Solve simple word problems involving addition and subtraction.

1. The Important Rule

A fraction describes part of a whole. When adding or subtracting fractions, the denominator tells us the size of the parts.

Never add or subtract the denominators. The denominator describes the size of the pieces, not how many pieces you have.

2. Add Fractions with the Same Denominator

When denominators match, keep the denominator and add the numerators.

Worked example: 2/7 + 3/7

1. The denominators are both 7, so the pieces are the same size.
2. Add the numerators: 2 + 3 = 5.
3. Keep the denominator: 7.

Answer: 5/7.

Another example: 3/10 + 4/10

Add 3 + 4 to get 7, and keep the denominator 10. The answer is 7/10.

3. Subtract Fractions with the Same Denominator

When denominators match, keep the denominator and subtract the numerators.

Worked example: 6/8 − 2/8

1. The denominators are both 8.
2. Subtract the numerators: 6 − 2 = 4.
3. Keep the denominator: 8.
4. Simplify 4/8 by dividing top and bottom by 4.

Answer: 4/8 = 1/2.

4. Add Fractions with Different Denominators

Fractions with different denominators have different-sized parts. Convert them into equivalent fractions with a common denominator before adding.

Worked example: 1/3 + 1/4

1. Find a common denominator for 3 and 4. The lowest common denominator is 12.
2. Convert 1/3 into twelfths: multiply top and bottom by 4 to get 4/12.
3. Convert 1/4 into twelfths: multiply top and bottom by 3 to get 3/12.
4. Add: 4/12 + 3/12 = 7/12.

Answer: 7/12.

Another example: 2/5 + 1/10

A common denominator is 10. Convert 2/5 to 4/10. Then 4/10 + 1/10 = 5/10 = 1/2.

5. Subtract Fractions with Different Denominators

The same common-denominator method works for subtraction.

Worked example: 3/4 − 1/6

1. A common denominator for 4 and 6 is 12.
2. Convert 3/4 to 9/12.
3. Convert 1/6 to 2/12.
4. Subtract: 9/12 − 2/12 = 7/12.

Answer: 7/12.

Another example: 5/6 − 1/3

Convert 1/3 to 2/6. Then 5/6 − 2/6 = 3/6 = 1/2.

6. A Reliable Four-Step Method

1. Check the denominators. Are they the same or different?
2. Find a common denominator if they are different.
3. Work with the numerators. Add or subtract them and keep the common denominator.
4. Simplify the answer if the numerator and denominator have a common factor.

7. Solve Everyday Problems

Example 1: A bottle of water

Sam drinks 1/4 of a bottle in the morning and 2/4 in the afternoon. What fraction of the bottle does Sam drink altogether?

1/4 + 2/4 = 3/4. Sam drinks 3/4 of the bottle.

Example 2: A ribbon

A ribbon is 5/6 metre long. A piece measuring 1/3 metre is cut off. How much remains?

Convert 1/3 to 2/6. Then 5/6 − 2/6 = 3/6 = 1/2. Half a metre remains.

Example 3: Reading time

Mia reads for 1/2 hour on Monday and 1/4 hour on Tuesday. How long does she read in total?

Convert 1/2 to 2/4. Then 2/4 + 1/4 = 3/4. She reads for 3/4 of an hour.

8. Common Mistakes to Avoid

9. Practice Exercises

Try these questions before revealing the answers.

1. 2/9 + 4/9
2. 7/10 − 3/10
3. 1/2 + 1/5
4. 3/4 − 1/8
5. 2/3 + 1/6
6. 5/6 − 1/4
7. A cake has 3/8 eaten at lunch and 2/8 eaten at dinner. What fraction is eaten altogether?
8. A jug contains 7/8 litre of juice. If 1/4 litre is poured out, how much remains?

10. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

11. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

12. Lesson Summary

• For matching denominators, add or subtract the numerators and keep the denominator.
• For different denominators, first find a common denominator.
• Convert each fraction into an equivalent fraction.
• Complete the addition or subtraction, then simplify the result.
• Check whether the answer is reasonable.