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Adding and Subtracting fractions
Lesson: Adding & Subtracting Fractions
Year 7 — Adding and subtracting fractions with same and different denominators (UK curriculum).
1. When denominators are the same
If the denominators are the same, simply add or subtract the numerators.
Example:
3/8 + 2/8 = 5/8
7/10 - 3/10 = 4/10 = 2/5 (simplify at the end)
2. When denominators are different
We must find a common denominator first.
Step-by-step method
- Find the lowest common denominator (LCM of denominators).
- Convert each fraction to an equivalent fraction with that denominator.
- Add or subtract the numerators.
- Simplify if possible.
Example: 2/3 + 1/4
LCM of 3 and 4 = 12
2/3 = 8/12, 1/4 = 3/12
So, 8/12 + 3/12 = 11/12
Example: 5/6 - 1/8
LCM of 6 and 8 = 24
5/6 = 20/24, 1/8 = 3/24
So, 20/24 - 3/24 = 17/24
3. Mixed number addition and subtraction
Convert mixed numbers into improper fractions first.
Example: 1 1/2 + 2 1/3
1 1/2 = 3/2, 2 1/3 = 7/3
LCM of 2 and 3 = 6
3/2 = 9/6, 7/3 = 14/6
9/6 + 14/6 = 23/6 = 3 5/6
4. Tips for Year 7 learners
- Always simplify your final answer.
- Double-check your equivalent fractions.
- Use common denominators from multiplication tables to speed up.
- For subtraction, ensure the larger fraction is first.
5. Practice
4/9 + 2/93/5 - 1/52/3 + 3/45/12 - 1/61 2/5 + 2 1/3
Answers (teacher)
4/9 + 2/9 = 6/9 = 2/33/5 - 1/5 = 2/5- LCM 12 →
2/3=8/12,3/4=9/12→17/12 = 1 5/12 1/6 = 2/12→5/12 - 2/12 = 3/12 = 1/41 2/5 = 7/5,2 1/3 = 7/3, LCM 15 →21/15 + 35/15 = 56/15 = 3 11/15