Adding and subtracting fractions with different denominators
To add or subtract fractions with different denominators, we first change them so they use the same denominator, which lets us compare them properly. This helps in everyday situations such as working with recipes, measurements, and lengths. Jump to the questions
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Topic guide
What this worksheet practises
This worksheet focuses on adding and subtracting fractions when the denominators (the bottom numbers) are different. This is a crucial non-calculator skill that relies heavily on your knowledge of equivalent fractions and common multiples.
Key method
You cannot add or subtract fractions unless their denominators are exactly the same. To solve these problems, follow these steps:
- Find a common denominator. This is a common multiple of the two current denominators (often the lowest common multiple is easiest).
- Convert both fractions into equivalent fractions using this new common denominator. Remember, whatever you multiply the bottom by, you must also multiply the top by.
- Add or subtract the numerators (the top numbers) while keeping the common denominator the same.
- Simplify your final answer if possible.
Worked examples
Example 1: Addition
Calculate 1/3 + 2/5
Step 1: The denominators are 3 and 5. A common multiple is 15.
Step 2: Convert 1/3. Multiply top and bottom by 5 to get 5/15.
Step 3: Convert 2/5. Multiply top and bottom by 3 to get 6/15.
Step 4: Add the numerators. 5/15 + 6/15 = 11/15. This cannot be simplified further.
Example 2: Subtraction
Calculate 3/4 − 1/6
Step 1: The denominators are 4 and 6. A common multiple is 12.
Step 2: Convert 3/4. Multiply top and bottom by 3 to get 9/12.
Step 3: Convert 1/6. Multiply top and bottom by 2 to get 2/12.
Step 4: Subtract the numerators. 9/12 − 2/12 = 7/12. This cannot be simplified further.
Common mistakes to avoid
The most frequent mistake is simply adding the top numbers together and adding the bottom numbers together (e.g., mistakenly thinking 1/2 + 1/3 = 2/5). Always ensure the denominators are the same before adding or subtracting.