Subtracting fractions · Grade 5
In Grade 5 you learn: subtracting fractions with related denominators, subtracting fractions with different denominators, and subtracting mixed numbers.
You can only subtract fractions when the pieces are the same size, so the denominators must match. If they don’t, change them to a common denominator first. With mixed numbers you may need to exchange a whole for fraction pieces.
Key facts
- Same denominator: add or subtract the tops. The bottom stays the same.
- Different denominators: first change both to a common denominator (the least common multiple is easiest). Then add or subtract.
- Never subtract the bottoms: 3/4 − 1/2 is not 2/2.
- When subtracting mixed numbers you may need to exchange a whole: 4 1/5 = 3 6/5.
- Check a subtraction by adding: your answer plus the fraction you took away gives the fraction you started with.
- Simplify the answer at the end.
Worked examples
Example 1
Work out 5/6 − 1/6.
Answer: 2/3
Example 2
Work out 7/9 − 4/9.
Answer: 1/3
Example 3
A jug is 7/10 full of juice. Sam pours out 3/10 of a jug. How full is the jug now?
Answer: 2/5 full
Example 4
Work out 3/4 − 3/8.
Answer: 3/8
Example 5
Work out 4/5 − 1/3.
Answer: 7/15
Example 6
Sipho earns $12,000 a month. He spends 1/4 of it on rent and 1/3 on food. How much is left?
Answer: $5,000
Example 7
Work out 3 1/4 − 1 2/3.
Answer: 1 7/12
Example 8
Work out 5 1/3 − 2 3/4.
Answer: 2 7/12