Subtracting fractions with the same denominator

1Summary 重點摘要

Same denominator: keep the denominator, just subtract the numerators.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Check the denominatorsBefore subtracting, check the denominators as with addition: in 68 − 28 both are 8, so subtract directly. Equal denominators mean equal pieces, and only then can counts of pieces be taken away. Checking first is step one of all fraction arithmetic.
2. Step 2: Subtract the numeratorsSubtract the top numbers: 6 − 2 = 4, the numerator of the new fraction. Holding 6 parts and using 2 leaves 4 parts, and that is exactly what the subtraction counts; write 4 above the line first.
3. Step 3: Keep the denominatorWrite the denominator 8 unchanged, giving 48. The denominator is never subtracted and never changes: 40 and 46 are both wrong, because the size of each part stayed the same throughout. The bottom number is always the original denominator.
4. Step 4: Understand whySix eighths take away two eighths leaves four eighths. Each part keeps its size; only the number of parts changes, so the denominator stays and the numerators subtract. It is the same idea as like-denominator addition, run backwards.
5. Step 5: Simplify if possibleAfter subtracting, check for simplifying: 48 with top and bottom divided by 4 gives 12. Simplifying makes the answer clearest to read. Not every problem needs it, but every problem deserves the check.
6. Step 6: Subtracting to zero37 − 37 = 07 = 0: all three parts are used and none is left, which is zero. A numerator of zero makes the whole fraction zero; 07 and plain 0 are both correct, and plain 0 is usually tidier.
7. Step 7: Word-problem formatWord problems need three parts: the expression, the working and the answer. A cup holds 68 litre and you drink 28 litre: write 68 − 28 = 48 = 12, then answer: 12 litre is left, remembering the unit at the end.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Same denominator first
• Subtract numerators, keep denominator
• Check if the result can be simplified
• The minuend must come first — never swap
• Subtracting everything gives 0, e.g. 37 − 37 = 0