Add and Subtract Fractions
Adding and subtracting fractions means combining or taking away parts of a whole — and it only works when the parts are the same size. In Year 5 (ACARA v9), students add and subtract fractions with the same denominator (like 1/5 + 2/5) and with related denominators, where one denominator is a multiple of the other (like 1/2 + 1/4). The key idea: you can only add or subtract the top numbers (numerators) once the bottom numbers (denominators) match, because the denominator names the size of each piece. When the denominators do not match, you rename one fraction as an equivalent fraction so the pieces are the same size, then add or subtract.
Worked examples
Same denominator: 1/5 + 2/5.
The denominators already match (fifths). Add the numerators: 1 + 2 = 3. Keep the denominator the same.
Answer: 3/5
Same denominator, subtraction: 5/8 - 2/8.
The pieces are the same size (eighths). Subtract the numerators: 5 - 2 = 3. Keep the denominator.
Answer: 3/8
Related denominators: 1/2 + 1/4.
Quarters are related to halves — 1/2 is the same as 2/4. Rename it, then add: 2/4 + 1/4 = 3/4.
Answer: 3/4
Real-world, related denominators: a recipe needs 3/4 cup of flour and you have already added 1/2 cup. How much more do you need?
Rename 1/2 as 2/4 so both are quarters. Subtract: 3/4 - 2/4 = 1/4.
Answer: 1/4 cup more
Tips
- •Match the pieces before you add. You can only add or subtract fractions when the denominators are the same — same-sized pieces are the whole trick.
- •For related denominators, rename the easier fraction. In 1/2 + 1/8, change 1/2 into 4/8 because 8 is a multiple of 2 — then just add the numerators.
- •Common mistake to watch for: children often add the denominators too, writing 1/5 + 2/5 = 3/10. Remind them the denominator names the size of the piece and does not change — only the count on top is added.
- •Use real amounts. Cups of flour, slices of pizza or lengths of ribbon make 'rename then add' something a child can see and check.