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Adding and subtracting fractions with unlike denominators
Can do: Finds a common denominator and adds or subtracts, including with mixed numbers.
Why it matters
This is the gateway skill of Grade 5 maths. It fails when equivalent fractions aren't solid — the fix is almost always further back.
What it looks like when it's wobbly
Adds numerators and denominators, or finds a common denominator and forgets to convert the numerators too.
⏱️ Two-minute check
"1/3 + 1/4? And 2 1/2 − 3/4?"
Solid looks like: 7/12 and 1 3/4, with the conversions visible.
The full activity for this topic · 20 minutes
Find the Common Ground
- 1Draw both fractions on identical rectangles split differently. You can't add them as drawn — that's the point.
- 2Redraw both with the same number of pieces and add them.
- 3Connect it to the numbers: multiply both parts of each fraction, not just the bottom.
- 4Do a set of five, checking each answer is sensible — 1/3 + 1/4 must be less than 1.
- 5Use a real one: two recipes to combine, or two pieces of timber to add.
If it's too hard
Denominators where one is a multiple of the other — halves and quarters.
If it's too easy
Mixed numbers with regrouping: 3 1/4 − 1 2/3.
Say this
"You changed the bottom — did you change the top by the same amount? It has to be the same fraction."