Same Math › Grade 5 › Area model for fraction multiplication
How does the area model for multiplying fractions work?
Kids shade one fraction across a square and the other fraction down it. The part where the shading overlaps is the answer. For 2/3 × 3/4, the overlap is 6 of 12 boxes, or 6/12.
- Shade 3/4 of the columns (blue).
- Shade 2/3 of the rows (green).
- The overlap is 6 of 12 boxes: 2/3 × 3/4 = 6/12 = 1/2
Why schools teach it
It explains the multiply-across rule
Fifth graders find areas of rectangles with fraction sides and show that it matches multiplying the fractions (5.NF.B.4). The grid makes the rule visible: 3 rows × 4 columns makes 12 boxes (the bottom number), and 2 × 3 overlap boxes (the top number).
It also shows why the answer is smaller than both fractions: you're taking part of a part. That surprises kids who expect multiplying to make things bigger.
At the kitchen table
What to say, and what to skip
Say this
How many boxes is the whole square split into?
That's the new denominator.How many boxes are shaded twice?
That's the numerator.Is the answer bigger or smaller than 3/4? Why?
Can you simplify it?
6/12 is 1/2.
Skip this
Just multiply across.
That's where 5th grade ends up, but the model explains it first.- Shading both fractions the same direction.One goes across, one goes down, or there's no overlap to read.
Multiplying always makes bigger numbers.
Not with fractions less than 1.
See it in action
Solving 1/2 × 2/5
Split a square into 5 columns, shade 2
2/5Split it into 2 rows, shade 1
1/2Count the overlap out of all the boxes
2 of 10: 1/2 × 2/5 = 2/10 = 1/5
Half of two fifths is one fifth, which the picture shows directly.
Free practice sheet
Make a fraction multiplication sheet
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Parents also ask
Why is the answer smaller?
You're taking a fraction of a fraction, like half of three quarters. A part of a part is smaller.
Does the model work for mixed numbers?
Yes, with more than one square. Most classes start with fractions less than 1.
Do kids still learn to multiply across?
Yes. The model explains the rule, then kids use the rule.
How is this related to the area model for whole numbers?
Same idea: multiplying sides to find an area, just with fraction sides.