Multiplying Fractions — the Area Model (Grade 5)
Multiplying fractions answers "what is a part of a part?" — for example, 1/2 of 1/3.
Understanding multiplying fractions
The rule is simple: multiply the tops together for the new top, and the bottoms together for the new bottom. 1/2 × 1/3 = (1×1)/(2×3) = 1/6.
Key Idea
The area model shows why. Draw a rectangle. Shade 1/3 of it going one way (columns) and 1/2 of it going the other way (rows). The little square where the two shadings overlap is the answer — and it's 1 square out of 6, so 1/6. Unlike adding, here you do NOT need a common denominator.
Seeing it in action
Worked example
1/2 × 1/3 = ?
Tops: 1 × 1 = 1. Bottoms: 2 × 3 = 6. → 1/6.
The overlap is 1 cell out of 6.
Worked example 2
2/3 × 3/4 = ?
Tops: 2 × 3 = 6. Bottoms: 3 × 4 = 12. → 6/12 = 1/2.
A common mistake, and the fix
Expecting the product to be bigger, or hunting for a common denominator.
1/2 × 3/4 = 3/8, which is less than both fractions, because taking a fraction of something takes part of it. Multiply the tops and the bottoms straight across; no common denominator is needed.
Try a few
1/2 × 1/2
2/5 × 3/4
3/4 × 2/3
Try it in Numeris.
A short lesson, then practice with feedback on every answer.
Put the reasoning on paper.
Try six fraction, angle, perimeter and area questions with explained answers, for grades 4–6.
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