Multiplying Fractions — the Area Model (Grade 5)
Multiplying fractions answers "what is a part of a part?" — for example, 1/2 of 1/3. 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.
Understanding multiplying fractions
Multiplying fractions answers "what is a part of a part?" — for example, 1/2 of 1/3. 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.
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.
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. (Visual: a 2×3 grid, 1 row and 1 column shaded; the overlap is 1 of 6 cells.)
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.
Try a few
1/2 × 1/2
2/5 × 3/4
3/4 × 2/3
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