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Grade 5 Math Lab: The Bridge to Algebra FREE
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Multiplying Fractions
Learning Objectives
- Multiply fractions using area models
- Understand multiplication as "of"
- Multiply fractions by whole numbers
- Simplify products
Key Concepts
Fraction × Fraction
Multiply numerators together, multiply denominators together
Area Model
A rectangle where one fraction is the width and one is the height
"Of" means Multiply
2/3 of 3/4 means 2/3 × 3/4
Theory
Multiplying fractions is finding a "fraction of a fraction." The area model shows this beautifully!
**The Area Model:**
To find 2/3 × 3/4:
1. Draw a unit square (1 × 1)
2. Shade 3/4 horizontally (blue layer)
3. Shade 2/3 vertically (yellow layer)
4. The overlap (green) is your answer!
**Count the Overlap:**
- Total squares: 3 × 4 = 12
- Overlapping squares: 2 × 3 = 6
- Answer: 6/12 = 1/2
**The Algorithm:**
(a/b) × (c/d) = (a×c)/(b×d)
2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2
**Why Does the Product Get Smaller?**
When you take a fraction of a fraction, you're taking a part of a part - so the result is smaller than either original fraction!
Examples
1/2 × 1/2
Solution: 1/4 (half of a half is a quarter)
2/3 × 4/5
Solution: (2×4)/(3×5) = 8/15
3/4 × 2/3
Solution: 6/12 = 1/2 (simplify by dividing by 6)
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Knowledge Check
Test your understanding of Translucent Lab!