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Grade 5 (age 10-11)

grade 5 Fraction Multiplication & Division

Fraction Multiplication & Division

Multiplying fractions means multiplying numerators together and denominators together. Taking one third of half a cake is that same idea: a part of a part. Dividing flips the divisor and multiplies, which is why counting how many quarter-meter pieces fit in a two-thirds-meter ribbon works. Slide the numerators and denominators and the area model and the length bars build each answer.

Multiplication — Area Model

🟩 Multiplication is the 'overlap area'
①Divide a rectangle horizontally and vertically into a grid
②Color rows for one fraction, columns for the other
③The overlap is the product!
2
3
3
4

Division — How Many Fit?

📏 Division asks 'how many groups fit'
①How many 3/4 m pieces fit in 2/3 m of ribbon? The picture uses the two fractions from the sliders above (first screen: 2/3 ÷ 3/4)
②Count how many divisor lengths fit in the total
③Multiply by a number less than 1 and the product can shrink; divide by a number less than 1 and the quotient can grow
↔️ Same two fractions
The second numerator and denominator above are the divisor. Move those sliders to change this picture.

Summary

Fraction Multiplication
ab × cd = a×cb×d
Multiply numerators, multiply denominators
Fraction Division
ab ÷ cd = ab × dc
Multiply by the reciprocal (flipped fraction)
🎯 Key Points
①Multiplication: numerators × numerators
②Division: flip and multiply
③A factor less than 1 can make the product smaller
④A divisor less than 1 can make the quotient larger
⑤Do not forget to simplify the answer

Examples and Unit Test

Example 1
Calculate 2/3 × 3/4 (with simplifying).
1
Multiply numerators and denominators: (2×3)/(3×4) = 6/12.
2
Reduce 6/12 by the GCD 6 → 1/2.
▸ 12
Multiplication is numerator × numerator, denominator × denominator; then simplify.
Example 2
Calculate 2/3 ÷ 1/4.
1
Flip the divisor (reciprocal) and multiply: 2/3 × 4/1.
2
(2×4)/(3×1) = 8/3.
▸ 83
Division means flip and multiply (multiply by the reciprocal).
Unit Test
What is the value of 1/2 × 4/5?
①58
②25
③410
④47
▸ ② 25
1
(1×4)/(2×5) = 4/10.
2
Reduce 4/10 by the GCD 2 → 2/5.
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Reduction & Common Denominator
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Decimal Multiplication & Division