Grade 5 (age 10-11)

Fraction Multiplication & Division

Multiplying fractions means multiplying numerators together and denominators together, like taking one third of half a cake. 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 to watch 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!

1st numerator2

1st denominator3

2nd numerator3

2nd denominator4

Division — How Many Fit?

📏 Division asks 'how many groups fit'

①You have 2/3 m of ribbon. How many 1/4 m pieces?

②Count how many divisor lengths fit in the total

③That is fraction division!

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

③Result of multiplication can be smaller than the original

④Result of division can be larger than the original

⑤Don't forget to simplify the answer!

Examples and Unit Test

Example 1

Calculate 2/3 × 3/4 (with simplifying).

Multiply numerators and denominators: (2×3)/(3×4) = 6/12.

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.

Flip the divisor (reciprocal) and multiply: 2/3 × 4/1.

(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

(1×4)/(2×5) = 4/10.

Reduce 4/10 by the GCD 2 → 2/5.

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Simplify & Common Denominator

Mixed Number Add/Sub