Topics › KS3 › Number

Multiplying & dividing fractions

mdf-01 Present from here

Work out $\frac{2}{3} \times \frac{4}{5}$

Option A: $\frac{6}{8}$

Option B: $\frac{10}{12}$

Option C: $\frac{8}{15}$

Option D: $\frac{8}{8}$

Answer and misconceptions

Option A: $\frac{6}{8}$ ✗
Adds numerators and adds denominatorsHas done 2 + 4 over 3 + 5, treating × like an addition rule.

Option B: $\frac{10}{12}$ ✗
Flips the second fraction when multiplyingHas used the division method: 2/3 × 5/4 = 10/12.

Option C: $\frac{8}{15}$ ✓ Correct

Option D: $\frac{8}{8}$ ✗
Multiplies numerators but adds denominatorsHas done 2 × 4 = 8 on top but 3 + 5 = 8 on the bottom.
mdf-02 Present from here

Work out $\frac{3}{4} \times 8$

Option A: $\frac{3}{32}$

Option B: $24$

Option C: $\frac{24}{32}$

Option D: $6$

Answer and misconceptions

Option A: $\frac{3}{32}$ ✗
Multiplies the denominator by the whole numberHas done 3 over 4 × 8, making the fraction smaller instead of larger.

Option B: $24$ ✗
Multiplies by the numerator, ignores the denominatorHas done 3 × 8 = 24 and forgotten to divide by 4.

Option C: $\frac{24}{32}$ ✗
Multiplies top and bottom by the whole numberHas made an equivalent fraction (still worth 3/4) instead of multiplying.

Option D: $6$ ✓ Correct
mdf-03 Present from here

Which calculation gives the same answer as $\frac{4}{5} \div \frac{2}{3}$?

Option A: $\frac{5}{4} \times \frac{2}{3}$

Option B: $\frac{4}{5} \times \frac{3}{2}$

Option C: $\frac{5}{4} \times \frac{3}{2}$

Option D: $\frac{4}{5} \times \frac{2}{3}$

Answer and misconceptions

Option A: $\frac{5}{4} \times \frac{2}{3}$ ✗
Flips the first fraction instead of the secondKnows to use a reciprocal but takes it of the dividend, not the divisor.

Option B: $\frac{4}{5} \times \frac{3}{2}$ ✓ Correct

Option C: $\frac{5}{4} \times \frac{3}{2}$ ✗
Flips both fractionsInverts every fraction before changing ÷ to ×.

Option D: $\frac{4}{5} \times \frac{2}{3}$ ✗
Changes ÷ to × without flippingRemembers "change the sign" but not "flip the second fraction".
mdf-04 Present from here

Work out $\frac{1}{2} \div 4$

Option A: $\frac{1}{8}$

Option B: $2$

Option C: $8$

Option D: $\frac{4}{8}$

Answer and misconceptions

Option A: $\frac{1}{8}$ ✓ Correct

Option B: $2$ ✗
Multiplies by the whole number instead of dividingHas done 1/2 × 4 = 4/2 = 2.

Option C: $8$ ✗
Reverses the order of the divisionHas worked out 4 ÷ 1/2 = 8 instead of 1/2 ÷ 4.

Option D: $\frac{4}{8}$ ✗
Makes an equivalent fraction instead of dividingHas multiplied top and bottom by 4; 4/8 is still a half.
mdf-05 Present from here

Work out $1\frac{1}{2} \times 1\frac{1}{3}$

Option A: $1\frac{1}{6}$

Option B: $\frac{9}{8}$

Option C: $2$

Option D: $\frac{4}{6}$

Answer and misconceptions

Option A: $1\frac{1}{6}$ ✗
Multiplies whole parts and fraction parts separatelyHas done 1 × 1 = 1 and 1/2 × 1/3 = 1/6, missing the cross terms.

Option B: $\frac{9}{8}$ ✗
Uses the division method (flips the second fraction)Has converted to 3/2 and 4/3 correctly, then done 3/2 × 3/4 = 9/8.

Option C: $2$ ✓ Correct

Option D: $\frac{4}{6}$ ✗
Converts mixed numbers by adding whole to numeratorHas written 1 1/2 as 2/2 and 1 1/3 as 2/3, giving 4/6.