Topics › KS3 › Number

Adding & subtracting fractions

asf-01 Present from here

Work out $\dfrac{1}{3} + \dfrac{1}{4}$

Option A: $\dfrac{7}{12}$

Option B: $\dfrac{2}{7}$

Option C: $\dfrac{2}{12}$

Option D: $\dfrac{1}{7}$

Answer and misconceptions

Option A: $\dfrac{7}{12}$ ✓ Correct

Option B: $\dfrac{2}{7}$ ✗
Adds numerators and adds denominatorsWorks out (1 + 1)/(3 + 4).

Option C: $\dfrac{2}{12}$ ✗
Changes denominators but not numeratorsUses 12 as the common denominator but keeps both numerators as 1.

Option D: $\dfrac{1}{7}$ ✗
Adds the denominators and keeps the numeratorThinks the numerator stays as 1 because both fractions have 1 on top.
asf-02 Present from here

Work out $\dfrac{2}{9} + \dfrac{5}{9}$

Option A: $\dfrac{7}{18}$

Option B: $\dfrac{10}{81}$

Option C: $\dfrac{7}{9}$

Option D: $\dfrac{7}{81}$

Answer and misconceptions

Option A: $\dfrac{7}{18}$ ✗
Adds the denominators as well as the numeratorsDoes not see that ninths plus ninths are still ninths.

Option B: $\dfrac{10}{81}$ ✗
Multiplies the fractions instead of addingMultiplies tops and bottoms as if the sign were x.

Option C: $\dfrac{7}{9}$ ✓ Correct

Option D: $\dfrac{7}{81}$ ✗
Multiplies denominators to get a common denominatorAdds the numerators but multiplies 9 x 9, though they already match.
asf-03 Present from here

Work out $\dfrac{3}{4} - \dfrac{1}{3}$

Option A: $\dfrac{2}{1}$

Option B: $\dfrac{5}{12}$

Option C: $\dfrac{2}{12}$

Option D: $\dfrac{3}{12}$

Answer and misconceptions

Option A: $\dfrac{2}{1}$ ✗
Subtracts numerators and subtracts denominatorsWorks out (3 - 1)/(4 - 3).

Option B: $\dfrac{5}{12}$ ✓ Correct

Option C: $\dfrac{2}{12}$ ✗
Changes denominators but not numeratorsUses twelfths but subtracts the original numerators 3 - 1.

Option D: $\dfrac{3}{12}$ ✗
Multiplies the fractions instead of subtractingWorks out (3 x 1)/(4 x 3).
asf-04 Present from here

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

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

Option B: $3\frac{2}{6}$

Option C: $3\frac{1}{6}$

Option D: $3\frac{5}{6}$

Answer and misconceptions

Option A: $3\frac{2}{5}$ ✗
Adds numerators and adds denominatorsAdds the wholes correctly, then works out (1 + 1)/(2 + 3).

Option B: $3\frac{2}{6}$ ✗
Changes denominators but not numeratorsUses sixths but keeps both numerators as 1.

Option C: $3\frac{1}{6}$ ✗
Multiplies the fraction parts instead of addingAdds the wholes but works out 1/2 x 1/3.

Option D: $3\frac{5}{6}$ ✓ Correct
asf-05 Present from here

Work out $3\frac{1}{4} - 1\frac{3}{4}$

Option A: $2\frac{1}{2}$

Option B: $1\frac{8}{4}$

Option C: $1\frac{1}{2}$

Option D: $0$

Answer and misconceptions

Option A: $2\frac{1}{2}$ ✗
Subtracts the smaller numerator from the largerDoes 3 - 1 for the wholes and 3/4 - 1/4 for the fractions, swapping the order.

Option B: $1\frac{8}{4}$ ✗
Exchanges a whole for 10 parts, not 4 quartersBorrows as in column subtraction: 1/4 becomes 11/4, then 11/4 - 3/4 = 8/4.

Option C: $1\frac{1}{2}$ ✓ Correct

Option D: $0$ ✗
Adds the whole number to the numeratorTurns both mixed numbers into 4/4 when converting to improper fractions.