Topics › KS3 › Number

Equivalent fractions

eqf-01 Present from here

Which fraction is equivalent to $\dfrac{2}{3}$?

Option A: $\dfrac{4}{5}$

Option B: $\dfrac{2}{6}$

Option C: $\dfrac{4}{3}$

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

Answer and misconceptions

Option A: $\dfrac{4}{5}$ ✗
Adds the same number to top and bottomAdds 2 to the numerator and denominator, which changes the value.

Option B: $\dfrac{2}{6}$ ✗
Multiplies only the denominatorDoubles the bottom but not the top, which halves the fraction.

Option C: $\dfrac{4}{3}$ ✗
Multiplies only the numeratorDoubles the top but not the bottom, which doubles the fraction.

Option D: $\dfrac{4}{6}$ ✓ Correct
eqf-02 Present from here

Write $\dfrac{12}{18}$ in its simplest form.

Option A: $\dfrac{2}{3}$

Option B: $\dfrac{6}{9}$

Option C: $\dfrac{2}{18}$

Option D: $\dfrac{3}{2}$

Answer and misconceptions

Option A: $\dfrac{2}{3}$ ✓ Correct

Option B: $\dfrac{6}{9}$ ✗
Stops before the simplest formDivides by 2 once but does not check for more common factors.

Option C: $\dfrac{2}{18}$ ✗
Simplifies only the numeratorDivides 12 by 6 but leaves 18 unchanged.

Option D: $\dfrac{3}{2}$ ✗
Writes the simplified fraction upside downPuts 18 / 6 on top and 12 / 6 on the bottom.
eqf-03 Present from here

$\dfrac{3}{5} = \dfrac{?}{20}$. What is the missing number?

Option A: $18$

Option B: $4$

Option C: $12$

Option D: $60$

Answer and misconceptions

Option A: $18$ ✗
Adds the same amount to top and bottomSees 5 + 15 = 20 so adds 15 to 3.

Option B: $4$ ✗
Gives the scale factor as the answerFinds 20 / 5 = 4 but forgets to multiply the numerator by it.

Option C: $12$ ✓ Correct

Option D: $60$ ✗
Multiplies the numerator by the new denominatorWorks out 3 x 20 instead of 3 x 4.
eqf-04 Present from here

Which fraction is equivalent to $\dfrac{15}{25}$?

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

Option B: $\dfrac{3}{5}$

Option C: $\dfrac{5}{15}$

Option D: $\dfrac{3}{25}$

Answer and misconceptions

Option A: $\dfrac{1}{2}$ ✗
Cancels matching digitsCrosses out the 5 in 15 and 25, leaving 1/2.

Option B: $\dfrac{3}{5}$ ✓ Correct

Option C: $\dfrac{5}{15}$ ✗
Subtracts the same number from top and bottomTakes 10 from both, which changes the value.

Option D: $\dfrac{3}{25}$ ✗
Simplifies only the numeratorDivides 15 by 5 but leaves the denominator unchanged.
eqf-05 Present from here

Which improper fraction is equal to $2\frac{3}{4}$?

Option A: $\dfrac{6}{4}$

Option B: $\dfrac{5}{4}$

Option C: $\dfrac{23}{4}$

Option D: $\dfrac{11}{4}$

Answer and misconceptions

Option A: $\dfrac{6}{4}$ ✗
Multiplies the whole number by the numeratorWorks out 2 x 3 = 6 instead of 2 x 4 + 3.

Option B: $\dfrac{5}{4}$ ✗
Adds the whole number to the numeratorWorks out 2 + 3 = 5, forgetting each whole is 4 quarters.

Option C: $\dfrac{23}{4}$ ✗
Writes the whole number and numerator side by sideJoins the digits 2 and 3 to make 23.

Option D: $\dfrac{11}{4}$ ✓ Correct
eqf-06 Present from here

Which fraction is exactly halfway between $\dfrac{1}{3}$ and $\dfrac{1}{2}$?

Option A: $\dfrac{2}{5}$

Option B: $\dfrac{5}{6}$

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

Option D: $\dfrac{1}{12}$

Answer and misconceptions

Option A: $\dfrac{2}{5}$ ✗
Adds the numerators and adds the denominatorsWorks out $\frac{1+1}{3+2}$. This gives a fraction between the two, but not halfway: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{2} = \frac{6}{12}$, so halfway is $\frac{5}{12}$.

Option B: $\dfrac{5}{6}$ ✗
Adds the fractions but does not halveWorks out $\frac{1}{3} + \frac{1}{2} = \frac{5}{6}$, which is the total, not the midpoint.

Option C: $\dfrac{5}{12}$ ✓ Correct

Option D: $\dfrac{1}{12}$ ✗
Finds the difference instead of the midpointWorks out $\frac{1}{2} - \frac{1}{3} = \frac{1}{12}$, the gap between the fractions.