Dividing by a fraction is new at P6, and it has one rule: keep the first fraction, then multiply by the reciprocal of the second — turn it upside down. Think of 6 ÷ 2/3 as asking how many two-thirds fit inside 6, which is why the answer, 9, is bigger than what you started with. Dividing a fraction by a whole number works the other way: the pieces get smaller, so the denominator grows.
Worked example
Problem Work out 3/4 ÷ 1/2.
Dividing asks how many halves fit inside 3/4.
Keep the first fraction and multiply by the reciprocal of the second: 3/4 ÷ 1/2 = 3/4 × 2/1.
Multiply across: 3 × 2 = 6 and 4 × 1 = 4, giving 6/4 = 1 1/2.
Watch out Flip the SECOND fraction only. Flipping both, or dividing numerator by numerator, is the usual slip.