Dividing a Unit Fraction by a Whole Number

1/2 ÷ 3 asks what each gets when half a thing is shared among 3.

Cut the half into three

Each part is a third of a half, which is a sixth of the whole.

The rule this gives

1/2 ÷ 3 = 1/6. Multiply the bottom number by the whole number.

The opposite of the last lesson

Dividing by a fraction grew the answer. Dividing a fraction by a whole shrinks it.

Sharing a small piece among several

1/4 ÷ 3 asks what each person gets when a quarter is shared between 3 people. Cut the quarter into 3 equal parts; each is a twelfth. So 1/4 ÷ 3 = 1/12 — smaller than the quarter, because you are splitting it further.

The opposite of the last lesson

Dividing a whole number by a unit fraction gave a bigger answer. Dividing a unit fraction by a whole number gives a smaller one. Which happens depends entirely on which is the divisor — and thinking about what the division means tells you before you calculate.

Seeing it in a rectangle

Shade a quarter of a rectangle. Now cut the whole rectangle into 3 horizontal strips. The shaded quarter is cut into 3 pieces, and the whole rectangle now has 12 pieces. So each shared piece is one twelfth of the original.

Check by multiplying

1/12 × 3 = 3/12 = 1/4, which returns the amount you shared out. Whenever a fraction division answer feels uncertain, multiply back. It is the same check you have used since Grade 3 and it has never stopped working.