Dividing with fractions and tape diagrams

To share a fraction equally among some people, cut that fraction into that many equal parts. Take 1/2 and cut it into 3 equal pieces. Six of these pieces would fill the whole, so each piece is 1/6. We write 1/2 ÷ 3 = 1/6. When the top number divides exactly we can share it directly: 3/4 is 3 quarters, and sharing 3 quarters between 3 people gives 1 quarter each, so 3/4 ÷ 3 = 1/4. When it does not divide exactly, first rename the fraction: 2/3 = 4/6, and 4 sixths shared between 4 gives 1/6 each. The quotient is smaller than the fraction we started with. We can always check by multiplying: 1/6 × 4 = 4/6 = 2/3.