A fraction of a fraction

Now both numbers are fractions. The tortoise walks 1/4 km an hour. How far in half an hour? 1/2 × 1/4 km.

Draw it. Let a square stand for 1 whole. Shade 1/4 of it: one of four equal strips. That's the distance in 1 hour.

In half an hour it goes half of that. Split the shaded strip into 2 equal parts and keep one.

Now look at the whole square: the cuts have made 8 equal pieces, and one is shaded. So it is 1/8 of the whole. The tortoise walks 1/8 km in half an hour: 1/2 × 1/4 = 1/8.

Harder: a faster tortoise does 2/5 km an hour. How far in 3/4 of an hour? That's 3/4 × 2/5. In steps:

• in 1/4 hour: split the 2/5 into 4 equal parts → 2/20
• in 3/4 hour: 3 times that → 6/20, which is 3/10

So 3/4 × 2/5 = 6/20 = 3/10.