A fraction of an hour

Now the other way round. Aaron walks 3 km in an hour. How far in 1/5 of an hour? Still multiply: 1/5 × 3.

What does it mean? In 1/5 of an hour he covers 1/5 of an hour's distance: split 3 km into 5 equal parts and take one. That's 3/5 km. So 1/5 × 3 = 3/5.

Notice: multiplying by a fraction less than 1 gave an answer smaller than 3. That makes sense: he walked for less than an hour.

In 2/5 of an hour? Two steps:

• distance in 1/5 hour = 3/5 km
• 2/5 is twice 1/5, so 2 × 3/5 = 6/5 km

So 2/5 × 3 = 6/5.

Look at what we did with 2/5: we divided by the bottom (5), then multiplied by the top (2). That is how to multiply any whole number by a fraction.

On a bill: 1 hour of internet costs ₹8 (back when phones had only a little data!). What do 1 1/4 hours cost? 1 1/4 = 5/4 hours, so 5/4 × 8 = (5 × 8) ÷ 4 = 40 ÷ 4 = ₹10.