Multiplying decimals through fractions

Arshad buys 5 pens at ₹9.5 each — 9 rupees and 50 paise. What should he pay? Multiplication, as always for repeated equal amounts.

One way is to add: 9.5 + 9.5 + 9.5 + 9.5 + 9.5 = 47.5. The other is to convert to fractions, which is the method that will generalise.

9.5 is 95/10, and 5 is 5/1. So the cost is 5/1 × 95/10. Multiply numerators and multiply denominators: (5 × 95)/(1 × 10) = 475/10 = 47.5. Five pens cost ₹47.5.

Now two decimals. A car travels 12.5 km per litre of petrol. How far on 7.5 litres? The distance is 12.5 × 7.5.

Convert both: 125/10 × 75/10 = (125 × 75)/(10 × 10) = 9375/100 = 93.75. The car covers 93.75 km — and note that nothing new was needed, only fraction multiplication you already had.

A longer one. Ajay's school is 827 m from home, and he walks there and back 6 days a week. How far in a week, in kilometres? Each way is 827 m = 0.827 km.

In a day he walks 0.827 × 2 = 827/1000 × 2 = 1654/1000 = 1.654 km. In a week, 1.654 × 6 = 1654/1000 × 6 = 9924/1000 = 9.924 km. And a rectangle of sides 5.7 cm and 13.3 cm has area 57/10 × 133/10 = 7581/100 = 75.81 sq cm.