Adding and subtracting capacities

In your book, Maths Mela (Chapter 8), Sam and Tina fill petrol in their bikes. Tina buys 2 l 500 ml of petrol. Sam buys 2 l 800 ml more than Tina. How much petrol does Sam buy?

Sam adds like quantities: litres with litres, millilitres with millilitres. 2 l + 2 l = 4 l. 500 ml + 800 ml = 1,300 ml. But 1,000 ml make 1 l, so 1,300 ml = 1 l 300 ml. Put the extra 1 l with the litres: 4 l + 1 l 300 ml = 5 l 300 ml.

Tina changes everything into millilitres: 2,500 ml + 2,800 ml = 5,300 ml, and 5,300 ml = 5 l 300 ml. Both ways give the same answer.

After refuelling, Sam's fuel gauge reads 9 l. How much fuel was in his bike before? We need 9 l − 5 l 300 ml. 9 l has no millilitres to take 300 ml from, so change 1 l into 1,000 ml: 9 l = 8 l 1,000 ml. Now 1,000 ml − 300 ml = 700 ml and 8 l − 5 l = 3 l. So the bike had 3 l 700 ml before. In ml: 9,000 ml − 5,300 ml = 3,700 ml.

This is just like adding and subtracting weights: carry 1 l when the millilitres reach 1,000 ml, and change 1 l into 1,000 ml when there are not enough millilitres to take away.