Equal fractions, two wholes

In a hall, one third of the boys is equal to one fifth of the girls. There are 48 children in the hall altogether. How many boys are there? Try it first. Pause if you like. One third of the boys is equal to one fifth of the girls, so those two amounts are the same size. That shared amount is 1 unit. One third of the boys is 1 unit, so the boys are 3 blue units. One fifth of the girls is that same unit, so the girls are 5 blue units. Look at 1 unit of the boys, and 1 unit of the girls. A dashed line down through both bars marks where each of them ends. They end at the same place, so they're exactly the same size. The same unit builds both bars — 3 units of boys, and 5 units of girls. Now put the boys and the girls together. Altogether that's the 48 children. Count the units: 8 of them, all the same size. So 8 units is 48. There are 8 equal units, so we share the 48 between them. 1 unit is 48 divided by 8. That's 6. Every unit is 6 children — the same 6 in each one. The question asks for the boys. The boys are 3 units, and each unit is 6. 3 times 6 is 18. So there are 18 boys. One third of the boys and one fifth of the girls are the same unit. That unit is 6 children. When a fraction of one whole equals a fraction of another, that equal part is one unit for both.