Sharing in a Ratio

Mia and Leo share 24 marbles in the ratio 5 to 3. Think in parts: Mia gets 5 parts and Leo gets 3, so there are 5 + 3 = 8 equal parts in all. Each part is 24 divided by 8, which is 3 marbles. Mia's 5 parts make 15 marbles and Leo's 3 parts make 9.

A shorter way: Mia gets 5 of the 8 parts, so her share is $\frac{5}{8}$ of all the marbles, and a fraction of a number is a product. Use a for her share: $a = 24\cdot \frac{5}{8}$, and on the next line $a = 15$. The ratio 5 to 3 is part to part; the fraction of the whole uses the part to whole ratio, 5 to 8.

Check by adding the shares back: 15 + 9 is 24, the whole amount. The common slip is dividing by one of the ratio numbers instead of the total number of parts. 24 divided by 5 is not even a whole number of marbles, a sign that something went wrong.