Skill: Solve part-to-whole ratio problems

A part-to-whole ratio tells how the parts compare and gives the total number of equal ratio units.

For a ratio of $a:b$:

1. Add the ratio numbers to find the total number of units:

$$a+b$$

2. Divide the whole amount by the number of units to find the value of one unit.
3. Multiply by the ratio number for each part.

Example

A basket has red and blue apples in a ratio of $2:3$. There are $25$ apples altogether. How many are red and how many are blue?

Step 1: Find the total number of ratio units.

The ratio is $2:3$, so the whole has:

$$2+3=5\text{ units}$$

The ratio numbers describe parts of the whole, not the actual number of apples yet.

Step 2: Find the value of one unit.

There are $25$ apples in $5$ equal units:

$$25\div 5=5$$

So, each ratio unit represents $5$ apples.

Step 3: Find each part.

Red apples:

$$2\times 5=10$$

Blue apples:

$$3\times 5=15$$

Check:

$$10+15=25$$

So, there are 10 red apples and 15 blue apples.