Skill: Scale quantities down using a ratio

To scale a quantity down, multiply it by a ratio less than $1$. The ratio tells how much of the original amount to keep.

Example

A recipe uses $8$ cups of flour. You want to make only $\frac{3}{4}$ of the recipe. How much flour do you need?

1. Identify the original quantity: $8$ cups.
2. Identify the scale-down ratio: $\frac{3}{4}$.
3. Multiply:

$$8 \times \frac{3}{4}$$

4. Divide $8$ by $4$, then multiply by $3$:

$$8 \times \frac{3}{4} = \left(8 \div 4\right)\times 3 = 2\times 3 = 6$$

You need $6$ cups of flour.

The ratio $\frac{3}{4}$ means the new amount is three out of every four equal parts of the original amount. This is different from subtracting a fixed amount, such as taking away $2$ cups. Scaling keeps the same multiplicative relationship for every quantity in the recipe.