Skill: Interpret multiplication as scaling

Multiplication can mean scaling—changing the size of a quantity by a factor.

• A factor greater than 1 makes the quantity larger.
• A factor between 0 and 1 makes the quantity smaller.
• A factor of 1 leaves the quantity unchanged.

Example

A ribbon is $12$ inches long. You use $\frac{3}{4}$ of it. How many inches do you use?

The phrase “$\frac{3}{4}$ of $12$” means multiply:

$$\frac{3}{4}\times 12$$

Since $\frac{3}{4}$ is between $0$ and $1$, the answer should be smaller than $12$.

To find $\frac{3}{4}$ of $12$:

1. Divide $12$ into $4$ equal parts:

$$12\div 4=3$$

So, $\frac{1}{4}$ of $12$ is $3$.

2. Take $3$ of those equal parts:

$$3\times 3=9$$

Therefore,

$$\frac{3}{4}\times 12=9$$

You use $9$ inches of ribbon. The fraction $\frac{3}{4}$ scaled $12$ down to $9$.