# Multiplicative Comparison – Definition with Examples

## What is Multiplicative Comparison?

A multiplicative comparison involves comparing two quantities such that when one is multiplied by a specified number, the other is produced.

For example, Sam has twice as many balloons as Sid.

Problems involving multiplicative comparison are generally word problems that can be solved by creating a multiplication equation.

A problem based on multiplicative comparison can have:

1. A statement that compares two sets of items.
2. It leads to a multiplication equation.
3. The equation could have a symbol or a letter standing for the unknown quantity.

Example:

A building is 18 feet tall. The building is 3 times Jerry’s height. How tall is Jerry?

Let Jerry’s height be h feet.

The height of the building is 18 feet, which is 3 times Jerry’s height.

Therefore, 18 = 3 × h

(Think: What multiplied by 3 is 18?)

We know: 18 = 3 × 6

Therefore, the h, standing for Jerry’s height in the equation 18 = 3 × h, must be 6.

So, Jerry is 6 feet tall.

Problems involving multiplicative comparison usually have phrases like:

• Times as many (Jake has 5 times as many stamps as Ben.)
• Times as much (My sister earns 3 times as much as I do.)
• Times as long (A yard is 3 times as long as a foot.)
• Times the height (The building is 4 times the height of the tree.)

Here is an example of how to solve a multiplicative comparison word problem using comparison bar models.