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.
Sid has 3 balloons.
Sam has twice as many balloons as Sid.
So, the number of balloons with Sam = 2 × 3 = 6
A problem based on multiplicative comparison can have:
A statement that compares two sets of items.
It leads to a multiplication equation.
The equation could have a symbol or a letter standing for the unknown quantity.
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:
Here is an example of how to solve a multiplicative comparison word problem using comparison bar models.