Multiplicative comparison - Definition with Examples

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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. 

multiplicative comparison 1

Sid has 3 balloons.

multiplicative comparison 2

Sam has twice as many balloons as Sid.

So, the number of balloons with Sam = 2 × 3 = 6

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.

Example of multiplicative comparison with bar model
 

  Fun Facts

  • Bar models help us understand what operation (addition, subtraction, multiplication, division) should be used to solve the given problem.

  • Any two factors and their product can be read as a comparison statement (5 × 6 = 30: 30 is 5 times as much as 6).

  • In a multiplicative comparison problem, one quantity is always smaller or larger than the other quantity.

 
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