Multiplication Word Problems Worksheet: Multiplier Unknown

The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also be “longer,” or “wider,” or “older,” or “taller” in problems involving measurement, or “faster” in problems involving a rate of speed.

These problems in which you know both the number in one set, and the number in the second set are called “Multiplier Unknown” comparisons, because the multiplier is the part that is unknown.

In order to answer the question you are being asked, you need to use the inverse (opposite) operation of multiplication: division. This kind of division is called “measurement” division.

Scott is 10 years old. His little sister, Kate, is only two years old. How many times older than Kate is Scott?

Start by clarifying what you understand, and what you are being asked to solve.

The words “older than” tell us that we are comparing. Scott’s age, 10, tells us that there are 10 years in the second set.  Kate’s age, 2, tells us that there are 2 years in one set. The part we are missing is the multiplier.

To solve the problem we have to use the inverse operation of multiplication: division. We divide Scott’s age, 10, by Kate’s age, 2.  Since 10 ÷  2 = 5, Scott is five times older than Kate.

This answer is reasonable because the problem tells us that Scott is older than Kate. We know that the second set is a multiple of the first set, so we can think, “how many sets of 2 will equal 10?”  2 x 5 = 10, so this answer makes sense.