# Multiplication Word Problems Worksheet: Multiplier Unknown

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## Reteach: Multiplicative Comparison Multiplier Unknown

 In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the number of items in the second set, which is a multiple of the first set. The "multiplier" amount is the part that is 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.

## Reteach: Guided Practice

 Let’s look at a “Multiplier Unknown” problem: 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.

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## Independent Practice: Multiplicative Comparison Multiplier Unknown

Solve each problem below by identifying the number in one set, and the number in the second set, which is a multiple of the first. Divide the second set by the first set. Go back to the problem to make sure you have answered the question being asked, and that your answer makes sense.

The plane goes 700 miles an hour. The car goes 50 miles an hour. How many times faster than the car is the plane?

The number in one set is   700  . The number in the second set is   50  .

700   ÷   50   =   14

The plane is   14   times faster than the car. If you multiply the speed of the car by your answer, you should get the speed of the plane. Is your answer reasonable?

Eric has 9 video games. Bryan has 54 video games. How many times more video games does Bryan have than Eric?

The number in one set is   54  . The number in the second set is   9  .

54   ÷   9   =   6

Bryan has   6   times as many video games as Eric. If you multiply the number of video games that Eric has by your answer, you should get the number of video games that Bryan has. Is your answer reasonable?

Shannon is 37 inches tall. Her teenaged brother, Rick, is 74 inches tall. How many times as tall as Shannon is Rick?

The number in one set is   74  . The number in the second set is   37  .

74   ÷   37   =   2

Rick is   2   times as tall as Shannon. If you multiply the number of inches in Shannon's height by your answer, you should get the number of inches in Rick's height. Is your answer reasonable?

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## Related Resources

The various resources listed below are aligned to the same standard, (4OA02) taken from the CCSM (Common Core Standards For Mathematics) as the Word problems Worksheet shown above.

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

### Worksheet

#### Multiplication and Division

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Use the four operations with whole numbers to solve problems