Multiplication Word Problems Worksheet: Product Unknown

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Reteach: Multiplicative Comparison Product Unknown

In some multiplicative comparison word problems, you are given the number of items in one set, and you are given the “multiplier” amount. The multiplier amount tells you how many times bigger (or more) the second set is than the first. “Bigger” can also mean “longer,” or “wider,” 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 multiplier are called “Product Unknown” comparisons, because the total is the part that is unknown.

In order to answer the question you are being asked, you need to multiply the number in the set by the multiplier to find the product.



Reteach: Guided Practice

Let’s look at a “Product Unknown” problem:

Jennifer can solve three multiplication problems in one minute. Peter can solve multiplication problems four times as fast as Jennifer. How many multiplication problems can Peter solve in one minute?

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

The words “as fast as” tell us that we are comparing. Jennifer’s 3 problems tells us that there are 3 problems in one set. “Four times” tells us that the multiplier is 4.

To solve the problem we have to multiply 3 x 4. Since 3 x 4 = 12, Peter can solve 12 problems in one minute.

This answer is reasonable because the problem tells us Peter is four times faster than Jennifer, so he should solve 4 times as many problems as her in one minute. 12 is 4 times more than 3, so this answer makes sense.

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Independent Practice: Multiplicative Comparison Product Unknown

Solve each problem below by identifying the number in one set, and the multiplier. Multiply the number in one set by the multiplier.  Go back to the problem to make sure you have answered the question being asked, and that your answer makes sense.

A rabbit can go two feet in one jump. A kangaroo can go five times as far as a rabbit. How far can a kangaroo go in one jump?

The number in one set is   2  . The multiplier is   5  .

  2   x   5   =   10  

The kangaroo can go   10   feet in one jump. Since you are multiplying a whole number by a whole number, the distance the kangaroo can go should be larger than the distance the rabbit can go. Is your answer reasonable?


Amanda grew two plants for the science fair. The first plant was eight centimeters tall. The second plant was three times as tall. How tall was the second plant?

The number in one set is   8  . The multiplier is   3  .

  8   x   3   =   24  

The second plant was   24   centimeters tall. Since you are multiplying a whole number by a whole number, the height of the second plant should be more than the height of the first plant. Is your answer reasonable?


Chris can go 10 miles per hour on his bicycle. Jill can go seven times that fast on her motorcycle. How fast can Jill go on her motorcycle?

The number in one set is   10  . The multiplier is   7  .

  10   x   7   =   70  

Jill can go   70   miles per hour on her motorcycle. Since you are multiplying a whole number by a whole number, the speed Jill can go on her motorcycle should be faster than the speed Chris can go on his bicycle. 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



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