In the previous sections, you used actions being done in a problem situation to identify the operation being described and write equations to represent the problem. In this section, you will think about equations and problems the other way. You will look at an equation, and write a problem that could be solved using that equation.

Use what you have learned so far about identifying operations and writing equations from word problems to match each equation below with the operation that is being performed and a problem that the equation could be used to represent. Drag each problem to the correct place. You may use each problem more than once.

Use the interactive to answer the questions that follow.

• If you have an equation with addition, what actions could you use to write your word problem?

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  Check Your Answer

  Addition means to combine two quantities, so use situations that require you to combine a given number and a variable.

• If you have an equation with subtraction, what actions could you use to write your word problem?

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  Check Your Answer

  Subtraction means to remove one quantity from another or to compare the sizes of two quantities by calculating the difference, so use situations that require you to remove a number from a variable (or a variable from a number) or to determine how much more one quantity is than the other.

• If you have an equation with multiplication, what actions could you use to write your word problem?

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  Check Your Answer

  Multiplication means to use repeated addition or to use an area model such as rows and columns, so use situations that require you to repeatedly add the same quantity or to use groupings such as rows and columns to calculate the number of items in the groupings.

• If you have an equation with division, what actions could you use to write your word problem?

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  Check Your Answer

  Division means to use repeated subtraction or to group a collection of items evenly, so use situations that require you to subtract the same quantity or to distribute a number of items evenly among a certain number of groups.

Practice

Write a problem situation for each of the equations below.

1. x + 16 = 50.2

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   Addition means to combine two quantities, in this case, an unknown value, x, and 16, to generate a total of 50.2.
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   Jeanine has 16 feet of ribbon. She needs a 50.2 feet of ribbon to complete a project. How many more feet of ribbon, x, does Jeanine need?
2. 2 over 3 2 3 x = 18

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   Multiplication means to use repeated addition, think in terms of rows and columns, or calculate a scaled portion of a quantity.
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   Michaela surveyed her math class and determined that 2 over 3 2 3 of her classmates like pepperoni pizza. If 18 students said they like pepperoni pizza, how many students, x, are in Michaela’s math class?
3. 81 ÷ x = 12

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   Division is a grouping operation. The dividend is evenly distributed among the number of groups in the divisor so that there are the same number of items in each group, represented by the quotient.
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   Monica needs to save a total of $81 over the next 12 months. How much money, x, does Monica need to save each month?
4. x − 31 over 4 1 4 = 15

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   Subtraction means to remove a quantity or to calculate how much larger one quantity is than the other.
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   Ethan has some landscaping timbers that he can use to build a flowerbed. After using 31 over 4 1 4 yards of landscaping timbers, he has 15 yards remaining. How many yards of landscaping timbers, x, did Ethan begin with?