Writing & Solving Subtraction Word Problems with One Variable

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  • 0:03 A Subtraction Word Problem
  • 1:14 Writing the Algebraic…
  • 2:15 Solve the Problem
  • 3:06 Example
  • 5:00 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

You will be able to solve subtraction word problems after watching this video lesson. Learn how to take your word problem from words into an algebraic expression that you can solve.

A Subtraction Word Problem

In this video lesson, we take a look at solving subtraction word problems. A subtraction word problem is a math problem written in words that includes the subtraction operation. In order to solve such a problem, you first need to write the algebraic expression that is described in the problem. Your algebraic expression is a mathematical statement written in numbers and symbols. Once you have your algebraic expression, you can go on to solve it to find your answer.

You will come across these subtraction word problems not only on your math tests and quizzes but also when dealing with problems and situations in everyday life. For example, this could be a problem that you might come across:

Sally is at the pet store looking to buy pet fish for her fish tank at home. She is told that her fish tank can only hold so many fish. Sally decides to purchase 13 fish. The pet store helper tells her that after she takes away these 13 fish from the amount her fish tank can hold, she will be left with another 18 fish that she can purchase. What is the total number of small fish that Sally can have in her aquarium?

Writing the Algebraic Expression

Before you can solve Sally's problem, you need to convert the problem into an algebraic expression. To do this, you need to fully understand your problem. You need to know what's going on and what the problem is asking of you. In a subtraction word problem, you know that you will have something being subtracted from something else equaling something else. So, one of your tasks is to figure out what is being subtracted from what and what it is equal to.

For Sally's problem, you can see that you can solve this problem by subtracting the 13 small fish from the total number of fish she can keep in her aquarium. This will equal 18. Because this total number of fish she can keep in her aquarium is the unknown number you are looking for, you can represent this with an x. So, you have your x subtracted by 13 equaling 18. The resulting algebraic expression is x - 13 = 18.

Solving the Problem

Now that you have your algebraic expression, how do you go about solving it? What you need to do is isolate your variable to get it by itself. To do this, you need to perform inverse operations to detach everything that the variable is attached to. If it is being added to, then you subtract. If something is being subtracted from it, you add. Whatever you do to one side, you also do to the other side.

For Sally's problem, your variable is being subtracted by a 13. To detach this 13 from the variable, you need to add 13 to both sides of the equation. You get x - 13 + 13 = 18 + 13. Evaluating this, you get x = 31. This means that Sally's aquarium can hold a total of 31 small fish, and you are done.


Let's look at another example:

Joseph started his day with $40 in his pocket. At the end of the day, he counts his money and sees that he has $5 left. How much did he spend throughout the day?

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