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Writing & Solving Division Word Problems with One Variable

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  • 0:01 A Division Word Problem
  • 0:48 Writing the Algebraic…
  • 1:49 Solving the Problem
  • 2:42 Example
  • 3:58 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.

After watching this video lesson, you should be able to solve word problems that involve the division operator. Learn how to write your math problem using an algebraic expression and then solve it.

A Division Word Problem

In this lesson, we'll talk about solving division word problems. A division word problem is a math problem that involves the division operator written in words. We actually come across these problems not just in our math classes but also in everyday life. Scientists and engineers will employ more complicated division word problems in their jobs. Here, we'll take a look at some simpler problems. For example, we might come across a word problem such as this when we are trying to figure out how much food to buy for a party:

Jacob is having a party for his friends. He is inviting nine of his friends, so there will be a total of ten people. How many pizza slices does Jacob need to buy so that after dividing the slices evenly among ten people, each person will get three slices?

Writing the Algebraic Expression

How do we go about solving this word problem? Well, we need to write an algebraic expression for our problem. An algebraic expression is a mathematical expression written in numbers and symbols. To write an algebraic expression from our problem, we need to understand fully what our problem is saying and what it is asking us to find. Sometimes it helps to visualize our problem.

If we visualize our problem, we would see Jacob buying pizza slices. We also see the group of ten people. We see the bunch of pizza slices, and then we see that each person gets three pizza slices. We don't know the number of pizza slices in the bunch. That is the number we are trying to find. We understand that the problem is asking us to divide our bunch of pizza slices by the number of people in the group, by ten. This should equal three. From this information, we write x / 10 = 3 for our algebraic expression. We used the variable x to represent the bunch of pizza slices since that is the number we want to find.

Solving the Problem

Now that we have our algebraic expression, we can go on and solve our problem by solving the algebraic expression for the variable. To do this, we want to isolate the variable - to get the variable by itself. To do that we need to perform the inverse operation of any numbers that are attached to our variable.

Looking at our algebraic expression, we see that we have division by ten. The inverse operation of division is multiplication, so we need to multiply both sides by ten. Remember that for algebraic expressions that have an equals sign in them, whatever we do to one side, we must also do to the other. So, we get (x / 10) * 10 = 3 * 10. This simplifies to x = 30. Our answer is 30. This means that Jacob needs 30 pizza slices for 10 people to each get 3 slices.

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