Writing & Solving Division Equations with One Variable

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  • 0:03 Division Equations
  • 0:41 Writing a Division Equation
  • 1:58 Solving a Division Equation
  • 2:54 Example Problem
  • 4:25 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.

In this video lesson, you will learn the proper format of a division equation. Learn what components are needed for a complete division equation. Also learn what steps you need to take to solve these division equations.

Division Equations

In this video lesson, we talk about division equations. Division equations are mathematical equations that involve the division operator. Division equations are useful not just in math class but also in our everyday life. For example, if we wanted to share a bag of candies evenly with our friends, we can use division to find our answer. Say we had 100 candies and 4 friends. To find out how many candies each person gets, we would divide 100 by 4. We find that our answer is 25, meaning that each friend gets 25 candies.

Writing a Division Equation

If we wanted to write a complete division equation to represent our problem, we would need an equals sign and something on both sides of the equals sign. One side will show our division and the other side will show what the division equals. For our problem, our job is to find what the division equals. We can represent this with a variable such as x. So, our complete division equation then will look like: 100 / 4 = x. We have an equals sign and things on both sides of it. One side has the division operator and the numbers that are being divided.

In math tests and quizzes, we might be asked to write a division equation to represent a problem. For example, we might be asked to write a division equation that shows a number divided by five is equal to ten. To answer this problem, we read what it wants us to write and then we write it accordingly, making sure that our division equation is complete. We make sure that we have an equals sign and we have the appropriate things being equal to each other.

In this problem, we have the division on one side. The division is between an unknown number that we will call x and the number 5. This is equal to 10. We write x / 5 = 10.

Solving a Division Equation

The problem could continue and ask us to solve the division equation that we have written. If this is the case, then we would need to isolate our variable to solve for it. Whenever we see a variable, it is most likely the problem wants us to find what it is equal to. To isolate our variable, we need to perform the inverse operation to any number that it is attached to.

For our problem, x / 5 = 10, we see that we have a division by 5 attached to our variable. The inverse operation here is multiplication. So, to detach the 5 from our variable, we need to multiply by 5 on both sides of the equation. Since we are dealing with equations, whatever we do to one side, we also must do to the other. So, we have (x / 5) * 5 = 10 * 5. This evaluates to x = 50. Our answer is 50, and we are done.

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