Writing & Solving Multiplication Equations with One Variable

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• 0:01 Multiplication Equations
• 1:21 Solving Them
• 2:38 Example 1
• 3:45 Example 2
• 4:27 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 will know the components that go into a complete multiplication equation. You will also learn the steps that are needed to solve a multiplication equation.

Multiplication Equations

In this video lesson, we talk about multiplication equations, how they are written and how to solve them. Multiplication equations are the equations that use the multiplication operation. These equations are seen not only in math tests and quizzes, but also in everyday life and work. For example, we come across multiplication equations when we calculate how many hours we have worked in a week to see if our paycheck is correct. So, what does a multiplication equation look like? Our multiplication equation to find out how many hours we have worked could look like this: 12x = 480.

This is a complete multiplication equation because on one side of our equal sign we have the numbers that are being multiplied together, a 12 and an unknown number x, and on the other side of the equal sign we have what they are equal to, 480. In this multiplication equation, the 12 is our hourly rate - what we are getting paid per hour. The 480 is the amount we were paid. The x represents the number of hours we have worked. Solving this problem for the variable allows us to find out how many hours we have worked to earn 480. We can use this equation as a check to see whether we are getting paid for all the hours that we have worked.

Solving Them

Let's see how we can solve this type of equation. We are solving for an unknown number, our variable. We need to isolate our variable to get it by itself. We need to detach any numbers that are attached to it. To detach numbers and other things from our variable, we need to perform inverse operations. In our case, we see that we have a 12 being multiplied with our x.

The inverse operation to multiplication is division. So, we need to divide both sides of our equation by 12. We remember that whatever we do to one side of an equation, we need to do to the other. You can remember this by looking at the equal sign. The equal sign tells you that everything that is done on one side must be the same as the other side. Both sides must be equal. If you divide on one side, you have to divide on the other side. So, dividing our equation by 12 on both sides, we get: 12x / 12 = 480 / 12. This turns into x = 40. This tells us that we got paid for 40 hours of work. If our records also show that we have worked 40 hours that week, then we have been paid correctly!

Let's look at a couple of examples to get a better feel for the process.

Example 1

Write a multiplication equation that shows five times an unknown number is equal to one-hundred-fifteen, and then solve it for the unknown number.

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