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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

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: 12*x* = 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.

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: 12*x* / 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.

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.

After reading this problem, we see that on one side of our equal sign we need to have five times an unknown number and on the other side we need to have 115. Using an *x* to represent our unknown number, we write our multiplication equation as 5*x* = 115.

Now we can go ahead and solve this for our variable. We see that our variable is being multiplied by a five. We need to perform the inverse operation to separate this five from our variable. The inverse operation to multiplication is division. So, we divide both sides of our equation by five: 5*x* / 5 = 115 / 5. Evaluating this, we find an answer of *x* = 23. Our complete answer is the equation 5*x* = 115, with *x* = 23.

Write a multiplication equation that shows nine times an unknown number equaling ninety, and then solve it for the unknown number.

Reading through the problem, we write a multiplication equation of 9*x* = 90. We have our nine times an unknown number on one side with the *x* representing the unknown number, and we have it equaling 90. To solve this problem we need to divide both sides by nine: 9*x* / 9 = 90 / 9. Evaluating this, we get *x* = 10. Our complete answer is 9*x* = 90, with *x* = 10, and we are done.

Let's review what we've learned. **Multiplication equations** are the equations that use the multiplication operation. A complete multiplication equation will have the numbers that are being multiplied together on one side of the equal sign, and what they are equal to on the other side of the equal sign. To solve these equations, we perform inverse operations to detach whatever numbers are attached to our variable. For multiplication equations, this inverse operation is most often division. Whatever we divide on one side, we also divide on the other.

When you are finished, you should be able to write and solve a multiplication equation with one variable.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Inverse Operations in Math: Definition & Examples 4:50
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