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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.

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.

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.

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.

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.

Let's look at one more example.

*Write a division equation that shows twenty-five divided by a number is equal to five, and then solve it.*

This problem is asking us to write a division equation and then to solve it. Reading through the problem, we see that our division is between 25 and an unknown number that we will call *x*. This is equal to 5. We write the division equation as 25 / *x* = 5.

Now we need to solve this equation. This equation is rather interesting because the variable is in the bottom. We want the variable in the top. To move it, we need to multiply by *x* on both sides of the equation. We get (25 / *x*) * *x* = 5 * *x*, which turns into 25 = 5 * *x*.

Now, to isolate our variable, we need to perform the inverse operation. We see a multiplication by 5 with our variable. The inverse operation here is division. So, we need to divide by 5 on both sides. We get 25 / 5 = (5 * *x*) / 5. This turns into 5 = *x*. Our answer is 5. Our complete answer is the division equation 25 / *x* = 5 along with the answer of *x* = 5.

Let's review what we've learned.

**Division equations** are mathematical equations that involve the division operator. A complete division equation includes an equals sign. One side will have the division operator and the numbers that are being divided. The other side shows what the division is equal to. To solve these problems, we perform inverse operations to isolate our variable. If the variable is in the bottom, we multiply by the variable on both sides of the equation to move the variable to the top. We then continue with performing inverse operations to isolate the variable.

After you've reviewed this video lesson, you will be able to:

- Define division equations
- Write and solve division equations

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

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