# 7.10: Single Variable Division Equation

**At Grade**Created by: CK-12

**Practice**Single Variable Division Equations

### Let’s Think About It

The incoming class at tennis camp is large this year. This is a special program that will have 6 people in each class. However, there is a maximum number of 42 classes. The incoming people need to be divided into groups of 6, so that the number of groups is 42. What is the maximum capacity,

In this concept, you will learn to solve single variable division equations.

### Guidance

To solve an equation in which a variable is divided by a number, you use the inverse of division, multiplication, to isolate the variable and solve the equation.

You can multiply both sides of an equation by a number because of the **Multiplication Property of Equality**, which states:

if

This means that if you multiply one side of an equation by a number

Here is an example.

Solve the equation for

First, use the multiplication property of equality, and multiply both sides of the equation by -4 to isolate the variable

Next, separate the fraction and simplify.

The answer is

Here is another example.

Solve for

First, use the multiplication property of equality to multiply both sides of the equation by 1.5.

Next, you separate the fraction and simplify.

### Guided Practice

Three friends evenly split the total cost of the bill for their lunch. The amount each friend paid was $4.25.

- Write a division equation to represent
c , the total cost, in dollars, of the bill for lunch. - Solve the equation to solve for the total cost of the bill.

Consider part *a* first.

First, rephrase the question to help you solve the problem: The total cost,

Then, express this as an equation.

Now consider part *b*.

Solve the equation by using the multiplication property of equality. Multiply both sides of the equation by 3.

Next, rearrange the multiplication of fractions.

Now, simplify and solve.

The answer is that the bill was $12.75.

### Examples

Solve each equation.

#### Example 1

First, use the multiplication property of equality and multiply both sides of the equation by -2.

Next, simplify and solve for

The answer is

#### Example 2

First, use the multiplication property of equality and multiply both sides of the equation by 5.

Next, simplify and solve for

The answer is

#### Example 3

First, use the multiplication property of equality and multiply both sides of the equation by -4.

Next, simplify and solve for

The answer is

### Follow Up

Remember the tennis camp? The incoming students need to be divided into groups of 6, but there can only be 42 classes in total. Can you write a division equation, where

First, translate the language into an equation. Let

Next, use the multiplication property of equality and multiply both sides of the equation by 6.

Then, re-write the multiplication by a fraction and simplify.

The answer is that there can be a maximum number of 252 students in the incoming class.

### Video Review

https://www.youtube.com/watch?v=zBqIH-E3ero&feature=youtu.be

### Explore More

Solve each single variable division equation for the missing value.

x5=2 y7=3 b9=−4 b8=−10 b8=20 - \begin{align*}\frac{x}{-3} =10\end{align*}
- \begin{align*}\frac{y}{18} = -20\end{align*}
- \begin{align*}\frac{a}{-9} = -9\end{align*}
- \begin{align*}\frac{x}{11} = -12\end{align*}
- \begin{align*}\frac{x}{3} = -3\end{align*}
- \begin{align*}\frac{x}{5} = -8\end{align*}
- \begin{align*}\frac{x}{1.3} = 3\end{align*}
- \begin{align*}\frac{x}{2.4} = 4\end{align*}
- \begin{align*}\frac{x}{6} = 1.2\end{align*}
- \begin{align*}\frac{y}{1.5} = 3\end{align*}

### Image Attributions

In this concept, you will learn to solve single variable division equations.

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