# One-step multiplication & division equations

Learn to solve equations like "4x = 20" or "y/3 = 7".

Based on our understanding of the balance beam model, we know that to keep a true equation, we always have to do the same thing to both sides of an equation.

But how do we know

*what to do*to both sides of the equation?# Multiplication and division are *inverse operations*

Here's an example of how division is the inverse operation of multiplication:

If we start with 7, multiply by 3, then divide by 3, we get back to 7:

Here's an example of how multiplication is the inverse operation of division:

If we start with 8, divide by 4, then multiply by 4, we get back to 8:

# Solving a *multiplication* equation using inverse operations

Let's think about how we can solve for in the following equation:

We want to get by itself on the left hand side of the equation. So, what can we do to

*undo*multiplying by 6?We should

*divide*by 6 because the inverse operation of multiplication is division!Here's how dividing by 6 on each side looks:

### Let's check our work.

It's always a good idea to check our solution in the original equation to make sure we didn't make any mistakes:

$\begin{aligned} 6t &= 54 \\
6 \cdot \greenD9 &\stackrel{\large?}{=} 54\\
54 &= 54 \end{aligned}$

Yes, is a solution!

# Solving a *division* equation using inverse operations

Now, let's try to solve a slightly different type of equation:

We want to get by itself on the left hand side of the equation. So, what can we do to cancel out

*dividing*by 5?We can

*multiply*by 5 because the inverse operation of division is multiplication!Here's how multiplying by 5 on each side looks:

### Let's check our work.

$\begin{aligned} \dfrac x5 &= 7 \\\\
\dfrac{\greenD{35}}{5} &\stackrel{\large?}{=} 7\\\\
7 &= 7 \end{aligned}$

Yes, is a solution!

# Summary of how to solve multiplication and division equations

Awesome! We just solved a multiplication equation and a division equation. Let's summarize what we did:

Type of equation | Example | First step |
---|---|---|

Multiplication equation | Divide each side by six. | |

Division equation | Multiply each side by five. |