6-5 One-Step Division Equations

Property

A real-world problem can be modeled by a division equation of the form $\frac{x}{a} = b$. In this equation, $x$ represents the total amount being divided, $a$ is the number of equal groups, and $b$ is the amount in each group.

Examples

• Maria and her two friends share a bag of candies equally. If each person gets 8 candies, what was the total number of candies in the bag? Let $c$ be the total number of candies. The equation is $\frac{c}{3} = 8$.
• A rectangular field is divided into 5 equal sections. If the area of each section is 30 square meters, what is the total area of the field? Let $A$ be the total area. The equation is $\frac{A}{5} = 30$.

Explanation

To write a division equation, first identify the unknown quantity and assign it a variable. This variable often represents the total amount that is being shared or divided. Then, determine the number of equal groups the total is being divided into and the amount in each group to form your equation.

Property

Inverse operations are mathematical operations that undo each other. Multiplication is the inverse operation of division.
If a variable $x$ is divided by a number $a$ (where $a \neq 0$), multiplying by $a$ will undo the division and isolate $x$:

Examples

• In the expression $\frac{x}{5}$, the variable $x$ is being divided by $5$. To undo this division, you multiply by $5$: