6-4 One-Step Multiplication Equations

Property

To write a multiplication equation from a word problem, identify the unknown quantity and assign it a variable ($x$). The problem will describe a relationship where a known quantity (the coefficient, $a$) is multiplied by the unknown quantity to equal a total amount ($b$). The general form is $ax = b$.

Examples

Maria earns 8 dollars per hour. If she earned a total of 56 dollars, how many hours did she work?

• Let $h$ be the hours worked. The equation is $8h = 56$.

A recipe calls for $\frac{3}{4}$ of a cup of flour for each batch of cookies. If you used 6 cups of flour in total, how many batches did you make?

• Let $b$ be the number of batches. The equation is $\frac{3}{4}b = 6$.

Explanation

To translate a real-world problem into a multiplication equation, first identify the quantity you need to find and represent it with a variable. Next, determine the constant factor or rate that is being multiplied by this variable. Finally, set their product equal to the total amount given in the problem. This equation models the situation and can be solved to find the value of the unknown.

Property

Inverse operations are mathematical operations that undo each other. Division is the inverse operation of multiplication.

If a variable $x$ is multiplied by a number $a$ (where $a \neq 0$), dividing by $a$ will undo the multiplication and isolate $x$: