Inverse Operation of Division
Multiplication is the inverse operation of division in 6th grade algebra. When a variable x is divided by a number a, you undo that division by multiplying both sides of the equation by a, isolating the variable. For x/5 = 3, multiply both sides by 5 to get x = 15. For y/8 = 4, multiply both sides by 8 to get y = 32. This concept, from Reveal Math, Course 1, Module 6, is the companion to the inverse operation of multiplication and is essential for solving all one-step division equations.
Key Concepts
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 $x$: $$\frac{{x}}{{a}} \cdot a = x$$.
Examples In the expression $\frac{x}{5}$, the variable $x$ is being divided by $5$. To undo this division, you multiply by $5$:.
$$\frac{x}{5}\times 5 = x$$.
Common Questions
What is the inverse operation of division?
The inverse operation of division is multiplication. Multiplying undoes division, so if a variable x is divided by 5, multiplying both sides by 5 isolates x.
How do I solve x/5 = 4 using inverse operations?
Multiply both sides by 5 to undo the division: (x/5) times 5 = 4 times 5, giving x = 20.
How do I solve x/8 = 6?
Multiply both sides by 8: x = 6 times 8 = 48.
Why does multiplying by the denominator isolate the variable?
Division and multiplication are inverse operations that cancel each other. Dividing by 8 then multiplying by 8 returns to the original value, leaving only x on one side.
What is the difference between using inverse operations for multiplication vs. division equations?
For multiplication equations (4x = 20), divide both sides by the coefficient. For division equations (x/5 = 4), multiply both sides by the denominator.
When do 6th graders learn the inverse operation of division?
Module 6 of Reveal Math, Course 1 covers inverse operations for division in the Equations and Inequalities unit.