How to Divide Equations

By Nicole Harms; Updated April 24, 2017
Dividing equations is as simple as mastering a formula.

Division in algebraic equations can be confusing. When you throw x's and n's into an already difficult type of math, then the problem may seem even more difficult. By taking a division problem apart piece by piece, however, you can reduce the complexity of the problem.

Copy your equation on a separate sheet of paper. For the first example, use 3n/5 = 12.

Begin by isolating the variable (n). In this equation, the first thing is to remove the /5. To eliminate division, you do the opposite operation -- which is multiplication. Multiply both sides of the equation by 5. (3n/5) * 5 = 12 * 5. This gives 3n = 60.

Isolate the variable by dividing by 3 on both sides of the equation. (3n/3 = 60/3). This gives n = 20.

Check your answer. (3*20)/5 = 12 is correct.

Solve more complex equations in the same manner. For example, (48x^2 + 4x -70)/(6x -7) = 90. The first goal is to isolate the variable. This requires simplifying the left hand side of the equation.

Factor the numerator and denominator of the equation completely. In this equation, the denominator is already simplified. You need to factor the numerator. The numerator factors into (8x + 10) (6x - 7).

Cancel the common factor. The 6x - 7 on the numerator and the 6x - 7 on the denominator cancel each other. This leaves 8x + 10 = 90. Solve for x by subtracting 10 from both sides and dividing by 8. You end up with x = 10.

Check your answer. (48 * 10^2 + 4 * 10 - 70)/(6 * 10 - 7) = 90. This gives you 4770/53 = 90, which is correct.

Tip

Always factor the equation completely before you begin to isolate the variable. If there is a common factor, factor it out. For instance, 6x + 12 has a common factor of 6. You would need to simplify this to 6(x + 2).

Warning

Never forget to do the same thing to both sides of the equation. If one side is divided by 2, the other side must be divided by 2, as well.

About the Author

Nicole Harms has been writing professionally since 2006, specializing in real estate, finance and travel. When she's not writing, she enjoys traveling and has visited several countries, including Israel, Spain, France and Guam. Harms received a Bachelor of Science in Education from Maranatha Baptist Bible College.