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Solve one-step division equations

A one-step division equation represents an unknown quantity divided by a known nonzero number, such as x/a=bx/a=b, and is solved by applying the inverse operation: multiplying both sides by aa, so x=abx=ab. The reasoning applies to rational numbers, including fractions and decimals, uses equality-preserving operations, and includes checking the solution by substitution; equations with a variable in the divisor or multiple operations are outside this scope.

Detailed Explanation: Solve one-step division equations

In an equation such as

xa=b,\frac{x}{a}=b,

the variable xx is being divided by aa. To undo division, use the inverse operation: multiply both sides by aa. Because you do the same operation to both sides, the equation stays balanced.

Example: Solve

x4=32\frac{x}{4}=\frac{3}{2}

  1. Multiply both sides by 44:

4(x4)=4(32)4\left(\frac{x}{4}\right)=4\left(\frac{3}{2}\right)

  1. Simplify. On the left, 44 and 44 cancel. On the right:

x=4â‹…32=6x=4\cdot\frac{3}{2}=6

  1. Check the solution by substituting 66 for xx in the original equation:

64=32\frac{6}{4}=\frac{3}{2}

This is true, so the solution is

x=6\boxed{x=6}

To solve a one-step division equation, multiply both sides by the nonzero number that divides the variable, then check your answer by substitution.

Learn by doing: Solve one-step division equations

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    One-Step Equation - Multiplication/Division - Solve

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