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Skill: Solve one-step division equations

Explanation and Free Practice Resources

A one-step division equation represents an unknown quantity divided by a known, nonzero number, as in x÷a=bx \div a=b. Solving preserves equality by applying the inverse operation—multiplying both sides by aa—with integers, fractions, or decimals as appropriate, then checking the result by substitution; this develops understanding of inverse operations and supports later work with multi-step equations, without extending to variable divisors or more complex rational equations.

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Detailed Explanation: Solve one-step division equations

A one-step division equation has the unknown divided by a known number, such as

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

To find xx, use the inverse of division: multiplication. Multiply both sides by the divisor aa.

Example

Solve:

x4=7\frac{x}{4}=7

  1. The variable xx is divided by 44. Multiply both sides by 44:

4⋅x4=7⋅44\cdot\frac{x}{4}=7\cdot4

  1. On the left, 4÷4=14\div4=1, so the left side becomes xx:

x=28x=28

  1. Check the answer by substituting 2828 for xx in the original equation:

284=7\frac{28}{4}=7

Since 7=77=7, the answer is correct.

x=28\boxed{x=28}

Learn by doing: Solve one-step division equations

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