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Math Practice

Linear Equations with Fractions Practice Problems

Practice clearing fractions from a linear equation and solving for x, from two simple fractional terms up to binomial numerators and fractions on both sides. Every equation is built to have a clean solution.

  1. 1.

    Solve for x: \(\dfrac{x}{4} + 5 = \dfrac{x}{3}\)

  2. 2.

    Solve for x: \(\dfrac{x}{6} - 4 = \dfrac{x}{2}\)

  3. 3.

    Solve for x: \(\dfrac{x}{3} - 2 = \dfrac{x}{6}\)

  4. 4.

    Solve for x: \(\dfrac{x}{2} - 4 = \dfrac{x}{4}\)

  5. 5.

    Solve for x: \(\dfrac{x}{4} + 5 = \dfrac{x}{2}\)

  6. 6.

    Solve for x: \(\dfrac{x}{4} - 2 = \dfrac{x}{6}\)

  7. 7.

    Solve for x: \(\dfrac{x}{2} + 3 = \dfrac{x}{3}\)

  8. 8.

    Solve for x: \(\dfrac{x}{2} - 3 = \dfrac{x}{3}\)

  9. 9.

    Solve for x: \(\dfrac{x}{2} - 6 = \dfrac{x}{6}\)

  10. 10.

    Solve for x: \(\dfrac{x}{3} + 2 = \dfrac{x}{4}\)
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Written by
Mathovia Team
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Linear Equations with Fractions Practice Problems

The Linear Equations with Fractions lesson shows how to clear denominators with the least common denominator; this practice set drills that first move and the solving that follows, with instant checking.

How the difficulty levels work

DifficultyWhat it drillsExample
EasyTwo fractional terms, one side
MediumA fraction plus a constant, fractions on both sides
HardA binomial numerator, fractions and a constant on both sides

Easy builds the core habit: find the LCD of the two denominators, multiply every term by it, combine like terms, divide.

Medium adds a whole-number term that also has to be multiplied by the LCD, and puts a fraction on each side of the equals sign.

Hard introduces a binomial numerator that must stay in parentheses through the multiplication, then be distributed.

Using the practice problems

Pick a difficulty and a number of questions, and the page fills in instantly. Enter each value of x, then:

  • Check Answers grades the whole set at once and marks each item.
  • Show Answers reveals every solution, useful for review or an answer key.
  • Print Worksheet produces a clean, ad-free printable page.

Write each step on paper. Clearing fractions is a place where a skipped line hides exactly the step a sign error happened on.

The rules these practice problems drill

RuleStatement
Clear the fractionsMultiply every term on both sides by the LCD of all denominators
Whole-number termsGet multiplied by the LCD too
Binomial numeratorKeep it in parentheses; distribute after the denominator cancels
Smallest LCDUse the least common multiple, not the product of the denominators
After clearingFinish with the standard isolate-the-variable steps

See the Linear Equations with Fractions lesson for worked examples of every case.

Common mistakes to watch for

Multiplying only the fractions by the LCD. Every term gets multiplied, including plain numbers.

Dropping the parentheses on a binomial numerator. , not .

Using the product of the denominators instead of the LCD. It still works but the numbers balloon.

Forgetting a denominator on the far side of the equals sign. The LCD has to cover every fraction in the whole equation.

Where to go next

Once the fractions are gone, the finish is ordinary linear-equation solving — drill that with the Algebra Equation Practice Problems. Rearranging a formula that contains fractions uses the same opening move; see the Solving for a Variable Practice Problems. For the full method and worked examples, see the Linear Equations with Fractions lesson.

Frequently Asked Questions

How do I enter my answer?+

Type the value of x — for example 6, or -6 for a negative solution. You can also write x = 6; both formats are accepted. Fractional answers, when they occur, are entered as 5/2 or -5/2.

What is the first step for every problem here?+

Multiply every term on both sides by the least common denominator of all the fractions. That clears every denominator at once and leaves an ordinary linear equation, which you finish with the standard steps.

Do the answers always come out as whole numbers?+

At Easy and Medium, yes — the equations are constructed so x is an integer. At Hard the equations still have clean solutions, occasionally a simple fraction, so you are practicing the method, not fighting the arithmetic.

Why is multiplying by the LCD better than adding the fractions first?+

It converts every fraction to a whole number in one step, so the rest of the work is integer arithmetic. Adding the fractions first keeps you doing fraction arithmetic at every stage, with more chances for a slip.

What do I do with a binomial numerator like (x + 2)/3?+

Keep the binomial in parentheses when you multiply by the LCD, then distribute. , not .

How many problems can I generate?+

Unlimited. Each set is freshly generated, so you can drill the same difficulty repeatedly without repeats.

More practice problems

Algebra Equation Practice Problems Solving for a Variable Practice Problems Quadratic Equations Practice Problems