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MathidiaMathematics Academy
Equations and inequalities
Lesson 23 of 75
Standard practice

Equations with fractions

Objective. Clear a numerical denominator before solving.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Equations with fractions contain a numerical denominator, and the most reliable method is to multiply every term on both sides by that denominator to clear the fraction before solving as a normal linear equation. For x/4 + 2 = 7, multiply every term by 4 to get x + 8 = 28, then subtract 8 to find x = 20. If there are two different denominators, multiply by their lowest common multiple instead. Clearing the fraction first prevents arithmetic mistakes that arise from working with fractions throughout the whole solving process.

Worked example

Solve the equation with fractions x/5 − 2 = 3.

-1013456−2
Number line from -1 to 6 with a jump of 2 backwards from 5
  1. 1Add 2 to both sides: x/5 = 5
  2. 2Multiply both sides by 5 to clear the fraction: x = 25
  3. 3Check by substituting back: 25/5 − 2 = 5 − 2
  4. 4Confirm the result equals 3, so x = 25 is correct

Answer: x = 25

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Common mistake. Pupils often multiply only the fractional term by the denominator and leave the other terms unchanged, turning x/3 + 1 = 5 into x + 1 = 5 instead of correctly multiplying every term by 3 to get x + 3 = 15.

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