Arithmetic & Basics
Basic

Mixed Number to Fraction

Convert a mixed number to an improper fraction.

Formula

abc=ac+bca\frac{b}{c} = \frac{ac + b}{c}

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Variables

aWhole
bNumerator
cDenominator

Example

2½ = 5/2

How it works

A mixed number combines a whole number and a fraction, so to turn it into one fraction, first rewrite the whole number in the same denominator as the fractional part. Since one whole equals c/c, a wholes becomes ac/c, and then you add the extra b/c to get (ac+b)/c. This works because both parts are now measured in the same size pieces.

When to use it

Use this when you need to do calculations with mixed numbers and want to compare, add, subtract, multiply, or divide them more easily. It is also common in algebra, measurement, and word problems where fractions should be written as a single fraction.

Worked example, step by step

Convert 3 2/5 to an improper fraction Whole number part: 3 = 3 × 5/5 = 15/5 Add the fractional part: 15/5 + 2/5 = 17/5 Final answer: 3 2/5 = 17/5

Common mistakes to avoid

  • Multiplying the whole number by the numerator instead of the denominator
  • Forgetting to keep the same denominator after converting the whole number
  • Adding the whole number directly to the numerator without converting it to equal-sized parts

Did You Know?

Mixed numbers like 2½ are an everyday hangover from Roman and medieval arithmetic, long before decimals became common.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026