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Average of Fractions Calculator

Find the exact mean of a list of fractions, mixed numbers and decimals by adding over a common denominator and dividing by how many there are.

Separate with commas or new lines. Mixed numbers (2 1/3), negatives and decimals are accepted.
Sum
2 112
Count
3
Average (fraction)
2536
Average (decimal)
0.6944444444
Smallest / largest
12 / 56
Average of 3 fractions253625/36 ≈ 0.69444444

Show the work

  1. Find the least common denominator: LCD(2, 4, 6) = 12 (2 = 2, 4 = 22, 6 = 2 · 3; take each prime the greatest number of times it appears: 22 · 3).
  2. Rewrite over 12 and add the numerators: 612 + 912 + 1012 = 2512
  3. Divide the sum by the number of fractions (3), which is the same as multiplying by 13: 2512 ÷ 3 = 2536
  4. As a decimal: 0.6944444444

The average (arithmetic mean) of a list of fractions is their sum divided by how many there are — exactly as for whole numbers. The only extra work is adding the fractions, which needs a common denominator. This calculator does the whole job with exact fractions, so the answer is not rounded until you ask for a decimal.

How to use the calculator

  1. Type the values separated by commas or on separate lines. Fractions (3/4), mixed numbers (1 1/2), negatives and decimals (2.25) can be mixed.
  2. The tape shows the average as a mixed number and an improper fraction, the decimal value, the sum, the count, and the smallest and largest values.
  3. The steps show the common denominator, the sum and the division.

The formula

mean = (x1 + x2 + … + xn) ÷ n

With fractions:

  1. Find the LCD of all the denominators and rewrite each fraction over it.
  2. Add the numerators to get the sum.
  3. Divide by the count n, which multiplies the denominator by n.
  4. Simplify and convert to a mixed number if needed.

Worked example: 1/2, 3/4 and 5/6

  1. The LCD of 2, 4 and 6 is 12.
  2. Rewrite: 6/12 + 9/12 + 10/12 = 25/12 (that is 2 1/12).
  3. Divide by 3: 25/12 ÷ 3 = 25/36.
  4. 25/36 is already in lowest terms, about 0.6944.

Check with decimals: (0.5 + 0.75 + 0.8333) ÷ 3 = 2.0833 ÷ 3 ≈ 0.6944. ✓

Why the exact fraction matters

Converting to decimals first works but introduces rounding: 5/6 is 0.8333…, and the rounding error carries into the average. Keeping fractions to the end gives the exact answer, 25/36, and you can round once at the end if you need a decimal.

A shortcut for two fractions

The average of two fractions is halfway between them on the number line:

mean of a/b and c/d = (a/b + c/d) ÷ 2

So the average of 1/2 and 1/4 is (2/4 + 1/4) ÷ 2 = 3/8. This also shows that between any two fractions there is always another fraction — their average.

Real uses

  • Measurements: averaging repeated measurements such as 2 3/8, 2 5/16 and 2 7/16 inches.
  • Recipes: finding a middle amount between two versions of a recipe.
  • Grades and scores: averaging quiz scores written as fractions like 17/20 and 22/25.

If some values should count more than others, use the weighted average calculator. For averages of ordinary numbers with the median and mode, see the mean calculator; to add fractions without dividing, use the adding fractions calculator.

Frequently asked questions

How do you find the average of fractions?

Add the fractions, then divide the sum by how many there are. For 1/2, 3/4 and 5/6: the sum is 6/12 + 9/12 + 10/12 = 25/12, and 25/12 ÷ 3 = 25/36.

How do you divide a fraction by the count?

Dividing by a whole number n is the same as multiplying by 1/n, which multiplies the denominator by n. 25/12 ÷ 3 = 25/(12 × 3) = 25/36. Simplify afterward if possible.

Is the average of fractions the same as adding the numerators and denominators?

No. The average of 1/2 and 1/4 is 3/8, not (1 + 1)/(2 + 4) = 1/3. Always add the fractions properly over a common denominator first.

Can the average be written as a mixed number?

Yes. If the mean is greater than 1 it is shown both ways; for example the average of 1 1/2, 2.25 and 3/4 is 3/2, or 1 1/2.

Last reviewed October 2026 by the CalcFluent editorial team. How we check our calculators.