Type your values in the box, one per line, and compare the mean with the smallest and largest value: it must fall between them. If you are not sure where to start, the example below shows every step. To find the middle fraction between just two values, see fraction between two fractions.
Worked example: three pieces of rope
A rope is cut into three pieces that measure 1/2 ft, 3/4 ft and 5/6 ft. How long is each piece if you make them all equal?
- Rewrite with a common denominator. The LCM of 2, 4 and 6 is 12, with 1/2 = 6/12, 3/4 = 9/12 and 5/6 = 10/12.
- Add. 6/12 + 9/12 + 10/12 = 25/12.
- Divide by the number of values. There are 3 pieces: 25/12 ÷ 3 = 25/36.
The result is 25/36 ft per piece.
Check. 25/36 is between 1/2 = 18/36 and 5/6 = 30/36, and 3 × 25/36 = 25/12 gives back the sum.
Why you divide by the number of values
The mean shares the total equally: if you add all the values and split the total into equal parts, each value becomes the sum divided by how many there are. With fractions, the common denominator is only there so you can add, and the divisor comes from counting the lines. Adding and dividing both use exact fractions, so nothing is lost to intermediate rounding. The two steps are the ones in adding fractions and dividing fractions, and OpenStax defines the mean as the sum of the data values divided by the number of values (accessed October 17, 2026).
How the mean changes with the data
| Values | Calculation | Mean |
|---|---|---|
| Two fractions: 3/5 and 7/10 | (6/10 + 7/10) ÷ 2 | 13/20 |
| Decimal, mixed number and whole number: 0.25; 1 3/4 and 2 | (0.25 + 1.75 + 2) ÷ 3 | 4/3 |
| Test scores: 7/10, 4/5 and 9/10 of the points | (7/10 + 8/10 + 9/10) ÷ 3 | 4/5 |
In every row the mean falls between the smallest and the largest value, even though it matches neither. If the scores carry different weights, you need a weighted average, which the calculator does not do directly; it is worked out in the questions at the end.
The mistake of averaging with the mediant
With two fractions, the mean is the exact midpoint between them, which is why the page fraction between two fractions gives the same number when you look for the middle fraction. The mediant, which adds numerators and denominators, also falls between the two, and that is why it misleads.
Other uses and limits
The arithmetic mean does not work for round-trip speeds, because each speed weighs differently depending on how long that leg takes, as average speed for a round trip explains. If your data are survey counts, relative frequency first turns them into fractions of the total. All values must be in the same unit: the calculator does not convert feet into inches.
Frequently asked questions
How do I find a weighted average of fractions?
The calculator does not ask for weights, but with whole-number weights you can repeat each value as many times as it weighs. A 9/10 with weight 3 and a 1/10 with weight 2 become five lines: (3 × 9/10 + 2 × 1/10) ÷ 5 = 29/10 ÷ 5 = 29/50.
Why not average the numerators and the denominators separately?
Because each fraction is a single number, and a numerator only makes sense next to its denominator. For 1/4 and 2/3, averaging separately gives 3/2 over 7/2, which is 3/7, but the correct mean is (3/12 + 8/12) ÷ 2 = 11/24.
How many values can I average at once?
From 2 to 50, one per line. Empty lines are ignored, so you can separate groups without changing the result. With a single value the mean would be that same number, which is why the calculator asks for at least a second one.
Is the mean the same as the median?
No. The mean adds and divides; the median is the middle value of the sorted list. With 1, 1 and 10 the mean is 12 ÷ 3 = 4 and the median is 1, because one extreme value moves the mean a lot and the median very little.