Fraction Calculator With Whole and Mixed Numbers

How this calculator works

Every number is turned into an improper fraction first. A mixed number such as 2 1/3 becomes 7/3: the whole number times the denominator, plus the numerator, over the same denominator.

To add or subtract, the fractions need a common denominator. The calculator uses the least common denominator — the smallest number both denominators divide into — because that is how it is taught, and it keeps the numbers small.

To multiply, multiply the numerators together and the denominators together. To divide, flip the second fraction upside down and multiply: dividing by 3/4 is the same as multiplying by 4/3.

The answer is then reduced to lowest terms by dividing the top and bottom by their greatest common divisor, and shown as a fraction, a mixed number and a decimal.

All of the arithmetic is exact. It works in whole numbers throughout rather than decimals, so 1/3 stays exactly 1/3 instead of becoming 0.333 and drifting.

The formula

Exactly what happens to your numbers, step by step.

Adding
```
a/b + c/d = (a×d + c×b) / (b×d)
```
Shown over the least common denominator in the steps.
Subtracting
```
a/b − c/d = (a×d − c×b) / (b×d)
```
Multiplying
```
a/b × c/d = (a×c) / (b×d)
```
Dividing
```
a/b ÷ c/d = a/b × d/c
```
Multiply by the reciprocal. The second fraction cannot be zero.

A worked example

Adding two mixed numbers: 2 1/3 + 1 3/4.

What you enter

First number: 2 1/3
Operation: Add
Second number: 1 3/4

Step by step

As improper fractions: 7/3 + 7/4
Least common denominator: 12
Rewritten: 28/12 + 21/12
Add the numerators: 49/12
As a mixed number: 4 1/12

2 1/3 + 1 3/4 = 49/12, which is 4 1/12

49/12 cannot be simplified, because 49 and 12 share no factor other than 1. As a decimal it is 4.0833…, with the 3 repeating forever.

Common fractions as decimals and percentages

Halves through sixteenths, each in its simplest form. Exact where the decimal ends; rounded and marked where it repeats forever.

Common fractions with their decimal and percentage equivalents
Fraction	Decimal	Percent
1/2	0.5	50%
1/3	≈ 0.3333	≈ 33.33%
2/3	≈ 0.6667	≈ 66.67%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
3/5	0.6	60%
4/5	0.8	80%
1/6	≈ 0.1667	≈ 16.67%
5/6	≈ 0.8333	≈ 83.33%
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/10	0.1	10%
3/10	0.3	30%
7/10	0.7	70%
9/10	0.9	90%
1/12	≈ 0.0833	≈ 8.33%
5/12	≈ 0.4167	≈ 41.67%
7/12	≈ 0.5833	≈ 58.33%
11/12	≈ 0.9167	≈ 91.67%
1/16	0.0625	6.25%
3/16	0.1875	18.75%
5/16	0.3125	31.25%
7/16	0.4375	43.75%
9/16	0.5625	56.25%
11/16	0.6875	68.75%
13/16	0.8125	81.25%
15/16	0.9375	93.75%

≈ marks a decimal that never ends, shown to four places: 1/3 is 0.3333…, never exactly 0.3333. Fractions that simplify, such as 2/4 or 6/8, are listed once, as 1/2 and 3/4. For any other fraction, use the calculator above.

Assumptions

Every result here rests on these. Change your inputs and the result changes with them.

Each number is a whole number, a fraction, or a mixed number made of both.
A minus sign on a mixed number applies to all of it: −1 1/2 means −(1 + 1/2), which is −3/2.
Numerators, denominators and whole numbers are whole numbers. For a value like 1.5, enter 1 and 1/2, or 3/2.

What this cannot tell you

It works on two numbers at a time. For a longer sum, do it in steps, using each answer as the next first number.
Decimals that never end are shown to ten places and marked as repeating, rather than rounded as if they stopped.

Questions people ask

How do you add fractions with different denominators?

Rewrite both over a common denominator, then add the numerators. For 1/3 + 1/4 the least common denominator is 12, so it becomes 4/12 + 3/12 = 7/12. The denominator stays the same; only the numerators are added.

How do you divide fractions?

Flip the second fraction and multiply. 2/3 ÷ 4/5 is 2/3 × 5/4 = 10/12, which simplifies to 5/6. Dividing by a fraction and multiplying by its reciprocal are the same operation.

Why does 1/3 never end as a decimal?

A fraction in lowest terms only ends as a decimal when its denominator has no prime factors other than 2 and 5, because those are the factors of 10. Three is neither, so 1/3 repeats forever as 0.333…

How do I enter a negative mixed number?

Put the minus sign on the whole number and leave the fraction positive: for −2 1/4, enter −2 as the whole number and 1/4 as the fraction. The calculator reads it as −(2 + 1/4), which is −9/4.

Sources and review

This calculator uses standard arithmetic with no external rules or published rates, so there is nothing to cite beyond the formulas shown above.

Methodology version 1.0.0 · Last reviewed October 10, 2026

Cite this calculator

For coursework, a resource list or your own site. How every calculator is built and checked is set out on the methodology page.

Citation

Chalk Calculator. (2026, October 10). Fraction Calculator (Methodology version 1.0.0). https://chalkcalculator.com/fraction-calculator/

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