What next?
Fractions, decimals, percentages and ratios are the same idea four ways.
How to use this calculator
- Enter the first fraction (numerator and denominator).
- Pick the operation and enter the second fraction.
- Read the simplified result and its decimal.
What your result means
The result is your answer reduced to its simplest form, with the decimal alongside. Simplifying divides top and bottom by their greatest common factor, so 6/8 becomes 3/4 — the same value written more cleanly.
Why this one is different
Every answer arrives as a reduced fraction, a decimal, a percentage and, where the top number is bigger, a mixed number, so whichever form the homework sheet or the recipe wants is already there. The working names the common denominator that was used and the divisor the answer was reduced by.
Add, subtract, multiply and divide any fractions
Adding or subtracting fractions needs a common denominator: multiply each fraction so both sit over the same bottom number, combine the tops, then simplify. Multiplying is easier — multiply tops together and bottoms together. Dividing flips the second fraction and multiplies.
This calculator does every step and then reduces the answer to its simplest form using the greatest common divisor, and also shows it as a decimal, a percentage and a mixed number.
Formula
Multiplication is a·c ÷ b·d; division is a·d ÷ b·c. The result is then divided by the greatest common divisor of the top and bottom to simplify.
Example calculation
Adding 1/2 + 1/3:
= 5 ÷ 6 = 5/6
Example
1/2 + 1/3: common denominator 6 gives 3/6 + 2/6 = 5/6 ≈ 0.833 = 83.33%.
3/4 ÷ 1/2: flip and multiply → 3/4 × 2/1 = 6/4 = 3/2 = 1½.
Frequently asked questions
Does it simplify the answer?＋
Yes. Every result is reduced to lowest terms using the greatest common divisor, and also shown as a decimal, percentage and mixed number.
Can I use negative fractions?＋
Yes. Enter a negative numerator or denominator and the calculator handles the sign correctly.
How do I add fractions with different denominators?＋
Convert both to a common denominator first, usually the lowest common multiple, then add the numerators. One half plus one third becomes three sixths plus two sixths, which is five sixths.
Why does dividing by a fraction make the answer bigger?＋
Because dividing asks how many of the divisor fit into the number. Two divided by one half is four, since four halves fit into two. The rule is to multiply by the reciprocal.
How do I convert a fraction to a decimal?＋
Divide the numerator by the denominator. Three eighths is 3 divided by 8, which is 0.375. Denominators with prime factors other than 2 and 5 give recurring decimals.
What is an improper fraction?＋
One where the numerator is larger than the denominator, such as seven quarters. It is the same value as the mixed number one and three quarters, and it is easier to calculate with.
Related calculators
Assumptions & limitations
Fractions are handled exactly, with a few boundaries worth knowing.
- All arithmetic is done on whole-number numerators and denominators, so results are exact — there is no decimal rounding error anywhere in the chain.
- Results are always reduced to lowest terms using the greatest common divisor, so 6/8 is returned as 3/4.
- A denominator of zero is undefined and is rejected rather than returning infinity.
- Very large numerators and denominators are limited by standard integer precision; beyond roughly sixteen digits the result may lose accuracy.
Sources & references
Fraction terminology and reduction rules follow standard school-curriculum definitions:
- NCETM — understanding multiplicative relationships: fractions, percentages, ratio and proportion
- National Curriculum in England — mathematics programmes of study
Further reading
Why the lowest common denominator matters
Adding and subtracting fractions requires a common denominator, and any common denominator works arithmetically — multiplying the two denominators together always produces one. Using the lowest one simply keeps the numbers small and the final simplification short: 5/12 + 7/18 over the product 216 gives 174/216, which reduces to 29/36; over the lowest common denominator of 36 it is 15/36 + 14/36 = 29/36 directly. Multiplication and division need no common denominator at all — multiply straight across, and divide by inverting the second fraction — which is why they are the easier pair despite looking harder.
Improper fractions, mixed numbers and exactness
A mixed number such as 2 3/4 is friendlier to read; an improper fraction such as 11/4 is easier to compute with, because every operation works on a single numerator and denominator. Convert to improper form before calculating and back afterwards if the answer needs to be read aloud. The reason to stay in fractions at all is exactness: a third is exactly a third, while 0.333 is not, and repeated rounding of a recurring decimal accumulates error that a fraction never carries. Where a result eventually has to be decimal — a measurement, a price — convert once at the end.