Fraction Calculator
History
Your results will appear here. Tap Use on any of them to carry it into the next calculation, in this calculator or another one. History is kept while this tab is open.
This fraction calculator adds, subtracts, multiplies and divides fractions, mixed numbers like 1 1/2 and whole numbers. Pick +, −, × or ÷, press Calculate, and you get the simplified fraction, the mixed number and the decimal: 1 1/2 + 3/4 = 9/4 = 2 1/4 = 2.25.
Mixed Numbers and Improper Fractions
A mixed number takes one row: the whole part goes in the left box, the fraction in the two boxes beside it.
To turn a mixed number into an improper fraction, multiply the whole part by the denominator and add the numerator. The denominator stays the same:
2 3/5 = (2 × 5 + 3)/5 = 13/5
To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole part, and the remainder becomes the new numerator:
9/4 = 9 ÷ 4 = 2, remainder 1 → 2 1/4
You don't have to do either by hand. An improper answer always shows its mixed number beside it. Fill in only the First row, and Calculate converts the number: 2 3/5 gives 13/5, 9/4 gives 2 1/4.
How It's Calculated
Mixed numbers are first rewritten as improper fractions, and the answer is always reduced to lowest terms. The line under the result shows that step.
Adding and Subtracting Fractions
Fraction addition and subtraction need a common denominator. Take the smallest number both denominators divide into, rewrite each fraction with it, then add or subtract the numerators and keep the denominator. If the denominators already match, go straight to the numerators.
a/b + c/d = (a·d + c·b)/(b·d)
a/b − c/d = (a·d − c·b)/(b·d)
Then reduce the result. In 1 1/2 + 3/4, the mixed number is 3/2, which is 6/4: 6/4 + 3/4 = 9/4 = 2 1/4. With unlike denominators, as in 5/6 − 1/4, the common one is 12: 10/12 − 3/12 = 7/12.
Multiplying Fractions
Fraction multiplication needs no common denominator. Multiply the numerators, multiply the denominators, then reduce:
a/b × c/d = (a·c)/(b·d)
For example, 2/3 × 3/4 = 1/2. A whole number works as a fraction over 1: 2/3 × 4 = 2/3 × 4/1 = 8/3, or 2 2/3.
Dividing Fractions
Fraction division comes down to multiplication. To divide a fraction, flip the second one (swap its numerator and denominator) and multiply:
a/b ÷ c/d = a/b × d/c
So 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2 = 1 1/2. Dividing by zero has no answer: for 3/4 ÷ 0/5 the display shows "Can't divide by 0".
Examples
Each row is one calculation, as the display shows it. It is also a fraction calculator with whole numbers: it reads 2 as 2/1.
| You enter | Result | Line under the result |
|---|---|---|
| 1 1/2 + 3/4 | 9/4 = 2 1/4 | 6/4 + 3/4 = 9/4 = 2.25 |
| 5/6 − 1/4 | 7/12 | 10/12 − 3/12 = 7/12 = 0.583333333333 |
| 2/3 × 3/4 | 1/2 | 2/3 × 3/4 = 1/2 = 0.5 |
| 3/4 ÷ 1/2 | 3/2 = 1 1/2 | 3/4 × 2 = 3/2 = 1.5 |
| 2 + 3/4 | 11/4 = 2 3/4 | 8/4 + 3/4 = 11/4 = 2.75 |
| −1/2 + 1/3 | −1/6 | −3/6 + 2/6 = −1/6 = −0.166666666667 |
| 1 1/2 × 2 2/3 | 4 | 3/2 × 8/3 = 4 |
| 36/48, First row only | 3/4 | 36/48 = (36 ÷ 12)/(48 ÷ 12) = 3/4 = 0.75 |
To turn a fraction into a percent, multiply its decimal by 100: 3/4 is 0.75, or 75%. For percent problems, use the percentage calculator.
FAQ
How do you multiply a fraction by a whole number?
Write the whole number over 1 and multiply the numerators; the denominator stays. For example, 2/3 × 4 = 8/3, which is 2 2/3.
How do you divide a fraction by a whole number?
Multiply the denominator by the whole number and keep the numerator. It's the same as multiplying by 1 over that number: 3/4 ÷ 2 = 3/4 × 1/2 = 3/8.
How do you add fractions with different denominators?
Rewrite both fractions with a common denominator first, then add the numerators: 1/4 + 1/6 = 3/12 + 2/12 = 5/12. The steps are in Adding and Subtracting Fractions.
What are the numerator and the denominator?
The numerator is the top number: how many parts you have. The denominator is the bottom number: how many equal parts the whole is split into, so it can't be 0. In the calculator, they're the upper and lower boxes of each row.
Can I use whole numbers and mixed numbers in the calculator?
Yes, it works as a mixed fraction calculator too. Type a whole number in the left box of a row, add a fraction beside it for a mixed number, and press ± for a negative one: 2 + 3/4 = 11/4 = 2 3/4.