Fraction Calculator
Half a cup of flour, a third of a cup of sugar. How much dry stuff is that in total? You can’t just add the tops. Halves and thirds are different-sized pieces, so the first job is to make them the same size. That gives 5/6. The calculator below adds, subtracts, multiplies, and divides fractions, then simplifies the answer to lowest terms. It also takes mixed numbers like 1 1/2.
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Why Halves and Thirds Don’t Add Straight Away
Take 1/2 + 1/3. You cannot add halves and thirds directly, because the pieces are different sizes. The fix is a common denominator. The smallest number both 2 and 3 divide into is 6.
Convert 1/2 by multiplying top and bottom by 3, which gives 3/6. Convert 1/3 by multiplying top and bottom by 2, which gives 2/6. Add the numerators: 3 + 2 = 5. Keep the denominator: 5/6. The GCD of 5 and 6 is 1, so 5/6 is already in lowest terms. As a decimal, 5 ÷ 6 = 0.8333…
Answer: 1/2 + 1/3 = 5/6 ≈ 0.8333. The same method handles subtraction. Two more checks from the calculator: 3/4 − 1/6 = 9/12 − 2/12 = 7/12, and 2/3 × 3/4 = 6/12 = 1/2 after simplifying.
The Four Operations
Every fraction has a numerator (the top number, how many parts you have) and a denominator (the bottom number, how many parts make a whole). Adding and subtracting need a common denominator, the same bottom number on both fractions. Multiplying and dividing do not.
- Add: a/b + c/d = (a×d + c×b) ÷ (b×d), then simplify
- Subtract: a/b − c/d = (a×d − c×b) ÷ (b×d), then simplify
- Multiply: a/b × c/d = (a×c) ÷ (b×d), then simplify
- Divide: a/b ÷ c/d = (a×d) ÷ (b×c), then simplify: flip the second fraction and multiply
- Simplify: divide the top and bottom by their GCD (greatest common divisor), the largest number that divides both exactly
- To a decimal: divide the numerator by the denominator
- To a mixed number: divide the numerator by the denominator; the whole part goes in front and the remainder stays over the denominator
Where It Goes Wrong
Every answer comes back three ways: the simplified fraction, the mixed number (for answers bigger than 1), and the decimal. If the decimal repeats, it is rounded to 4 places and shown with an ellipsis, like 0.8333…
Two limits. Denominators cannot be zero, because a fraction with 0 on the bottom has no meaning. Very large numerators or denominators may be rounded in the decimal display, but the fraction itself stays exact.
Worth running through once: 1/2 + 1/4 = 3/4, a half plus a quarter. 3/4 − 1/6 = 7/12, the subtraction check above. 2/3 × 3/4 = 1/2, where multiplying cancels nicely. And simplify 12/18 = 2/3, dividing top and bottom by their GCD, 6.
Common Questions
How do I add fractions with different denominators?
Find a common denominator, the smallest number both denominators divide into. Convert each fraction to that denominator, add the numerators, keep the denominator, then simplify. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
How do I simplify a fraction?
Divide the numerator and denominator by their GCD, the largest number that divides both exactly. For 12/18, the GCD is 6, so 12/18 = 2/3.
What is a mixed number?
A mixed number is a whole number plus a fraction, like 1 1/2. It means the same as the improper fraction 3/2. To convert, divide the numerator by the denominator: the whole part goes in front, the remainder stays over the denominator.
From here: the Percentage Calculator shows how fractions and percentages are two ways of saying the same thing, the Ratio Calculator simplifies ratios and splits shares, the Average Calculator covers mean, median, and mode for any set of numbers, and the Cooking Converter halves or doubles recipe fractions. How to Calculate Percentage turns any fraction into a percent. All Math Calculators · All Calculators