Fraction Calculator
Add, subtract, multiply or divide two fractions, mixed numbers or whole numbers. Every step is shown: the common denominator, the rewritten fractions and the simplification of the answer, with the answer as a fraction, a mixed number, a decimal and a percentage.
How Do Fractions Work?
A fraction a/b is a part of a whole: the whole is cut into b equal pieces (the denominator) and you take a of them (the numerator). The same amount can be written in many ways: 1/2 = 2/4 = 3/6. A fraction is simplified (in lowest terms) when the numerator and denominator have no common factor left.
To add or subtract, the pieces must be the same size, so first rewrite both fractions with a common denominator, the smallest being the least common multiple. To multiply, multiply the tops and the bottoms. To divide, multiply by the reciprocal: flip the second fraction upside down.
Fraction Bars
barsStep-by-Step Solution
Worked Techniques
lcm(4, 6) = 12. Multiply the top and bottom of 3/4 by 3 and of 5/6 by 2, then add the numerators.
Turn mixed numbers into improper fractions before you calculate, and back at the end: divide the numerator by the denominator; the remainder stays on top.
“Keep, change, flip”: keep the first fraction, change ÷ into ×, flip the second one.
Sources & Verification
- H.-H. Wu, Understanding Numbers in Elementary School Mathematics, American Mathematical Society, 2011 — Part 2 (Fractions: equivalent fractions, adding, multiplying and dividing).
- K. H. Rosen, Elementary Number Theory and Its Applications, 6th ed., Pearson, 2011 — Ch. 3 (the greatest common divisor and least common multiple used to simplify and add).
Frequently Asked Questions
How do you add fractions with different denominators?
Rewrite both fractions so they have the same denominator, then add the numerators. Example: 3/4 + 5/6.
1. Find the lowest common denominator: the least common multiple of 4 and 6 is 12.
2. Rewrite: 3/4 = 9/12 (top and bottom × 3) and 5/6 = 10/12 (× 2).
3. Add the numerators: 9/12 + 10/12 = 19/12.
4. 19 and 12 have no common factor, so 19/12 is in lowest terms; as a mixed number it is 1 7/12.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. Example: 2/3 × 9/10 = 18/30, and dividing the top and bottom by their greatest common divisor 6 gives 3/5. No common denominator is needed.
How do you divide fractions?
Multiply by the reciprocal of the second fraction: keep the first, change ÷ into ×, flip the second. Example: 3/4 ÷ 5/6 = 3/4 × 6/5 = 18/20 = 9/10. Dividing by a fraction smaller than 1 makes the answer bigger: 5 ÷ 1/4 = 20, because 1/4 fits 20 times into 5.
Is the answer simplified?
Yes. Every answer is given in lowest terms, with the simplifying step shown: 2/3 × 9/10 = 18/30, and dividing the top and bottom by their greatest common divisor 6 gives 3/5. To simplify a single fraction with the full GCD steps, use the Simplify tab.
How do you calculate with mixed numbers?
First turn each mixed number into an improper fraction: whole number × denominator + numerator, over the denominator, so 2 1/3 = 7/3 and 1 3/4 = 7/4. Then calculate as usual: 7/3 − 7/4 = 28/12 − 21/12 = 7/12. Turn the answer back into a mixed number if it is larger than 1.
Can I use decimals and whole numbers?
Yes. A whole number is a fraction with denominator 1 (5 = 5/1), and a decimal is turned into an exact fraction first (0.25 = 1/4). So 0.25 + 1/3 = 1/4 + 1/3 = 7/12. The calculator works with exact whole numbers of any length, so there are no rounding errors.