Fraction calculator
Enter two fractions, get the simplified answer with the steps.
Type 3/4, a mixed number like 1 1/2, a whole number or a decimal like 0.125.
How do I add fractions?
Give them a common denominator, then add the numerators. 1/2 + 1/3: the common denominator is 6, so 3/6 + 2/6 = 5/6.
How do I subtract fractions?
The same way: common denominator, then subtract the numerators. 3/4 − 1/6 = 9/12 − 2/12 = 7/12.
How do I multiply and divide fractions?
To multiply, multiply the tops and the bottoms: 2/3 × 3/4 = 6/12 = 1/2. To divide, flip the second fraction and multiply: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
How do I work with mixed numbers?
Turn them into improper fractions first: 1 1/2 is 3/2 and 2 3/4 is 11/4. Then 3/2 + 11/4 = 6/4 + 11/4 = 17/4, which is 4 1/4. Type mixed numbers with a space, like 1 1/2.
How do I turn a decimal into a fraction?
Write it over a power of ten and simplify: 0.125 = 125/1000 = 1/8. You can type decimals straight into the calculator.
Why do I need a common denominator to add but not to multiply?
Adding means counting pieces of the same size, so the pieces must be the same size first: halves and thirds cannot be added until both are sixths. Multiplying a fraction by a fraction takes a part of a part, which works for any denominators: 1/2 of 1/3 is 1/6.
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common factor. 18/24: the greatest common factor is 6, so 18/24 = 3/4. The calculator always reduces the result to lowest terms and shows a mixed number when the value is above 1.
How do I tell which of two fractions is larger?
Cross-multiply: for a/b and c/d, compare a × d with c × b, which is the same as putting both over the common denominator b × d. For 5/8 and 7/12, 5 × 12 = 60 and 7 × 8 = 56, so 5/8 is the larger. Subtracting also works: the sign of the difference tells you the order.
How do I turn a fraction into a decimal or a percent?
Divide the numerator by the denominator: 7/8 = 0.875, and multiplying by 100 gives the percent, 87.5%. Some fractions never end: 2/7 = 0.285714… repeats forever, and the calculator rounds such decimals to six places. A fraction ends as a decimal only when its denominator, in lowest terms, has no prime factors other than 2 and 5. Stay with the fraction when you need the exact value.
How are negative mixed numbers and zero handled?
A minus sign in front of a mixed number applies to the whole quantity: −2 3/8 means −(2 + 3/8), which is −19/8, not −2 + 3/8. Adding 1/2 to it gives −15/8. A denominator of zero is not allowed, so a fraction such as 3/0 is not accepted, and dividing by a fraction whose numerator is 0 (dividing by zero) shows a message instead of a result.
The rules behind each operation
To add or subtract, rewrite both fractions over a common denominator (the least common multiple of the denominators keeps the numbers small) and combine the numerators. To multiply, multiply numerators and denominators, which can be shortened by canceling common factors first. To divide, multiply by the reciprocal of the second fraction. Mixed numbers are converted to improper fractions first, and the answer is reduced by dividing out the greatest common factor.
Worked example: four operations
3/4 + 5/6: the least common multiple of 4 and 6 is 12, so 9/12 + 10/12 = 19/12, which the calculator gives as 19/12 or 1 7/12. 2 1/3 − 1 3/4 = 7/3 − 7/4 = 28/12 − 21/12 = 7/12. 2 2/3 × 3/8 = 8/3 × 3/8 = 1, because the 3s and 8s cancel. 5/6 ÷ 10/9 = 5/6 × 9/10 = 45/60 = 3/4.
Common mistakes
Adding the denominators as well as the numerators (1/2 + 1/3 = 2/5) is the classic error: the answer is 5/6. Another is dividing by a fraction without flipping it. A third is leaving a mixed number's whole part behind when subtracting: borrow 1 from the whole number as a fraction (1 = 4/4) or convert to improper fractions to avoid it. Finally, a negative sign belongs to the whole fraction; −3/4, 3/−4 and −(3/4) are the same number.
Sources: OpenStax Prealgebra 2e, chapter 4 (fractions: visualize, add, subtract, multiply and divide fractions and mixed numbers). Related: decimal to fraction calculator, fraction to percent calculator, LCM and GCF calculator and ratio calculator.