Calculating fractions...
Enter two fractions, choose an operation, and get the simplified answer with steps.
What Is a Fraction Calculator?
A fraction calculator solves arithmetic problems where values are written as a numerator over a denominator. This calculator can add fractions, subtract fractions, multiply fractions, and divide fractions, then simplify the answer to lowest terms. It also shows the improper fraction, mixed number form when one applies, decimal approximation, and step-by-step work.
Fractions appear in homework, recipes, construction measurements, medicine dosing, sewing, woodworking, and everyday comparisons. A calculator is useful because the final answer is only part of the job. You often need to know how the common denominator was found, why the reciprocal is used, or how the result was simplified.
How Fraction Operations Work
Use a common denominator
1/2 + 1/3 = 3/6 + 2/6 = 5/6
Multiply numerator by numerator and denominator by denominator
2/3 x 3/5 = 6/15 = 2/5
Multiply by the reciprocal of the second fraction
3/4 / 2/5 = 15/8 = 1 7/8
How to Add Fractions
To add fractions with the same denominator, add the numerators and keep the denominator. For example, 2/7 + 3/7 = 5/7. The denominator stays 7 because both fractions already describe the same size pieces.
To add fractions with different denominators, first rewrite them with a common denominator. For 1/2 + 1/3, a common denominator is 6. Rewrite 1/2 as 3/6 and 1/3 as 2/6. Then add the numerators: 3/6 + 2/6 = 5/6. The calculator uses the cross-multiply formula a/b + c/d = (a*d + c*b) / (b*d), then simplifies.
How to Subtract Fractions
Subtracting fractions follows the same common-denominator rule. If the denominators match, subtract the numerators. If they are different, rewrite both fractions so the denominators match, then subtract. For example, 3/4 - 1/8 becomes 6/8 - 1/8, which equals 5/8.
Negative answers are valid. If you subtract a larger fraction from a smaller fraction, the numerator becomes negative after simplification. The calculator keeps the denominator positive and places the sign on the numerator, so -1/4 is shown instead of 1/-4.
How to Multiply Fractions
Multiplying fractions is more direct than adding or subtracting. Multiply the numerators together, multiply the denominators together, then simplify the result. For example, 2/3 x 3/5 gives 6/15, and 6/15 simplifies to 2/5.
You do not need a common denominator for multiplication. This is why fraction multiplication is often faster by hand. If possible, you can cross-cancel before multiplying, but this calculator also simplifies after multiplying so the final answer still reaches lowest terms.
How to Divide Fractions
To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal flips the numerator and denominator. For example, 3/4 divided by 2/5 becomes 3/4 x 5/2. The result is 15/8, which is also 1 7/8 as a mixed number.
You cannot divide by a zero fraction, because division by zero is undefined. A zero fraction has a numerator of 0, such as 0/3 or 0/8. The denominator still cannot be zero in any fraction.
How to Simplify Fractions
A fraction is simplified when the numerator and denominator share no common factor other than 1. To simplify 20/32, find the greatest common divisor of 20 and 32, which is 4. Divide both parts by 4 to get 5/8.
This calculator simplifies every result automatically. Whole-number results display as plain numbers, so 4/4 becomes 1 instead of 1/1. A result of zero is normalized to 0, because 0/3, 0/9, and 0/100 all represent the same value.
Improper Fractions and Mixed Numbers
An improper fraction has a numerator whose absolute value is greater than the denominator, such as 15/8. Improper fractions are convenient for calculation because they keep the value in one fraction. Mixed numbers combine a whole number with a proper fraction, such as 1 7/8.
Both forms represent the same value. In school math, improper fractions are often preferred while solving. In recipes and measurements, mixed numbers can be easier to read. The calculator shows the mixed-number form whenever the simplified result is improper.
Fraction Calculator FAQ
How do you add fractions with different denominators? +
Find a common denominator, rewrite both fractions with that denominator, add the numerators, and simplify the result.
How do you subtract fractions? +
Use a common denominator, subtract the second numerator from the first numerator, keep the common denominator, and reduce the answer.
How do you multiply fractions? +
Multiply numerator by numerator and denominator by denominator, then simplify the new fraction.
How do you divide fractions? +
Flip the second fraction to make its reciprocal, multiply by that reciprocal, and simplify.
How do you simplify a fraction? +
Divide the numerator and denominator by their greatest common divisor. Repeat until no common factor remains.
What is an improper fraction? +
An improper fraction has an absolute numerator greater than or equal to its denominator, such as 9/4 or -7/3.
What is a mixed number? +
A mixed number combines a whole number and a proper fraction, such as 2 1/2. It is another way to write an improper fraction.
Can denominators be negative? +
A denominator can be typed as negative, but standard fraction form moves the sign to the numerator. For example, 1/-2 becomes -1/2.
Learn More About Fractions
For additional worked lessons, see OpenStax Prealgebra, Khan Academy fraction arithmetic, and Math is Fun's fractions guide. These references cover common denominators, reciprocals, simplification, and mixed numbers in more depth.
Related Calculators
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