A fraction calculator adds, subtracts, multiplies or divides fractions and gives the answer in lowest terms. 1/2 + 1/3 = 5/6, or about 0.8333.
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How to use the fraction calculator
- Enter the numerator and denominator of the first fraction.
- Choose add, subtract, multiply or divide.
- Enter the second fraction.
- Read the simplified answer and its decimal value.
How the fraction calculator works
The fraction calculator adds, subtracts, multiplies or divides two fractions and reduces the answer to lowest terms. It uses the standard rules:
- Add: a/b + c/d = (ad + bc) ÷ bd
- Subtract: a/b − c/d = (ad − bc) ÷ bd
- Multiply: a/b × c/d = ac ÷ bd
- Divide: a/b ÷ c/d = ad ÷ bc (multiply by the reciprocal)
After each operation, the numerator and denominator are divided by their greatest common factor, so 10/12 becomes 5/6. The result is also shown as a decimal.
Fraction calculator worked examples
To add 1/2 and 1/3: (1 × 3 + 1 × 2) ÷ (2 × 3) = 5/6. To divide 5/8 by 1/4, flip the second fraction and multiply: 5/8 × 4/1 = 20/8 = 5/2, which is 2 1/2 as a mixed number.
| Problem | Answer | Decimal |
|---|---|---|
| 1/2 + 1/3 | 5/6 | 0.8333 |
| 3/4 − 1/6 | 7/12 | 0.5833 |
| 2/3 × 9/10 | 3/5 | 0.6 |
| 5/8 ÷ 1/4 | 5/2 | 2.5 |
| 7/12 + 5/12 | 1 | 1 |
| −1/2 + 1/5 | −3/10 | -0.3 |
Using the least common denominator
By hand it is often easier to use the least common denominator rather than multiplying the denominators. For 3/4 − 1/6, the least common multiple of 4 and 6 is 12, so 3/4 = 9/12 and 1/6 = 2/12, giving 7/12. Multiplying the denominators gives 18/24 − 4/24 = 14/24, which reduces to the same 7/12. The fraction calculator always reduces, so both routes give the same answer.
Simplifying fractions
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. Divide both by their greatest common factor: 18/24 has a GCF of 6, so it simplifies to 3/4. A quick check is that if both numbers are even, the fraction can be reduced further.
Mixed numbers and improper fractions
A mixed number such as 2 1/2 combines a whole number and a fraction. To enter it, convert it to an improper fraction: multiply the whole number by the denominator and add the numerator, keeping the denominator, so 2 1/2 = 5/2. To convert an answer back, divide: 17/5 is 3 with a remainder of 2, or 3 2/5.
Negative fractions and zero
Enter a negative fraction with a minus sign on the numerator, such as −1/2. The calculator moves any negative sign in the denominator to the numerator, so the answer is always written with a positive denominator. A denominator can never be zero, and dividing by a fraction equal to zero is undefined, so the fraction calculator reports those inputs as errors.
Fractions and decimals
Divide the numerator by the denominator to get a decimal: 3/8 = 0.375. Fractions whose denominators have only 2 and 5 as prime factors give terminating decimals; others repeat, such as 1/3 = 0.333…. To turn a terminating decimal into a fraction, write it over a power of 10 and simplify: 0.75 = 75/100 = 3/4.
Everyday uses
- Scaling recipes: half of 3/4 cup is 3/8 cup.
- Woodworking and sewing measurements in inches, such as 5/8 + 3/16 = 13/16.
- Homework checks for adding, subtracting, multiplying and dividing fractions.
Order of operations with fractions
When a problem has more than two fractions, work it in steps. Multiplication and division come before addition and subtraction, so 1/2 + 1/3 × 3/4 is 1/2 + 1/4 = 3/4, not (5/6) × 3/4. Solve each part, then use the result as the first fraction in the next step. Keeping answers as fractions until the end avoids rounding errors that creep in when you convert to decimals too early; 1/3 written as 0.33 and multiplied by 3 gives 0.99 instead of exactly 1.
Related converters and calculators
Related calculators:
- GCF calculator: simplifying
- LCM calculator: common denominators
- Percentage calculator: percentages
- Scientific calculator: math
Sources
OpenStax Prealgebra 2e, 4.1: Visualize fractions.
Formula and method
a/b + c/d = (ad + bc)/bd; a/b − c/d = (ad − bc)/bd; a/b × c/d = ac/bd; a/b ÷ c/d = ad/bc. Simplify by dividing top and bottom by their greatest common divisor.
Integer fraction arithmetic with canonical reduction. Denominators must be nonzero; division rejects a zero second numerator.
Questions about this calculator
What is 1/2 + 1/3?
5/6.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second.
How do I enter a mixed number?
Convert it to an improper fraction, such as 2 1/2 = 5/2.
Does the calculator simplify answers?
Yes, it reduces to lowest terms.
Can I use negative fractions?
Yes, put the minus sign on the numerator.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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