Plot No. 58 · Education
Fraction Calculator
Add, subtract, multiply or divide two fractions and get the answer reduced to lowest terms plus a decimal. Addition and subtraction use a common denominator (the two denominators multiplied), then the result is simplified by dividing the top and bottom by their greatest common divisor.
Working: 1/2 + 1/3 = 5/6. The answer is reduced by dividing the top and bottom by their greatest common divisor.
The link saves your inputs so you can bookmark or share this exact result.
How the fraction calculator works
This tool combines two fractions using whichever operation you pick and returns the answer reduced to lowest terms alongside its decimal value. For addition it computes the top as n1 times d2 plus n2 times d1 over d1 times d2, and subtraction is the same with a minus; multiplication multiplies the tops and the bottoms straight across; division flips the second fraction and multiplies, so n1 times d2 over d1 times n2.
After the raw result is formed, the calculator divides the top and bottom by their greatest common divisor to simplify, and it pushes any negative sign onto the numerator so the denominator stays positive. If the simplified bottom is 1 the answer is shown as a whole number. The decimal is the raw value rounded to four places.
How to use the fraction calculator
- Type the numerator and denominator of the first fraction.
- Choose add, subtract, multiply or divide from the operation dropdown.
- Type the second fraction. The reduced result and its decimal update as you type.
Worked examples
Adding two simple fractions
Inputs: 1/2 add 1/3
Result: The common denominator is 6, giving 3/6 plus 2/6 equals 5/6, or about 0.8333 as a decimal.
Dividing fractions
Inputs: 1/2 divide 1/3
Result: Dividing flips the second fraction, so 1/2 times 3/1 equals 3/2, which displays as 3/2 and 1.5000 as a decimal.
Limitations and common mistakes
Edge cases and limitations
- Inputs are whole numbers, so mixed numbers like 2 and 1/4 must first be converted to an improper fraction such as 9/4.
- The decimal is rounded to four places, so repeating decimals like 0.8333 are shown truncated rather than exact.
- A zero in either denominator, or dividing by a fraction whose numerator is zero, is undefined and the result shows a guard message.
Common mistakes
- Adding the numerators and denominators straight across (1/2 plus 1/3 is not 2/5); you must use a common denominator first.
- Forgetting that dividing by a fraction means multiplying by its reciprocal, not dividing top by top and bottom by bottom.
Frequently asked questions
How do you add two fractions?
Put both fractions over a shared denominator, add the numerators, then reduce. For 1/2 plus 1/3, the common denominator is 6, so you get 3/6 plus 2/6, which is 5/6 (about 0.8333). This calculator does that step automatically.
How do you divide fractions?
Dividing by a fraction is the same as multiplying by its reciprocal: flip the second fraction and multiply. So 1/2 divided by 1/3 becomes 1/2 times 3/1, which is 3/2 or 1.5.
What does it mean to simplify a fraction?
Simplifying means dividing the numerator and denominator by their greatest common divisor so the fraction uses the smallest whole numbers possible. For example 4/8 simplifies to 1/2 because both share a factor of 4.
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