Fraction Calculator
Add, subtract, multiply, and divide fractions quickly and accurately. Enter two fractions and choose an operation to calculate the result.
What Is a Fraction?
A fraction is a number that represents a part of a whole. It consists of a numerator and a denominator.
The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up the whole.
Fraction Operations
Fractions can be added, subtracted, multiplied, and divided. The method used depends on the operation.
Adding Fractions
To add fractions with different denominators, first find a common denominator. Then convert each fraction to an equivalent fraction with that denominator and add the numerators.
a/b + c/d = (ad + bc) / bd
3/4 + 1/6 = 11/12
Subtracting Fractions
Fraction subtraction follows the same basic process as addition. Find a common denominator, convert the fractions, and subtract the numerators.
a/b − c/d = (ad − bc) / bd
3/4 − 1/6 = 7/12
Multiplying Fractions
To multiply fractions, multiply the numerators together and multiply the denominators together. Then simplify the resulting fraction if possible.
a/b × c/d = ac/bd
3/4 × 1/6 = 1/8
Dividing Fractions
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
a/b ÷ c/d = a/b × d/c = ad/bc
3/4 ÷ 1/6 = 9/2
Simplifying Fractions
A fraction is in simplest form when the numerator and denominator have no common factor other than 1. To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF).
220/440 = 1/2
21/98 = 3/14
Converting Between Fractions and Decimals
Decimals can be converted to fractions by using the place value of the last digit and then simplifying the resulting fraction.
0.1234 = 1234/10000 = 617/5000
1/2 = 0.5
5/100 = 0.05
For fractions whose denominators are powers of 10, the conversion to a decimal can be done directly. Other fractions can be converted using division.
Frequently Asked Questions
What is a fraction?
A fraction represents a part of a whole and consists of a numerator and a denominator. The numerator shows the number of parts being considered, while the denominator shows the total number of equal parts.
Can a denominator be zero?
No. A denominator cannot be zero because division by zero is undefined. The calculator will display an error if a zero denominator is entered.
How are fractions added?
Fractions with different denominators must first be converted to equivalent fractions with a common denominator. The numerators are then added and the result is simplified.
How are fractions multiplied?
Multiply the numerators together and multiply the denominators together. The resulting fraction is then simplified if necessary.
How are fractions divided?
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to its lowest terms by dividing the numerator and denominator by their greatest common factor.
Can fractions be converted to decimals?
Yes. A fraction can be converted to a decimal by dividing the numerator by the denominator.
Disclaimer
This calculator is provided for general mathematical and educational purposes. While we aim to provide accurate results, SmartMyTools does not guarantee that the results are suitable for professional, academic, financial, engineering, or other specialized applications.