A fraction is a number that represents a part of a whole. It has two parts: the numerator, which shows how many parts we have, and the denominator, which shows how many equal parts make up the whole. Fractions can be proper, improper, or mixed, depending on the relationship between the numerator and denominator. You can use fractions to represent quantities that are not whole numbers and perform operations such as addition, subtraction, multiplication, and division.
Addition
When adding fractions, the denominators need to be the same. If they are different, first find a common denominator. Then add the numerators and simplify the answer.
Formula:
a/b + c/d = (ad + bc)/bd
Example 1:
Let us add 2/7 and 3/5.
2/7 + 3/5 = (2 × 5)/(7 × 5) + (3 × 7)/(5 × 7)
= 10/35 + 21/35
= 31/35
Example 2:
Now consider three fractions:
1/4 + 2/3 + 1/6
A common denominator for 4, 3, and 6 is 12. Convert each fraction to a denominator of 12:
1/4 + 2/3 + 1/6 = 3/12 + 8/12 + 2/12
= 13/12
= 1 1/12
Subtraction
Formula:
a/b − c/d = (ad − bc)/bd
Example:
Let us subtract 3/4 from 5/6.
5/6 − 3/4 = (5 × 4)/(6 × 4) − (3 × 6)/(4 × 6)
= 20/24 − 18/24
= 2/24
= 1/12
Multiplication
Multiplying fractions is usually simpler than adding or subtracting them. You do not need a common denominator. Simply multiply the numerators together and the denominators together, then simplify the result.
Formula:
a/b × c/d = (a × c)/(b × d)
Example:
Let us multiply 3/8 by 5/6.
3/8 × 5/6 = (3 × 5)/(8 × 6)
= 15/48
= 5/16
Division
To divide fractions, keep the first fraction as it is, change the division sign to multiplication, and take the reciprocal of the second fraction. Then multiply the fractions and simplify the answer.
Formula:
a/b ÷ c/d = a/b × d/c = (a × d)/(b × c)
Example 1:
Let us divide 3/5 by 2/7.
3/5 ÷ 2/7 = 3/5 × 7/2
= (3 × 7)/(5 × 2)
= 21/10
= 2 1/10
Example 2:
Now consider another example:
4/9 ÷ 2/3 = 4/9 × 3/2
= 12/18
= 2/3
FAQ About Fraction Calculator
How Does the Fraction Calculator Work?
Enter the numerator and denominator for each fraction you want to calculate. If you are working with a mixed fraction, you can also enter the whole number; otherwise, leave the whole-number field empty. Select the operation you want to perform, such as addition, subtraction, multiplication, or division, and click the calculate button. The calculator processes the fractions, simplifies the result, and displays the answer in the simplest form.
What Is the Least Common Denominator?
The least common denominator (LCD) is the smallest number that can be used as the denominator for two or more fractions. It is especially helpful when adding or subtracting fractions that have different denominators. For example, take the fractions 1/4 and 1/6. Their denominators are 4 and 6, and the smallest number that both can divide into evenly is 12. So, 12 is the LCD.
We can rewrite the fractions as:
1/4 = 3/12
1/6 = 2/12