Fraction Calculator
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Fraction Calculators
Best fraction calculators to add, subtract, multiply, and divide fractions with step-by-step explanations. You can also simplify fractions and convert fractions to decimals and decimals to fractions.
What Is a Fraction?
A fraction is a number that shows a part of a whole.
A fraction has two numbers:
- Numerator: The top number. It tells us how many parts we have.
- Denominator: The bottom number. It tells us how many equal parts make up the whole.
For example, in 3/8:
- 3 is the numerator.
- 8 is the denominator.
Imagine a pizza divided into 8 equal slices. If you have 3 slices, you have 3/8 of the pizza.
The denominator cannot be 0 because a fraction with zero as the denominator is undefined.
In short:
Numerator = parts you have
Denominator = total equal parts
Main Types of Fractions
Fractions can be grouped into different types based on their numerator, denominator, or how they relate to other fractions.
Proper Fraction
A fraction where the numerator is smaller than the denominator. Its value is less than 1.
Examples: 2/3, 4/5
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator. Its value is 1 or more.
Examples: 7/6, 11/9, 5/5
Mixed Fraction
A whole number combined with a proper fraction. It represents a value greater than 1.
Examples: 3 1/3, 5 2/3
Unit Fraction
A fraction with 1 as its numerator.
Examples: 1/2, 1/3, 1/4
Like Fractions
Fractions that have the same denominator.
Examples: 2/7, 3/7, 5/7
Unlike Fractions
Fractions that have different denominators.
Examples: 2/3, 4/5, 9/50
Equivalent Fractions
Different fractions that have the same value.
Examples: 3/4, 6/8, 9/12
How to Add Fractions?
To add fractions, the fractions must have the same denominator. If the denominators are different, first find a common denominator.
Adding Fractions With the Same Denominator
If the denominators are already the same, add the numerators and keep the denominator.
For example:
2/9 + 4/9 = 6/9 = 2/3
Adding Fractions With Different Denominators
When the denominators are different, find a common denominator first. Using the least common multiple (LCM) is usually the easiest method.
For example:
2/5 + 1/3
The LCM of 5 and 3 is 15.
Convert both fractions to a denominator of 15:
- 2/5 = 6/15
- 1/3 = 5/15
Now add the numerators:
6/15 + 5/15 = 11/15
Adding Three or More Fractions
The same method works for three or more fractions.
For example:
1/3 + 1/4 + 1/6
The LCM of 3, 4, and 6 is 12.
- 1/3 = 4/12
- 1/4 = 3/12
- 1/6 = 2/12
Now add the numerators:
4/12 + 3/12 + 2/12 = 9/12 = 3/4
Quick Steps for Adding Fractions
- Find a common denominator.
- Convert the fractions to that denominator.
- Add the numerators.
- Keep the common denominator.
- Simplify the answer if possible.
How to Subtract Fractions?
Subtracting fractions works almost the same way as adding fractions. The fractions must have the same denominator before you subtract them.
Subtracting Fractions With the Same Denominator
If the denominators are already the same, subtract the numerators and keep the denominator.
For example:
8/11 - 3/11 = 5/11
Subtracting Fractions With Different Denominators
If the denominators are different, find a common denominator first.
For example:
5/6 - 1/4
The LCM of 6 and 4 is 12.
Convert both fractions to a denominator of 12:
- 5/6 = 10/12
- 1/4 = 3/12
Now subtract the numerators:
10/12 - 3/12 = 7/12
Quick Steps for Subtracting Fractions
- Find a common denominator.
- Convert the fractions to that denominator.
- Subtract the numerators.
- Keep the common denominator.
- Simplify the answer if possible.
How to Multiply Fractions?
Multiplying fractions is simple. You do not need to find a common denominator. Just multiply the numerators together and the denominators together.
For example:
2/3 × 4/5 = 8/15
The steps are:
- Multiply the numerators: 2 × 4 = 8
- Multiply the denominators: 3 × 5 = 15
- Write the result as 8/15
If the result can be reduced, simplify the fraction.
For example:
3/4 × 2/3 = 6/12 = 1/2
Quick Steps
- Multiply the numerators.
- Multiply the denominators.
- Write the products as a fraction.
- Simplify the answer if possible.
How to Simplify Fractions?
Simplifying a fraction means reducing it to its lowest terms. This makes the fraction easier to read and use.
To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF).
For example:
20/40 = 1/2
The GCF of 20 and 40 is 20. Divide both numbers by 20:
- 20 ÷ 20 = 1
- 40 ÷ 20 = 2
So, 20/40 simplifies to 1/2.
Quick Steps
- Find the GCF of the numerator and denominator.
- Divide both numbers by the GCF.
- Write the resulting fraction in its lowest terms.
How to Convert Fractions and Decimals?
You can convert a decimal to a fraction by using the place value of the last digit. You can convert a fraction to a decimal by dividing the numerator by the denominator.
How to Convert a Decimal to a Fraction
Count the number of digits after the decimal point. Use the corresponding power of 10 as the denominator.
For example:
0.125
There are three digits after the decimal point, so use 1,000 as the denominator:
0.125 = 125/1000
Now simplify the fraction:
125/1000 = 1/8
So, 0.125 = 1/8.
How to Convert a Fraction to a Decimal
To convert a fraction to a decimal, divide the numerator by the denominator.
For example:
3/8
Divide 3 by 8:
3 ÷ 8 = 0.375
So, 3/8 = 0.375.
For fractions with denominators such as 10, 100, or 1,000, you can also convert them by using decimal place values.
For example:
7/10 = 0.7
7/100 = 0.07
Quick Steps
Decimal to fraction:
- Count the digits after the decimal point.
- Write the decimal digits as the numerator.
- Use 10, 100, 1,000, and so on as the denominator.
- Simplify the fraction.
Fraction to decimal:
- Divide the numerator by the denominator.
- Write the result as a decimal.
Fraction to Percentage Conversion Chart
Fraction to percentage conversion chart from 1 to 20. It provides the fractional percentages for numbers divided by 1-20, such as 1/1 = 100%, 1/2 = 50%, etc. The chart tables provide the fractional percentages for easy reference.
