Fraction Calculator

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

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

1. Find a common denominator.
2. Convert the fractions to that denominator.
3. Add the numerators.
4. Keep the common denominator.
5. 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

1. Find a common denominator.
2. Convert the fractions to that denominator.
3. Subtract the numerators.
4. Keep the common denominator.
5. 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

1. Multiply the numerators.
2. Multiply the denominators.
3. Write the products as a fraction.
4. 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

1. Find the GCF of the numerator and denominator.
2. Divide both numbers by the GCF.
3. 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:

1. Count the digits after the decimal point.
2. Write the decimal digits as the numerator.
3. Use 10, 100, 1,000, and so on as the denominator.
4. Simplify the fraction.

Fraction to decimal:

1. Divide the numerator by the denominator.
2. Write the result as a decimal.