Online Fraction Calculator with "Step by Step" explanation of the solution

Add fractions, subtract fractions, multiply fractions, divide fractions

With this fraction calculator, you can add, subtract, multiply and divide fractions. This is how the calculator works:

1. Create 2 fractions by typing numbers in the Entry fields.
2. Choose to add, subtract, multiply or divide.
3. Click on "Calculate".

This calculator provides the result and "Step by Step" explanation of the entered sum.

Tip: If you do not understand the result of a calculation with fractions, you can have it calculated by calculator and then study the "Step by Step" explanation.

Allowed Inputs

Fractions with and without whole numbers (integer and non-integer)

In this calculator you can enter fractions with and without whole numbers (integers).

• A fraction with whole(s) is made by entering a number in 3 fields.
• In the case of a fraction without a whole, you leave the left Entry field empty.
• Only whole numbers (integers) without a fraction are allowed.
  

Fractions and negative numbers

The calculator also accepts negative numbers. Below are some examples of allowed entries with negative numbers.

Explanation of fractions

Adding fractions

When adding fractions, it is important whether the fractions are eponymous or dissimilar. If the fractions to be added are eponymous, then the following applies to the result:

Numerator = Sum of Numerators
Denominator = Denominator of the fractions to be added

Example: 2/4 + 1/4

• Sum of Numerators = 2 + 1 = 3
• Denominator of fractions to be added = 4

So: 2/4 + 1/4 = 3/4

If the fractions to be added are dissimilar, they must first be made eponymous (similar).

Example: 1/2 + 1/3

• 1/2 = 3/6
• 1/3 = 2/6

So: 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Subtracting fractions

Subtracting fractions works almost the same as adding fractions. The only difference is that Numerators now do not have to be added but subtracted from each other.

Multiplying fractions

The product of 2 or more fractures is a fraction for which the following applies:

Numerator = Product of Numerators
Denominator = product of the Denominators

Example: 3/2 × 5/2

• product of the Numerators = 3 × 5 = 15
• product of the Denominators = 2 × 2 = 4

So: 3/2 × 5/2 = 15/4
The result as a composite fraction: 3 3/4

To calculate the product of composite fractions in this way, you must first write them as ordinary fractions.

Example: 3 1/4 × 2 1/2

3 1/4 × 2 1/2 =
13/4 × 5/2 =
65/8 =
8 1/8

Instead of the above calculation, you can also choose to write the composite fractions as a sum of whole number(s) and a regular fraction. After that you can get rid of the brackets and then work out the result.

3 1/4 × 2 1/2 =
(3 + 1/4) × (2 + 1/2) =
3×2 + 3×1/2 + 1/4×2 + 1/4×1/2 =
6 + 3/2 + 2/4 + 1/8 =
6 + 1 1/2 + 1/2 + 1/8 =
8 + 1/8 =
8 1/8

Both calculations show: 3 1/4 × 2 1/2 = 8 1/8

Dividing fractions

The outcome of a division with a fraction can be found using the following rule:

divide = multiply by the reverse

Example: 2/5 ÷ 4/3

2/5 ÷ 3/4 =
2/5 × 4/3 =
8/15

So: 2/5 ÷ 3/4 = 8/15

Remember:

• The inverse of an integer is a fraction with that number as denominator and 1 as numerator (so the inverse of 2 is 1/2).
  
• The inverse of a composite fraction can be found by first making a regular fraction (e.g.: 1 1/2 = 3/2 and the inverse of that is 2/3).