Fraction Calculator with Step by Step Details

Add, subtract, multiply, or divide two fractions by entering the fractions, using a slash (/) symbol as the separator, and a math operator.

Add, subtract, multiply, or divide these fractions

Solution:

23+34=1512

Find the least common denominator so that all of the denominators match
The least common denominator of 3 and 4 is 12
Find the multiple for each fraction that can be multiplied by the denominator to get the least common denominator
Find the multiple by dividing the least common denominator by each fractions denominator
Fraction 1 Multiple: 12 ÷ 3 = 4
Fraction 2 Multiple: 12 ÷ 4 = 3
Multiply each fractions numerator and denominator by the multiple
2 × 43 × 4+3 × 34 × 3=812+912
Now that the denominators of each fraction are the same, simply add the numerators
8 + 912=1712
Reduce the fraction by finding the greatest common factor. The greatest common factor of 17 and 12 is 1
Divide the numerator and denominator by the greatest common factor (1)
17 ÷ 112 ÷ 1=1712
Convert the fraction to a mixed fraction by finding the whole number and remainder
17÷12=1R5
1712=1512
Find the decimal by dividing the numerator by the denominator
1712=17÷12=1.4166666666667


Using the Fraction Calculator

Enter your fractions in the fields above and select the appropriate operator to add, subtract, multiply, or divide the fractions. The calculator will show it’s work and provide a detailed explanation of how it arrived at the answer. If you’re adding inch fractions see our inch fraction calculator. Also see our complete suite of fraction math tools.

How to Add & Subtract Fractions

Adding and subtracting fractions is a little different than adding normal whole numbers. There are 3 easy steps to add or subtract fractions.

Follow along to see an example showing how to add 13 and 14.

one pie graph with three total slices and one slice highlighted and a second pie graph with four total slices and one slice highlighted

Step One: Convert to Fractions with a Common Denominator

The first step when adding or subtracting fractions is to convert the fractions to equivalent fractions that have the same denominator.

To do this, start by finding the lowest common denominator for the denominators of both fractions. The lowest common denominator is the smallest number that both denominators can be divided into evenly.

If you’re not sure how to find the lowest common denominator, check out our lowest common denominator calculator.

Next, find the multiple for each denominator that can be multiplied to reach the common denominator. This can be found by dividing the common denominator by each denominator.

Then, multiply both the numerator and denominator by the multiple to find the equivalent fractions with matching denominators.

For example, let’s convert the fractions 13 and 14 to fractions that have the same denominator.


Find the least common denominator. The least common denominator of 3 and 4 is 12.


Find the multiple for 13
multiple = lcd ÷ denominator
multiple = 12 ÷ 3 = 4

Find the equivalent fraction of 13 using the multiple 4
13 = (1 × 4)(3 × 4)
13 = 412


Find the multiple for 14
multiple = lcd ÷ denominator
multiple = 12 ÷ 4 = 3

Find the equivalent fraction of 14using the multiple 3
14 = (1 × 3)(4 × 3)
14 = 312


Thus, the equivalent fractions of 13 and 14 are 412 and 312

one pie graph with twelve total slices and four slices highlighted and a second pie graph with twelve total slices and three slices highlighted

Step Two: Add or Subtract the Numerators

Once the denominators are all the same, adding and subtracting fractions is as simple as adding or subtracting the numerators.

To add, simply add the numerators together and put them over the common denominator.

To subtract, find the difference of the numerators and put the difference over the common denominator.

For example, let’s continue the previous example and add 412 & 312.

412 + 312 = (4 + 3)12
412 + 312 = 712

After both fraction denominators are the same, add numerators together to solve

Step Three: Simplify the Fraction

The final step to adding or subtracting fractions is to simplify the result fraction. Start by finding the greatest common factor of both the numerator and the denominator. Learn more about finding the greatest common factor for more details.

Then, divide both the numerator and denominator by the greatest common factor to reduce. Use our reduce fraction calculator to simplify a fraction and show the work needed to do so.

How to Multiply Fractions

Multiplying two fractions is quite a bit simpler than adding or subtracting them, and it can be done in two easy steps.

Step One: Multiply the Numerators and Denominators

The first step is to multiply the numerators together and multiply the denominators together. The resulting fraction might be an improper fraction, but we’ll reduce it in the next step.

For example, let’s multiply 23 × 34.

23 × 34 = (2 × 3)(3 × 4)
23 × 34 = 612

Step Two: Simplify the Fraction

Like adding and subtracting, the final step of multiplying fractions is to simplify. To simplify, find the greatest common factor of both the numerator and denominator, then divide both of them by the common factor.

To simplify 612, find the greatest common factor.

The greatest common factor of 6 and 12 is 6.


Next, divide both the numerator and denominator by the greatest common factor.

612 = (6 ÷ 6)(12 ÷ 6)
612 = 12

How to Divide Fractions

There are two steps to divide one fraction by another.

Step One: Multiply Each Numerator by the Opposite Denominator

To divide one fractoin by another, start by multiplying the first numerator by the second denominator. Then multiply the second numerator by the first denominator.

For example, let’s divide 23 by 34.

23 ÷ 34= (2 × 4)(3 × 3)
23 ÷ 34= 89

Step Two: Simplify the Fraction

Just like when multiplying fractions, the final step of dividing them is to simplify the fraction. See the instructions to simplify a fraction above.