Adding Fractions Calculator
Add two fractions by entering them below. You can optionally add a whole number for a mixed fraction as well.
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Steps to Solve Expression with Fractions
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How to Add Fractions
A fraction is a numerical value that is not a whole number, and it generally represents a portion of a whole (like one slice of a pizza).
Adding fractions is a bit different from adding regular whole numbers, but you can use a few methods to do it.
Fraction Addition Formula
The first method for adding fractions is to use a formula.
a / b + c / d = ad + bc / bd
To add two fractions, divide the sum of the product of the numerator of the first fraction a and denominator of the second fraction d and the product of the denominator of the first fraction b and numerator of the second fraction c by the product of the denominators of both fractions b and d.
By multiplying the denominators together, the formula ensures that they both match and are both raised to a common denominator.
The numerators are also multiplied using the same multiple as the denominator, resulting in an equivalent fraction.
Then, the resulting numerators can simply be added together.
You can put this formula to practice and add two fractions in three easy steps.
Follow along with this example showing how to add 1 / 3 and 1 / 4.
Step One: Convert to Fractions with a Common Denominator
The first step to adding fractions is to make the denominators of each fraction match. Convert each one to an equivalent fraction with a matching denominator to the other.
Find the Lowest Common Denominator
You’ll need to find the lowest common denominator for each of the fraction’s denominators. The lowest common denominator is the smallest number that the different denominators can evenly divide into.
Find the Multiplier
Next, find the multiple for each denominator that can be multiplied by to equal the lowest common denominator. To find the multiple for each fraction, divide the least common denominator by the denominator.
Multiply by the Multiplier
Then, multiply both the top and bottom number of the fraction by the multiple to find the equivalent fractions with matching denominators. You can also use an equivalent fractions calculator to find one with a matching denominator.
For example, let’s convert the fractions 1 / 3 and 1 / 4 to fractions with the same denominator.
Find the least common denominator. The least common denominator of 3 and 4 is 12.
Find the multiple for 1 / 3
multiple = lcd ÷ denominator
multiple = 12 ÷ 3 = 4
Find the equivalent fraction of 1 / 3 using the multiple 4
1 / 3 = 1 × 4 / 3 × 4
1 / 3 = 4 / 12
Find the multiple for 1 / 4
multiple = lcd ÷ denominator
multiple = 12 ÷ 4 = 3
Find the equivalent fraction of 1 / 4using the multiple 3
1 / 4 = 1 × 3 / 4 × 3
1 / 4 = 3 / 12
Thus, the equivalent fractions of 1 / 3 and 1 / 4 are 4 / 12 and 3 / 12
Step Two: Add the Numerators
Once the bottom numbers of each fraction match, add the top numbers of each together to find the result.
Simply add the numerators together and put them over the common denominator.
For example, let’s continue the previous example and add 4 / 12 & 3 / 12.
4 / 12 + 3 / 12 = 4 + 3 / 12
4 / 12 + 3 / 12 = 7 / 12
Step Three: Simplify the Fraction
The final addition step is to reduce the resulting fraction to its simplest form. Start by finding the greatest common factor of the top and bottom parts of the result.
Then, divide both the top and bottom numbers by the greatest common factor to reduce it to the lowest terms. An even easier way to reduce is to use our fraction simplifier.
We also have a calculator to multiply fractions or divide fractions.
How to Add Mixed Numbers
A mixed number is a number with both a whole number and a proper fraction. The process of adding mixed numbers is nearly the same as adding a normal fraction with one more step.
The first thing to do when adding mixed numbers is to make the fractions improper fractions by removing the whole number and moving it to the numerator. You can use a mixed number to fraction calculator or follow the steps below.
To do this, multiply the whole number by the denominator, then add this to the fraction numerator.
For example, let’s convert the mixed number 1 2 / 3 to an improper fraction.
Multiply the whole number by the denominator.
1 × 3 = 3
Next, add the result to the numerator.
3 + 2 = 5
Finally, rewrite the fraction.
1 2 / 3 = 5 / 3
How to Add Negative Fractions
A negative fraction is one with a minus sign either in front of the fraction or in front of the numerator or denominator.
–a / b = -a / b = a / -b
Negative fractions have only one negative sign. So, if both the numerator and the denominator have a negative sign, then the fraction is actually positive.
When adding negative fractions, it’s easiest to put the sign on the numerator, which allows you to use the fraction addition formula above.