Mixed Number Calculator
Use our mixed number calculator below to add, subtract, multiply, or divide mixed fractions.
Result:
Result as a Decimal:
Steps to Solve Expression with Fractions
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How to Calculate Mixed Numbers
A mixed number is a whole number and fraction (representing a part of the whole) combined. Calculating mixed numbers is very similar to calculating fractions, but with one extra step.
You can use the calculator above to calculate mixed numbers, but you can also calculate them by hand as well.
You can add or subtract mixed numbers in a few simple steps,
Step One: Convert the Mixed Numbers to Improper Fractions
The first step in calculating mixed numbers is to convert each one to an improper fraction. An improper fraction is a fraction with a numerator that is greater than or equal to the denominator.
To convert a mixed number to an improper fraction, multiply the whole number by the fraction’s denominator, then add that product to the fraction’s numerator. The result is the numerator for the improper fraction. Use the denominator from the original fraction as the new denominator.
Repeat this process for each mixed number.
Step Two: Convert to Fractions with Matching Denominators
To calculate mixed numbers in improper fraction form, you need to make sure the fractions have the same denominator. Convert each fraction to an equivalent fraction with the same denominators.
To do this, find the lowest common denominator (LCD), which is the smallest number that both denominators can divide into evenly.
Once you have found the lowest common denominator, you will then find what factor you need to multiply each fraction to make the denominators match. To do this, divide the LCD by the denominator of each fraction.
Then, multiply both the numerator and denominator by the factor to find the equivalent fractions with matching denominators.
For example, let’s convert the fractions 5/3 and 7/4 to fractions with the same denominator.
5 / 3 = 5 × 4 / 3 × 4 = 20 / 12
7 / 4 = 7 × 3 / 4 × 3 = 21 / 12
Step Three: Add or Subtract the Numerators
Once the denominators are matching, you can add or subtract the numerators to calculate the improper fraction.
To add the mixed numbers, add the numerators together and put the result over the common denominator.
To subtract them, subtract one numerator from the other and put the result over the common denominator.
For example, continuing the previous example, let’s add 20/12 and 21/12.
20 / 12 + 21 / 12 = 20 + 21 / 12 = 41 / 12
Step Four: Simplify the Improper Fraction
The final step is to simplify the resulting fraction back into a mixed number. Start by finding the greatest common factor of both the numerator and the denominator.
Then, divide both the numerator and denominator by the greatest common factor to reduce.
And finally, if the resulting numerator is greater than or equal to the denominator, you’ll need to convert it to a mixed number.
You can do this using long division to find the quotient and remainder of the fraction. The quotient will be the whole number, and the remainder will be the numerator of the new fraction.
For example, the fraction 41/12 is already in its simplest form, but it can still be converted to a whole number.
Using long division, 41 divided by 12 is equal to 3 with a remainder of 5.
41 ÷ 12 = 3 R 5
So, we can rewrite the fraction 41/12 as the mixed number 3 5/12.
You can also use our improper fraction to mixed number calculator to convert this.