Mixed Fraction Calculator

Mixed fraction calculator at a glance#

A mixed fraction calculator adds, subtracts, multiplies or divides mixed numbers like 2 1/2 and 1 1/3. It first turns each mixed number into an improper fraction, does the operation, then converts the answer back to a mixed number in simplest form.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator, keeping the same denominator. So 2 1/2 is (2 times 2) plus 1, over 2, which is 5/2. In the same way 1 1/3 is (1 times 3) plus 1, over 3, which is 4/3.

Example: 2 1/2 + 1 1/3#

Convert both to improper fractions: 2 1/2 is 5/2 and 1 1/3 is 4/3. Put them over a common denominator of 6: 5/2 is 15/6 and 4/3 is 8/6. Add the numerators: 15/6 plus 8/6 is 23/6. Convert back by dividing 23 by 6, which is 3 with a remainder of 5, so the answer is 3 5/6.

Enter your mixed numbers and the operation in the calculator above for the exact result, shown as a mixed number and a fraction. Answers are reduced to lowest terms, and the same convert-to-improper method works for subtraction, multiplication and division.

Adding and subtracting mixed fractions#

To add or subtract mixed fractions, convert each one to an improper fraction, put them over a common denominator, then add or subtract the numerators. The denominator stays the same; only the numerators combine. Convert the answer back to a mixed fraction at the end.

Subtract 3 1/4 minus 1 2/3. As improper fractions these are 13/4 and 5/3. The common denominator of 4 and 3 is 12, giving 39/12 and 20/12. Subtract the numerators: 39/12 minus 20/12 is 19/12, which is 1 7/12.

Multiplying and dividing mixed fractions#

Multiplication and division skip the common denominator. Convert both mixed fractions to improper fractions first. To multiply, multiply the numerators together and the denominators together. To divide, flip the second fraction and multiply.

Multiply 1 1/2 by 2 2/3. These are 3/2 and 8/3. Multiply across: (3 times 8) over (2 times 3) is 24/6, which reduces to 4. To divide 2 1/2 by 1 1/4, write them as 5/2 and 5/4, flip the second to 4/5, then multiply: (5 times 4) over (2 times 5) is 20/10, which is 2.

Reducing the result to lowest terms#

Always reduce the final fraction. Find the greatest common factor of the numerator and denominator, then divide both by it. For 24/6 the greatest common factor is 6, so it reduces to 4/1, a whole number. Reducing first, before converting back to a mixed fraction, keeps the numbers small and the answer in its standard form.

A scaling example#

Mixed fractions show up whenever you scale a recipe. A recipe uses 2 1/2 cups of flour for 4 portions, and you want 8 portions. Doubling means multiplying 2 1/2 by 2. As an improper fraction 2 1/2 is 5/2, and 5/2 times 2 is 10/2, which is 5 cups. The same convert, multiply, reduce steps handle any scaling factor.

Frequently asked questions#

How do you add two mixed fractions?#

Convert each to an improper fraction, put them over a common denominator, add the numerators, then convert back. For 1 1/2 plus 2 1/3, use 3/2 and 7/3 over a denominator of 6: 9/6 plus 14/6 is 23/6, which is 3 5/6.

How do you divide mixed fractions?#

Turn both into improper fractions, flip the second one, and multiply. Dividing 3 1/2 by 1 3/4 means 7/2 divided by 7/4, which is 7/2 times 4/7. That gives 28/14, or 2.

Why convert mixed fractions to improper fractions before calculating?#

An improper fraction holds the whole part and the fraction part as one number, so a single rule covers the operation. Working on the whole numbers and fractions separately invites mistakes, especially with subtraction that borrows or with multiplication and division.

What is the difference between a mixed fraction and an improper fraction?#

A mixed fraction writes a value greater than one as a whole number plus a proper fraction, like 1 3/4. An improper fraction writes the same value as a single fraction whose numerator is at least its denominator, like 7/4. They are equal; the mixed form is easier to read, the improper form is easier to calculate with.

Can the answer come out as a whole number?#

Yes. When the final improper fraction reduces to a denominator of 1, the result is a whole number. For example, 1 1/2 times 2 2/3 works out to 24/6, which is 4 with no fraction left over.