Mixed Number Calculator

Mixed number calculator at a glance#

A mixed number calculator converts between improper fractions and mixed numbers and operates on them. To turn an improper fraction into a mixed number, divide the numerator by the denominator: the whole-number part is the quotient and the leftover sits over the same denominator. So 7/2 is 7 divided by 2, which is 3 with a remainder of 1, written 3 1/2.

To go the other way, multiply the whole number by the denominator and add the numerator. So 2 3/4 is (2 times 4) plus 3, over 4, which is 11/4.

Enter your fraction or mixed number in the calculator above for the exact conversion and simplest form. The result is reduced to lowest terms, so a value that simplifies, such as 4/2, returns as the whole number 2 rather than 2/1.

Converting a mixed number to a decimal#

To write a mixed number as a decimal, divide the numerator of the fraction part by its denominator, then add the whole number. The whole number sits to the left of the decimal point and the fraction becomes the digits to the right.

For 3 1/2, divide 1 by 2 to get 0.5, then add 3, giving 3.5. For 2 3/4, divide 3 by 4 to get 0.75, then add 2, giving 2.75. Some fractions repeat: 1 1/3 is 1 plus 0.333..., written 1.3 with the 3 repeating, so round to as many places as you need.

Converting a decimal back to a mixed number#

Going the other way, the digits before the decimal point are the whole number. Put the digits after the point over their place value, then reduce. For 3.5, the whole part is 3 and 0.5 is 5/10, which reduces to 1/2, so the mixed number is 3 1/2. For 2.875, the whole part is 2 and 0.875 is 875/1000, which reduces to 7/8, giving 2 7/8.

Reducing to simplest form#

After any conversion, reduce the fraction part by dividing the numerator and denominator by their greatest common factor. A mixed number is only in standard form when its fraction part is proper, meaning the numerator is smaller than the denominator, and fully reduced. If the fraction part reduces to a whole, the result is a plain whole number: 4/2 becomes 2, not 2 0/1.

Negative mixed numbers#

A negative mixed number applies the minus sign to the whole value, not just the whole-number part. So -2 1/4 means the negative of 2 1/4, which is -9/4 as an improper fraction and -2.25 as a decimal. Treat the sign separately, convert the size, then put the sign back on the result.

Frequently asked questions#

How do you convert an improper fraction to a mixed number?#

Divide the numerator by the denominator. The quotient is the whole number, the remainder goes over the original denominator, and you reduce if possible. For 17/5, 17 divided by 5 is 3 with a remainder of 2, so the mixed number is 3 2/5.

How do you turn a mixed number into a decimal?#

Divide the fraction part and add the whole number. For 5 1/4, 1 divided by 4 is 0.25, plus 5 is 5.25. Fractions like thirds and sevenths give repeating decimals, so round them where needed.

What is 35.875 as a mixed number?#

The whole part is 35. The decimal 0.875 is 875/1000, which reduces to 7/8. So 35.875 is 35 7/8.

Why does the calculator turn some answers into whole numbers?#

When the fraction part reduces to a denominator of 1, there is no leftover fraction, so the value is a whole number. For instance, 6/3 is 2, and the calculator shows 2 rather than 2 0/1 or 2/1.

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

They represent the same value greater than one in two formats. A mixed number splits it into a whole number and a proper fraction, like 2 3/4. An improper fraction keeps it as a single fraction with the numerator at least as large as the denominator, like 11/4.