Fraction to Mixed Number Calculator

What is a fraction to mixed number calculator?

A fraction to mixed number calculator rewrites an improper fraction, where the numerator is greater than or equal to the denominator, as a mixed number. A mixed number combines a whole number with a proper fraction, and this calculator also reduces that fraction to its lowest terms. For example, 7/2 becomes 3 1/2, and 9/3 becomes the whole number 3. Mixed numbers are how we usually read fractions in recipes, on tape measures, and in everyday measurements, because 3 1/2 is easier to picture than the top-heavy 7/2.

How does it work?

Given a numerator $n$ and a denominator $d$ (with $d \neq 0$), the whole part is the integer result of the division and the remainder is what is left over:

The remainder over the original denominator is the fractional part. To present it in lowest terms, divide both the remainder and the denominator by their greatest common divisor $g = \gcd(\text{remainder}, d)$:

When the remainder is 0 the fraction disappears and the result is simply the whole number. The calculator stays blank until both fields are filled in and the denominator is not zero.

Worked examples

Convert 7/2 to a mixed number.

• Whole part: $\left\lfloor 7 / 2 \right\rfloor = 3$
• Remainder: $7 - 3 \cdot 2 = 1$
• The fraction 1/2 is already reduced, so 7/2 equals 3 1/2.

Convert 11/4 to a mixed number.

• Whole part: $\left\lfloor 11 / 4 \right\rfloor = 2$
• Remainder: $11 - 2 \cdot 4 = 3$
• The fraction 3/4 is already reduced, so 11/4 equals 2 3/4.

Convert 9/3 to a mixed number.

• Whole part: $\left\lfloor 9 / 3 \right\rfloor = 3$
• Remainder: $9 - 3 \cdot 3 = 0$
• With no remainder the result is just the whole number 3.

Practical notes

• The fractional part is always reduced. For instance 8/6 gives a whole part of 1 and a remainder of 2 over 6, which reduces from 2/6 to 1/3, so the mixed number is 1 1/3.
• If the numerator is smaller than the denominator, the whole part is 0 and you simply get the original proper fraction back.
• A zero or blank denominator has no value, because division by zero is undefined, so the calculator leaves the result empty.
• To go the other way and turn a mixed number back into a single fraction, use the mixed number calculator. To put any fraction in lowest terms on its own, try the fraction simplifier, and to express a fraction as a decimal use the fraction to decimal calculator.