Fraction To Mixed Number Converter

What this converter does

So, you have a top-heavy fraction like 17/5 and you want it in a form you can actually picture. This converter rewrites an improper fraction as a mixed number, so 17/5 becomes 3 2/5, a whole number sitting next to a proper fraction.

There are two boxes, a numerator and a denominator. It is built for improper fractions, the ones where the top is at least as big as the bottom.

How to use it

1. Type the numerator, the top number.
2. Type the denominator, the bottom number.
3. Press Calculate.

Feed it an improper fraction to get a mixed number back. If you enter a proper fraction, one already less than a whole, it simply comes back with a whole-number part of zero, since there is no whole to pull out.

Improper fractions and mixed numbers

This is the reverse of turning a mixed number into an improper fraction. An improper fraction such as 17/5 is a single fraction worth 1 or more. A mixed number such as 3 2/5 splits that same value into its whole part and what is left over. Both are correct; the mixed form is just easier to read at a glance, since 17/5 does not immediately tell you it lands somewhere past 3, while 3 2/5 says so directly.

The method it uses

The conversion is a single division. Divide the top by the bottom. The whole-number part of the mixed number is how many whole times the bottom goes into the top, and the remainder becomes the new numerator, sitting over the same denominator.

For 17/5, five goes into seventeen three times with 2 left over, so the whole part is 3 and the remainder 2 becomes the fraction 2/5, giving 3 2/5. In short, the whole number is the quotient and the fraction is the remainder over the denominator.

A worked example, step by step

Take 11/4.

• Divide: 11 ÷ 4 is 2, with a remainder of 3.
• The whole part is 2.
• The remainder 3 goes over the denominator 4, giving 3/4.

So 11/4 is 2 3/4. The same routine turns 23/6 into 3 5/6, since 6 goes into 23 three times with 5 to spare.

The leftover comes back reduced

There is a nice extra here. The tool runs on math.js, a JavaScript maths library, whose fraction type keeps everything in lowest terms, so the leftover part is tidied automatically. Take 20/6. Six goes in 3 times with 2 left over, which would be 3 2/6, but 2/6 reduces to 1/3, so the tool shows 3 1/3 rather than 3 2/6. It converts and simplifies the fractional part in one go, which saves you a second step.

Questions people ask

What is a mixed number?

A whole number written next to a proper fraction, such as 3 2/5, read as three and two fifths. It is the same value as the improper fraction it came from.

What if my fraction is already proper?

Then there is no whole part to extract, so it comes back with a whole number of 0 and the fraction essentially unchanged.

Does it reduce the leftover fraction?

Yes. The fractional part is returned in lowest terms, so 20/6 becomes 3 1/3 rather than 3 2/6.

How do I go the other way?

To turn a mixed number back into an improper fraction, use the mixed number to fraction converter, which is the inverse of this one.

Why use mixed numbers at all?

They are easier to read and to estimate with. A mixed number tells you at a glance which two whole numbers the value falls between, where an improper fraction makes you work that out.

References

On the two forms. An improper fraction has a value of 1 or more; a mixed number carries that same value as a whole number plus a proper fraction. This converter moves from the first to the second, tidying the leftover fraction on the way.

1. Eric W. Weisstein, "Improper Fraction," from MathWorld, a Wolfram resource, on a fraction whose value is 1 or greater.
2. Eric W. Weisstein, "Mixed Fraction," from MathWorld, a Wolfram resource, on the whole-number-plus-proper-fraction form.