Mixed Number To Fraction Converter

What this converter does

So, you have a mixed number like 2 3/4 and you need it as a single top-heavy fraction, 11/4. This converter does exactly that swap. You feed it the whole part and the fraction, and it gives you one improper fraction that carries the same value.

There are three boxes: a whole number, a numerator, and a denominator. Together they are the mixed number you want to convert.

How to use it

1. Type the whole number part.
2. Type the numerator and the denominator of the fraction part.
3. Press Calculate.

The numerator and denominator should be positive whole numbers, since a mixed number carries a genuine proper fraction alongside its whole part.

Mixed numbers and improper fractions

A mixed number is a whole number written next to a proper fraction, like 2 3/4, read as two and three quarters. An improper fraction is a single fraction whose top is at least as big as its bottom, like 11/4. They are two ways of writing the same amount.

There is a good reason mathematicians lean on the improper form for actual work. The spacing in 2 3/4 can be read as a multiplication, two times three quarters, which is a different and smaller number. Writing it as 11/4 removes any doubt, which is part of why it is the form you hand to a calculation.

The method it uses

The conversion is one clean step: multiply the whole number by the denominator, add the numerator, and keep the same denominator. In symbols, a whole number a with a fraction b/c becomes

(a × c + b) / c

The thinking behind it is simple. Each whole is made of c of the fractional pieces, so a wholes are a × c pieces, and you add the b pieces you already had. For 2 3/4, each whole is 4 quarters, so 2 wholes are 8 quarters, plus the 3 you had makes 11 quarters, which is 11/4.

A worked example, step by step

Take 3 2/5.

• Multiply the whole by the denominator: 3 × 5 = 15.
• Add the numerator: 15 + 2 = 17.
• Keep the denominator: the answer is 17/5.

The denominator never changes through the conversion; only the top is rebuilt. So 5 1/2 becomes 11/2 the same way: 5 × 2 + 1 is 11, over 2.

Why you would want the improper form

Improper fractions are easier to compute with. To multiply or divide mixed numbers, the standard first move is to convert each into an improper fraction, and only then multiply or divide. That is exactly what the fraction arithmetic calculators do quietly inside themselves. This converter is the standalone version of that step, useful whenever you want the single-fraction form on its own, whether to carry into another calculation or just to write an answer the way a maths teacher expects to see it.

Questions people ask

What is an improper fraction?

A fraction whose numerator is at least as large as its denominator, so its value is 1 or more. 11/4 and 5/5 are both improper.

Does the denominator change?

No. The denominator you enter stays put. Only the numerator is rebuilt, as the whole number times the denominator plus the original numerator.

Does it reduce the result?

It keeps your denominator and gives the direct improper fraction. If you then want that in lowest terms, the simplify fractions calculator will reduce it.

Why convert at all?

Because improper fractions are far easier to multiply and divide. Converting first is the standard opening step for arithmetic with mixed numbers.

How do I go the other way?

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

References

On the two forms. A mixed number is a whole number plus a proper fraction; an improper fraction is a single fraction of value 1 or more. Converting between them is a matter of rewriting the same value, not changing it.

1. Eric W. Weisstein, "Mixed Fraction," from MathWorld, a Wolfram resource, on the mixed-number form and its relation to an improper fraction.
2. Eric W. Weisstein, "Improper Fraction," from MathWorld, a Wolfram resource, on a fraction whose value is 1 or greater.