How to Change an Improper Fraction to a Mixed Number

An improper fraction has a top at least as big as its bottom, like 17/5. A mixed number shows the same amount as a whole number plus a proper fraction, like 3 2/5.

Try it with your own problem ↓

The steps

Divide the numerator by the denominator (long division if you need it).
The whole number part of the answer (the quotient) is the whole number of the mixed number.
The remainder becomes the new numerator.
Keep the same denominator.
To go back: multiply the whole number by the denominator, add the numerator, and put that over the denominator.

A worked example

Write 17/5 as a mixed number.

Divide: 17 ÷ 5 = 3 with a remainder of 2, because 5 × 3 = 15 and 17 − 15 = 2.
The whole number is 3.
The remainder 2 is the new numerator, and the denominator stays 5.
So 17/5 = 3 2/5.
Going back: 3 × 5 = 15, and 15 + 2 = 17, so 3 2/5 = 17/5.

17/5 = 3 2/5. Check: 3.4 = 17 ÷ 5. ✓

Why it works

17/5 means 17 fifths. Every 5 fifths make one whole, so the question is how many groups of 5 fit into 17. There are 3 groups, with 2 fifths left over. That is 3 wholes and 2/5, written 3 2/5.

Try it with your own problem

Open the free The Fraction Bar with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 17/5 as a mixed numberOpens The Fraction Bar with this example

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Common mistakes

Putting the quotient over the denominator. The remainder goes on top, not the quotient.
Changing the denominator. It stays the same.
Forgetting to simplify the fraction part. 30/12 gives 2 6/12, which simplifies to 2 1/2.
Adding in the wrong order going back. Multiply the whole number by the denominator first, then add the numerator.

Questions people ask

Is an improper fraction wrong?

No. The name is just a label. Improper fractions are often easier to multiply and divide with.

What if the remainder is 0?

Then the fraction is a whole number. 15/5 = 3.

Which should I give as my answer?

Follow your teacher's rule. Mixed numbers are common for real-life answers, and improper fractions in algebra.

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