### Converting to Mixed Numbers

*For improper fractions, check out: What is an Improper Fraction?*

## Introduction

It is not uncommon to get answers that are improper fractions while working with fractional values. However, you might rather have it be a mixed number, so you would *convert* it! Many math problems require answers to be simplified into mixed number format, as it is commonly regarded as simpler than an improper fraction. Some examples of this conversion:

- 7/2 = 3 1/3
- 4/3 = 1 1/3
- 15/12 = 1 3/12

As you can see, **mixed numbers **are numbers that are a combination of whole numbers and fractions, therefore they are considered to be “mixed”. There is always a whole number first, then immediately following it there is a fractional part.

## How is it done?

To convert to mixed number, the first step is to **find out how many times the denominator fits into the numerator**. If the denominator is 5, and the numerator is 22, (the fraction is 22/5) then how many times does 5 fit in to 22? 5*4=20 with a remainder of 2.

So, **the mixed number is 4 and 2/5 because for the left over 2, the denominator is still 5** because we couldn’t get a whole number out of it, and we shouldn’t be changing anything. If the denominator is larger than the numerator, then we don’t need to convert because this would not be a mixed number. As we can see, the 4 comes from how 5 fits into 22 4 whole times.

The outcome of 4 and 2/5 from 22/5 makes sense mathematically because 4 is the same as 20/5. Adding this with the 2/5 makes 20/5 + 2/5 = 22/5, back to the original improper fraction!

## More examples of the conversion at work…

- If we have the improper fraction 45/6, we can first divide 45 by 6 to see how many whole numbers we can get. This would be 7 with a remainder of 3, as 6 * 7 = 42 and 45 – 42 = 3. We would not change the denominator for the remainder, so it would be 7 and 3/6, which can be further simplified to 1/2.
- With the improper fraction of 23/5, dividing 23 by 5 gives us 4 with a remainder of 3 because 5 * 4 = 20 and 23 – 20 = 3. There would be no denominator change for the remainder, so the final mixed number becomes 4 and 3/5.
- 90/4 is a large mixed number, but it is still convertible! Simply start by dividing 90 by 4, which gives us 22 with a remainder of 2. (22 * 4 = 88, 90 – 88 = 2). We would then have 22 and 2/4, which simplifies to 22 and 1/2.