Converting Between Mixed Numbers & Improper Fractions

Sometimes you'll be asked to convert mixed numbers into improper fractions, and vice versa. Once you get the hang of it, you'll be doing it in your sleep.

Let's start by looking at mixed numbers and improper fractions visually.

This is 

If we divide each whole circle into fourths, we can count the number of blue fourths. Shazam! There are 11 blue fourths, or 

This is 

As you can see we have 3 wholes and 1 section remaining, or 3 1/3.

You could also think of mixed numbers as sums of whole numbers and their parts. For example 3 1/3 is really 3 + 1/3

And try another example...

is 

This time the common denominator is 4.

How to Change a Mixed Number into an Improper Fraction

1. Multiply the denominator by the whole number. 
2. To that, add the numerator. 
3. Place that number over the original denominator.

Example 1

Example 2

Change an Improper Fraction into a Mixed Number

1. Divide the denominator into the numerator. 
2. The result will be a whole number with a remainder. The remainder becomes the numerator of the fraction part. The denominator remains the same.