Converting Between Improper Fractions and Mixed
Fractions
Three Types of Fractions
There are three types of fraction:
So we can define the three types of fractions like this:
In Case You Didn’t Notice
In case you didn’t notice, mixed numbers and improper fractions are 2 ways of
representing THE SAME THING.
When telling someone an “amount” for them to imagine, mixed fractions are better.
20 and 1/3 is easier to image than 61/3.
But when working mathematically, like adding or multiplying, improper fractions are
easy to work with because they are simply fractions, not a combination of fraction
and wholes.
So it important to represent amounts as both MIXED FRACTIONS and IMPROPER
FRACTIONS and to be able to convert between the two forms.
Converting TO MIXED
Start with the improper fraction:
e.g.
Note, for every 4 quarters we make a whole.
How many fours go into 7? 1 (and 3 remainder)
So we make 1 whole. And how many remainders? 3
So our answer is 1 whole and 3 remaining QUARTERS.
Answer: 1 ¾.
7/4
Example: Convert 30/7 into a mixed number
Solution:
30 divided by 7 = 4 wholes, remainder 2.
So we have 4 wholes. The 2 remaining parts must still be
sevenths.
So we have 4 and 2/7.
Example: Convert 15/12 into a mixed number
Solution:
15 divided by 12 = 1 whole, 3 remainder.
So we have 1 whole. The 3 remaining parts must still be
twelfths.
So we have 1 and 3/12.
NOTE: This teacher likes putting the “and” between the 2 parts of a mixed fraction,
but it is not standard, although useful for reminding you what it means.
Converting TO IMPROPER
Start with the mixed:
e.g. 1 and ¾
If we break the whole into quarters as well:
Everything is in quarters…. Count them… I think there are 7 quarters there.
If we line our quarters up we make it more obvious:
So the answer is 7 quarters (7/4).
Example: Convert 4 and ½ to an improper fraction
Solution:
We are already dealing with halves so our answer will be over 2.
Our 4 wholes need to be cut into 2 (to make halves). 4 x 2 = 8
halves
Add the 1 halve we initially had to the 8 we just made. We have
9.
So our final answer is 9 halves or 9/2.
Example: Convert 7 and 3/5 into an improper fraction.
Solution:
We are already dealing with fifths, so our denominator will be 5.
Our 7 wholes need to be cut into 5 (to make fifths). 7 x 5 = 35
fifths.
Add the 3 fifths we initially had to the 35 we just made. We
have 38 fifths.
So our final answer is 38 fifths or 38/5.