Converting

Improper Fractions

Into

Mixed Numbers

Sometimes we get fractions where the numerator is bigger than the denominator. When this occurs we call the fraction an improper fraction.

94

numerator

Denominator

We call it an improper fraction because that’s not how people typically talk.

94

Hey, I’ve collected 15 quarters

Dude, I ate 5 halves of candy bars yesterday

We call it an improper fraction because that’s not how people typically talk. We tend to talk using a mix of whole numbers and fractions when possible.

94

Hey, I’ve collected 3 dollars and 75 cents

Dude, I ate two and a half of candy bars yesterday

So, how do we convert an improper fraction to a mixed number?

94

Before we start we need to remember how we get improper fractions in the first place.

When we add fractions we have to remember that the denominator stays the same and we simply add the numerators together

1+25

25

15 + = = 3

5

If the numerators are big it can result is an improper fraction.

4+35

35

45 + = = 7

5

So to convert an improper fraction to a mixed number we need to work backwards and figure out the addition problem that created the situation.

?+?7

?7

?7 + = = 9

7

While there are lots of different combinations that would give us the numerator we want, we should choose the one that results in a whole number.

5+47

47

57 + = = 9

7

While there are lots of different combinations that would give us the numerator we want, we should choose the one that results in a whole number.

6+37

37

67 + = = 9

7

While there are lots of different combinations that would give us the numerator we want, we should choose the one that results in a whole number.

7+27

27

77 + = = 9

7

We want to choose this combination because we can convert this to a whole number.

7+27

27

77 + = = 9

7

We want to choose this combination because we can convert this to a whole number.

7+27

271+ = = 9

777

We have now successfully converted an improper fraction into a mixed number.

271 = 9

7

Some times the numerator is large enough to pull more than one whole from the numerator.

?4

?4 + = 9

4?4+

Some times the numerator is large enough to pull more than one whole from the numerator.

44

44 + = 9

414+

In this case we create as many whole numbers as possible.

+ = 94

14+1 14

444

We finish things off by combining the whole numbers.

=94

142