Improper and Mixed Fractions

Improper Fractions

Improper fractions are fractions that are greater than 1. We know they are improper when the numerator is greater than the denominator.

Ex.      5          
           4

We know this fraction is an improper fraction because the numerator is 5 and the                     denominator is 4.

Just like proper fractions the denominator tells us how many parts are needed to make up the whole
The numerator tells us how many parts there are. In this case there is one whole and 1 part left over.

Mixed Fractions

Mixed fractions are fractions that are a combination of a whole number and a fraction.
We can convert a improper fraction to a mixed fraction, because it makes it easier to know how many wholes there are.

Ex:         5       =      1 1/4
              4

I can convert an improper fraction into a mixed fraction 3 ways:

1. Division.
    I can divide the denominator by the numerator. The denominator only goes into the numerator 1 time and I have 1 left over.

The one time represents the 1 whole. The left over is the number I put over the the denominator 4 so that it shows I have a whole plus 1/4 quarter.


2. Draw a model
    Another way of converting improper fractions to mixed fractions is by drawing a model.

1. To draw my model I begin by making an area model that has four parts. I know there are four parts because that is what my denominator tells me.
2. Then I shade in the number of parts that we are talking about. In this case there are 5 parts that we are talking about. So I coloured in 5 parts.
3. Finally I can determine how many wholes I have and what I have left over.
4. I have 1 whole and 1/4 left over

3. Use manipulatives.
    I can use manipulatives to show 5/4 and convert it to a mixed number.
    pattern blocks - if you are at school
    fraction circles - available online if you google fraction circles or strips images
    fraction strips
    counters

 

In this picture there are 5 parts and there are 4 parts that make up the whole. I have more than one whole in this case.



Show the fraction and determine the mixed number. How many wholes do you have.

Try This!


What is the mixed fraction for these improper fractions. Be sure to show how you know.


a)  10/3
b)   17/4
c)   8/2
d)   7/5
e)  15/6


Show this mixed number as a model


a)   1 1/2
b)   2 2/3
c)   4  7/8
d)   3  1/2