Improper Fractions
Three Types of Fractions
There are three types of fraction:
So we can define the three types of fractions like this:
Proper Fractions
All the fractions we have been working with so far have been proper fractions. Proper
fractions tell us what part out of the whole we are dealing with.
e.g.
¼ of an orange tells us we have 1 part out of 4 of a whole orange.
Now, as far as proper fractions go, it is IMPOSSIBLE to have the numerator greater
then the denominator as you can’t have MORE THAN THE WHOLE.
Improper Fraction
An Improper fraction has a top
number
larger than (or equal to) the
bottom number,
It is "top-heavy"
7
/4
(seven-fourths or seven-quarters)
Examples
3
/2
7
/4
16
/15
15
/15
99
/5
See how the top number is bigger than (or equal to) the bottom number?
That makes it an Improper Fraction, (but there is nothing wrong about Improper
Fractions).
So, an improper fraction is just a fraction where the top number (numerator) is
greater than or equal to the bottom number (denominator).
In other words, it is top-heavy.
How can they exist?
If we start with an orange as our “whole”, and chop it up into 4, each part will be ¼
of that whole – one quarter of an orange.
Now let’s ignore that 1 orange was our “whole”. If I chop up THREE “whole” oranges,
each into quarters, I’ll have 3 lots of 4 = 12 quarters (quarter = quarter of one
orange).
An improper fraction allows me to talk about having so many of a particular size
piece WITHOUT having to use words.
Having 12 quarters can be written as 12/4 where the denominator is simply a shorthand way of saying “quarter”. So I read it as “12 quarters”.
So, once you have defined ONE of something (1 half, 1 quarter, 1 eighths, 1 third, 1
fifth, etc.) it can be become a unit (like dogs and cats and bananas and people) and
you can have as many of them as you like!!!
e.g. This is a quarter
This is 5 quarters:
This is 9 quarters:
Example Question: How much pizza can you see below?
Solution:
There are 15 pieces. Each piece is a quarter.
So 15 quarters.
As an improper fraction, this is 15/4.
Example Question: Which of the following are Improper Fractions?
3/5
6/4
Solution:
9/11
11/9
3/2
11/5
6/10
Compare the numerators and denominators (tops and bottoms). If the
top is bigger, it must be more than one whole, and thus be an
improper fraction.
So answer is 6/4, 11/9, 3/2, and 11/5.
Improper Fractions on the Number line
We saw in the last concept, that when you go beyond 1, you can start talking 1 and a
fraction. For example, counting in 3rds, you get:
0, 1/3, 2/3, 1, 1 and 1/3, 1 and 2/3, 2, 2 and 1/3, 2 and 2/3 etc.
An alternative way to count is to just keep working out how many LOTS OF one third
you have moved.
So you could have:
0, 1/3, 2/3, 3/3, 4/3, 5/3, 6/3, 7/3, 8/3.
Here is what improper fractions can look like on the number line:
Example: Find the value of Q on the number line below:
Solution:
Note, one whole (between 0 and 1) has been divided into 4 equal
parts. So we are dealing in quarters. If we count from 0, we count 10
of these parts to get to Q. So it’s 10 quarters. So Q = 10/4.
NOTE: This is equivalent to 2 wholes and 2/4 (or 2 wholes and ½).