Understanding Fractions

Definitions
In module A, all the numbers that we encountered were whole numbers.
Although the whole numbers are important, they only tell part of the
story. Module B is the study of fractions
which are defined as parts of the whole.
Example
Consider the picture below which might represent what is left of a
pizza. We see that the pizza was originally cut into eight slices and
there are three slices left. We say that there is
3
8
of the pizza remaining. The number 3 is
called the numerator
of the fraction and the number 8 is called the denominator
of the fraction.
Example
Write the fraction of red circles in the diagram below.
Solution
We see that there are 9 total circles, 5 of
which are red. The total number of circles is the denominator and the
number of reds is the numerator:
5
9
Exercise

Use a fraction to represent the shaded part of the
whole.
Hold the mouse over the yellow rectangle
for the solution:

Draw a sketch to illustrate 4/5.

Some Properties of
Fractions
Recall that there were several properties of division. Since
fractions are really division problems, we arrive at the same properties:

If the numerator and denominator
are the same then the fraction equals 1:
4
= 1
4

If the denominator is 1 then the
fraction is just the numerator
6
= 6
1

If the numerator is 0 and the
denominator is not 0, then the fraction equals 0
0
= 0
9

If the denominator is zero then
the fraction is undefined
2
is undefined
0

Applications
Application of fractions are encountered everywhere.
Example Use a fraction to describe each situation

Out of ten problems on the test you scored nine correct
Solution:
You got 9/10 of the problems right

Of the 75 patrons on
Ellie's run, 61 were boarders
Solution:
The fraction of boarders on Ellie's run was 61/75

Of the 51 bicycles at your rental shop, you discovered
that 8 needed repair.
Solution:
8/51 of the bicycles needed repair.
Exercises Use a fraction to describe each
situation

Of the seven students left in the class, three are
women.
Solution:

Seven days of January were snowy.
Solution:

Fifteen of the ninetyone tourists are from Sacramento.
Solution:
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