If the numerator of a fraction is less than its denominator, the fraction is called a
proper fraction.A proper fraction is less than 1. If the numerator of a fraction is
greater than or equal to its denominator, the fraction is called an improper fraction.
An improper fraction is greater than or equal to 1.
Proper fractions Improper fractions
and and
5
1
16
16
,
98
97
,
7
2
,
98
99
2
3
,
1
4
,
3.1 An Introduction to Fractions 209
The Language of Mathematics The phrase improper fractionis somewhat
misleading. In algebra and other mathematics courses, we often use such
fractions “properly” to solve many types of problems.
There are times when a negative fraction is needed to describe a quantity. For
example, if an earthquake causes a road to sink seven-eighths of an inch, the amount
of downward movement can be represented by Negative fractions can be written
in three ways. The negative sign can appear in the numerator, in the denominator, or
in front of the fraction.
Notice that the examples above agree with the rule from Chapter 2 for dividing
integers with different (unlike) signs:the quotient of a negative integer and a positive
integer is negative.
15
4
15
4
15
4
7
8
7
8
7
8
^78.
EXAMPLE (^2) Write fractions that represent the shaded and unshaded
portions of the figure below.
StrategyWe will determine the number of equal parts into which the figure is
divided. Then we will determine how many of those parts are shaded.
WHYThe denominator of a fraction shows the number of equal parts in the
whole. The numerator shows how many of those parts are being considered.
Solution
Since the figure is divided into 3 equal parts, the denominator of the fraction is 3.
Since 2 of those parts are shaded, the numerator is 2, and we say that
of the figure is shaded. Write:
Since 1 of the 3 equal parts of the figure is not shaded, the numerator is 1, and we
say that
of the figure is not shaded. Write:
number of parts not shaded
number of equal parts
1
3
number of parts shaded
number of equal parts
2
3
Self Check 2
Write fractions that represent the
portion of the month that has
passed and the portion that
remains.
Now TryProblems 25 and 101
DECEMBER
1 2 3 4 5 6 7
8 9 1011121314
15161718192021
22232425262728
293031
iStockphoto.com/Jamie VanBuskirk
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