Rational numbers are frequently used in daily life. They consist of all positive
and negative fractions. All integers are also rational numbers because integers
can be expressed as fractions with 1 in the denominator. For example, 2 equals 
and –3 equals 
.
Some examples of rational numbers and their form as a
fraction are listed in the table below.
Rational numbers can be graphed on a number line in the same
manner as integers.
Graphing rational numbers on a number line helps you to
compare them. Just as with integers, the numbers on a number line increase in
value as you move to the right and decrease in value as you move to the left.
The following statements can be made about the number line
above.
A mathematical sentence that uses and to compare two expressions is called an inequality. When
you compare two numbers, the following property applies.
Example
Replace each ○ with <, >, or = to make a true sentence.
1. 1.5
○ –8
Alternative Solutions :
Since
any positive number is greater than any negative number,
1.5 > –8.
2. –14
+ 8 ○ 2(–3)(5)
Alternative Solutions :
–14 +
8 ○ 2(–3)(5)
–6 ○ –30 Find
the value of each side.
–6 is
to the right of –30 on a number line and –6 > –30.
So, –14
+ 8 > 2–3)(5).
3.
Since any
negative number is less than any positive number, 
.
To compare two fractions with different denominators, you can
use cross products.
Cross products are the products of the diagonal terms of two fractions.
This example illustrates the following property
Example
Replace each ○ with <, >, or = to make a true sentence.
Another way to compare rational numbers is to express them as
terminating or repeating decimals.
Example
You can use the cost per unit, or unit cost, to compare the costs of similar
items. Many people use unit cost to comparison shop. The least unit cost is the
best buy.
unit cost = total cost number of
units
Example
Shopping Link
7. Rolando
needs to buy colored pencils. The cost of a package of 12 pencils is $6.39. A
package of 24 pencils costs $12.89. Which is the better buy? Explain.
Alternative Solutions :
Find
the unit cost of each package.
In
each case, the unit cost is expressed in cents per pencil.
unit
cost of package of 12:
6.39 ÷
12 = 0.5325 or about $0.53 per pencil
unit
cost of package of 24:
12.89÷ 24 = 0.5371 or about $0.54 per pencil
Since $0.53
< $0.54, the package of 12 pencils is the better buy.
Sumber
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