Inequalities

After studying this lesson, you will be able to compare numbers using inequality symbols.

Rational Numbers are numbers that can be expressed in the form where a and b are integers and b is not equal to zero.

Inequality Symbols:

> greater than

< less than

less than or equal than

greater or equal than

Comparing Rational Numbers

To compare two fractions, cross multiply. Then use an inequality to symbol to compare the numbers.

Example 1

Compare .

Solution

Cross multiply 3 times 11 equals 33

Cross multiply 8 times 4 equals 32

Compare 33 ____ 32 (put the greater than symbol in the blank)

33 > 32

Therefore, .

Example 2

Compare

Solution

Cross multiply 6 times 12 equals 72

Cross multiply 11 times 7 equals 77

Compare 72 ____ 77 (put the less than symbol in the blank)

72 < 77

Therefore,

Example 3

Compare

Solution

First, make 4 a fraction - rewrite as

Cross multiply -2 times 1 equals -2

Cross multiply 3 times 4 equals 12

Compare -2 ____ 12 (put the less than symbol in the blank)

-2 < 12

Therefore,