1. ALGEBRA READINESS
Chapter 5 Section 1

2. 5.1: Compare and Order Rational Numbers
A rational number is a number that can be written as a/b where a and b are integers and b ≠ 0.
Every rational number can also be written either as a terminating decimal or a repeating decimal.

3. Show that (a) 1.9 and (b) 8.25 are rational numbers. –
Example 1
Identifying Rational Numbers
Show that (a) 1.9 and (b) are rational numbers. – = 1 10 9
Write as mixed number. a.
1.9 = 10 19
Write as improper fraction.
Write as mixed number. = 8 4 1 – b.
8.25 = – -8 25
100
Write as improper fraction. = 4 33 –
Both numbers are rational numbers because they are quotients of two integers.

4. Practice for Example 1
Show that the number is a rational number by writing it as a quotient of two integers.
ANSWER 5 2 1.
0.4
ANSWER 20 23 2.
1.15
ANSWER 5 6 – 3.
1.2 –
ANSWER 5 13 – 4.
2.6 –

5. Graph 3.9 and on a number line. Then tell which is greater.
Example 2
Graphing and Comparing Rational Numbers 7
Graph and on a number line. Then tell which
is greater. – – 2
The number is nine-tenths to the left of 3 on the number line. The number is equal to , which
is five-tenths to the left of 3 on the number line. 2 7 –
On the number line, is to the right of So, 2 7 –
3.9.
>

6. Graph the numbers on a number line. Then tell which number is greater.
Practice for Example 2
Graph the numbers on a number line. Then tell which number is greater. 5.
and 5 2 –
ANSWER 5 2 6.
and 8 11 –
ANSWER 8 11 – 7.
7.1 and – 4 29
ANSWER
7.1 –

7. Order the rational numbers 2.2, -1.7, , , 0, least to greatest.
Example 3
Ordering Rational Numbers
Order the rational numbers 2.2, , , , 0, least to greatest. 5 2 3 1 –
and from
Begin by graphing the numbers on a number line.
From least to greatest, the numbers are , , 0, ,
and 2.2. – 3 1 5 2

8. Order the rational numbers from least to greatest.
Practice for Example 3
Order the rational numbers from least to greatest. 8.
2, 1.5, 3, –
ANSWER
3, , 1.5, 2 – 9.
0, , , –
ANSWER
0.6, , , 0 –

9. Order the rational numbers from least to greatest.
Practice for Example 3
Order the rational numbers from least to greatest.
10.
3.2, 1, 2.5, – 2 1
ANSWER
3.2, , 1, 2.5 – 2 1 ,
11. – 5 1 3 2 –1
ANSWER –1 – 3 2 1 , 5

10. The table shows the change in temperature every hour
Example 4
Comparing Data Values
The table shows the change in temperature every hour
during a winter snowstorm.
Hour 1 2 3 4 5 6
Change in
Temperature (°F)
– 0.8
1.2
– 1.6
– 2.9
0.5
– 1.3 a.
Which hour shows the greatest increase in
temperature? b.
Which hour shows the greatest absolute decrease in temperature?

11. Example 4
Comparing Data Values
SOLUTION a.
Hour 2 shows the greatest increase in temperature, because 1.2 is the greatest positive number. b.
The negative number that has the greatest absolute value is , so hour 4 shows the greatest absolute decrease in temperature. – 11

12. Practice for Example 4
12.
In Example 4, does hour 2 or hour 5 show the greater increase in temperature?
ANSWER
Hour 2
In Example 4, does hour 3 or hour 6 show the greater absolute decrease in temperature?
13.
ANSWER
Hour 3