1. Warm Up Simplify. 1. ( ) 2 + 50 5 ANSWER 260 2. ( ) 25 – + 18 ANSWER 7
Real Numbers and Number Operations
Simplify. 1. ( ) 2 + 50 5
ANSWER
260 2. ( ) 25 – + 18
ANSWER 7 – 3.
What is the difference between a daily low temperature of 5°F and a daily high temperature
of 18°F? –
ANSWER
23°F

2. . Example 1 3 5 – Graph the real numbers , , and 2.6. 2 SOLUTION
Graph Numbers on a Number Line 3 5 –
Graph the real numbers , , and 2.6. 2
SOLUTION
First, recall that , so is between and Then, approximate as a decimal to the nearest tenth: Finally, graph the numbers. 3 5 – 2 1 ≈ = 2 3 5 –
2.6 1 4 .

3. Example 2
Compare Real Numbers
Graph the numbers and Then compare them using the symbol < or >. – 1 – 4
SOLUTION
Begin by graphing both numbers on a real number line. . 1 2 3 – 7 6 5 4 – 4
Because is to the left of , it follows that is less than , or < You can also say that is greater than , or > 1

4. Example 3
Order Temperatures
Science The table shows the record low temperatures for five months at the South Pole. Use a number line to order the temperatures from lowest to highest.
Month
May
June
July
Aug.
Record low temp.
111°F –
109°F
117°F
113°F
108°F
Sept.
SOLUTION –
119
117
115
109
107
111
113
108 .

5. From lowest to highest, the temperatures are , , , , and . 117°F –
Example 3
Order Temperatures
ANSWER
From lowest to highest, the temperatures are , , , , and
117°F –
113°F –
111°F –
109°F –
108°F –

6. Checkpoint
Graph and Order Real Numbers
Graph the numbers on a number line. Then write the numbers in order from least to greatest. . . . – 3 – 2 5 1. – 2, 3 5,
ANSWER – 5 – 4 – 3 – 2 – 1 1 2 3 4 5 – 2, 3, 5
ANSWER – 6, 3
10, 2 14 12 10 8 6 4 . 2. – 6, 3, 10

7. Checkpoint
Graph and Order Real Numbers
Graph the numbers on a number line. Then write the numbers in order from least to greatest.
ANSWER 2 3 –
0.5, , 1 .
0.5 3. 2 3 – 2,
0.5 ,

8. Show how you can use the distributive property to evaluate . 203 • 5
Example 4
Use Properties of Real Numbers
Show how you can use the distributive property to evaluate
203 • 5
SOLUTION =
203 • 5 ( ) 3 +
200
Rewrite 203 as = ( ) 3 +
200 5
Distributive property = +
1000 15
1015
Simplify.

9. a. Find the difference of 4 and 9. –
Example 5
Operations with Real Numbers
a. Find the difference of 4 and 9. – ( ) 9 – 4 = +
Add 9, the opposite of 9.
Simplify. = 13
b. Find the quotient of 15 and . – 3 1 – 15 ÷ 3 1 = •
Multiply by 3, the reciprocal
of .
Simplify. = – 45

10. Select and perform an operation to answer the question.
Checkpoint
Operations with Real Numbers
Select and perform an operation to answer the question. 4. 2 1 –
What is the quotient of 16 and ?
ANSWER 32 5.
What is the product of 5 and 8? –
ANSWER 40 –