1. Add Real Numbers
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up = ?
ANSWER
1.7 = 5 6 2 3 ?
ANSWER 7 1 2

3. Warm-Up
3. Ned wants to ship 3 books in a box with a weight limit of 25 pounds. The books weigh 8.4 pounds, 7.9 pounds, and 9.2 pounds. Can he ship them in the box? Explain.
ANSWER
No; the total weight of the books is 25.5 pounds and 25.5 > 25.

4. Example 1
Use a number line to find the sum.
a. – 3 + 6
ANSWER
The final position is 3. So, – = 3.

5. Example 1
b. – 4 + (– 5)
ANSWER
The final position is – 9. So, – 4 + (– 5) = – 9.

6. Guided Practice
Use a number line to find the sum.
(– 2)
(– 11)
ANSWER 5
ANSWER
– 3
4. –1 + (– 4)
– 8 + 4
ANSWER
– 4
ANSWER
– 5

7. Example 2 Find the sum. a. – 5.3 + (– 4.9) = – ( – 5.3 + – 4.9 )
= – ( – – 4.9 )
Rule of same signs
= – ( )
Take absolute values.
= – 10.2
Add.
b (–12.2)
= – –12.2
Rule of different signs
= 19.3 – 12.2
Take absolute values.
= 7.1
Subtract.

8. Guided Practice
Find the sum.
5. – (– 6.7)
= – 7.3
(– 16.2)
= – 6.1
7. –
= – 4.4

9. Example 3
Identify the property being illustrated.
Statement
Property illustrated
a. (x + 9) + 2 = x + (9 + 2)
Associative property of addition
b (– 8.3) = 0
Inverse property of addition
c. – y = (– y)
Commutative property of addition

10. Guided Practice
Identify the property being illustrated.
(– 7) = 0
Inverse property of addition
9. – = – 12
Identity property of addition
= 8 + 4
Commutative property of addition

11. Example 4
BUSINESS
The table shows the annual profits of two piano manufacturers. Which manufacturer had the greater total profit for the three years?

12. Example 4
SOLUTION
STEP 1
Calculate the total profit for each manufacturer.
Manufacturer A:
Manufacturer B:
Total profit
= –
Total profit
= –
= – ( )
= – ( )
= –
= –
= 9.7
= 9.6
STEP 2
Compare the total profits: 9.7 > 9.6.
ANSWER
Manufacturer A had the greater total profit.

13. Profit (millions) for manufacturer A
Guided Practice
11.
WHAT IF? In Example 4, suppose that the profits for year 4 are – $1.7 million for manufacturer A and – $2.1 million for manufacturer B. Which manufacturer has the greater total profit for the four years?
Year
Profit (millions) for manufacturer A
Profit (millions) for manufacturer B 1
– $5.8
– $6.5 2
$8.7
$7.9 3
$6.8
$8.2 4
– $1.7
– $2.1
ANSWER
Manufacturer A has the greater total profit.

14. Lesson Quiz
Find the product.
(–9)
ANSWER
–1.4
2. –
ANSWER
12.8
What property is illustrated by (–y + 3) + 6 = –y + (3 + 6)? 3.
ANSWER
Associative property of addition

15. Lesson Quiz
The table shows the account ledgers for the Science Club and the Astronomy Club. Which club has the greater assets at the end of 3 weeks? 4.
ANSWER
The Astronomy Club has greater assets since $92.50 > $90.55.