1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Multiply.
 76
63,992
2. 1,240  83
102,920
 712
584,552
 15
4,530 2

3. number of adults, children, and students who attended the meet
Problem of the Day
Tickets to the district swim meet cost $7.50 for adults, $3.50 for children, $5.00 for senior citizens, and $4.00 for students. The total revenue for the meet was $8,570. What information is needed to find how many senior citizens were at the meet?
number of adults, children, and students who attended the meet 3

4. Sunshine State Standards
MA.7.A.3.2 …Multiply…terminating decimals and perform exponential operations with rational bases and whole number exponents including solving problems in everyday contexts.

5. You can use decimal grids to model multiplication of decimals
You can use decimal grids to model multiplication of decimals. Each large square represents 1. Each row and column represents 0.1. Each small square represents The area where the shading overlaps shows the product of the two decimals.
0.7
0.8
0.56  =

6. 7  8 56 0.7  0.8 0. 56 1 decimal place 1 decimal place
To multiply decimals, multiply as you would with integers. To place the decimal point in the product, count the number of decimal places in each factor. The product should have the same number of decimal places in the factors. 7
 8 56
0.7
 0.8
1 decimal place
1 decimal place + 0. 56
2 decimal places
Same digits

7. Additional Example 1: Multiplying Integers by Decimals
0 decimal places 7
 0.1
1 decimal place
0.7
0 + 1 = 1 decimal place
B. –3 · 0.03
0 decimal places –3
 0.03
2 decimal places
– 0.09
0 + 2 = 2 decimal places. Use zero
as a place holder.

8. Additional Example 1: Multiplying Integers by Decimals
2.45
 35
2 decimal places
0 decimal places
12 25
85.75
2 + 0 = 2 decimal places

9. Check It Out: Example 1
Multiply.
A. 3 · 1.2
B. –5 · 0.05 3
 1.2 6
+ 30
3.6 –5
 0.02
– 0.25

10. Check It Out: Example 1
Multiply.
C · 11
6.04
 11
604
+ 6040
66.44

11. Additional Example 2A: Multiplying Decimals by Decimals
Multiply. Estimate to check whether each answer is reasonable.
–3.84 · 0.9
–3.84
 0.9
2 decimal places
1 decimal place
–3.456
2 + 1 = 3 decimal places
Estimate
–4 · 1 = –4
–3.456 is a reasonable answer.

12. Additional Example 2B: Multiplying Decimals by Decimals
Simplify. Estimate to check whether each answer is reasonable.
(2.9)²
(2.9)(2.9)
2.9 is a factor 2 times
2.9
 2.9
1 decimal place
1 decimal place
261
+ 580
8.41
1 + 1 = 2 decimal places
Estimate
(2.9)² = 3 · 3 = 9
8.41 is a reasonable answer.

13. Check It Out: Example 2A
Simplify. Estimate to check whether each answer is reasonable.
–0.05  0.5
–0.05
 0.5
–0.025

14. Check It Out: Example 2B
Simplify. Estimate to check whether each answer is reasonable.
1.36  0.22
1.36
 0.22
272
2720 +
0.2992

15. Simplify. Estimate to check whether each answer is reasonable.
Check It Out: Example 2C
Simplify. Estimate to check whether each answer is reasonable. 3
(-0.6)
(–0.6) (–0.6) (–0.6)
–0.6
 –0.6
0.36
–0.216

16. Simplify. Estimate to check whether each answer is reasonable.
Check It Out: Example 2D
Simplify. Estimate to check whether each answer is reasonable. 2
(4.2)
(4.2) (4.2)
4.2
 4.2 84
+1680
17.64

17. Additional Example 3: Application
To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is What would a person who weighs 85 pounds on Earth weigh on Mars?
0.38
 85
2 decimal places
0 decimal places
1 90
32.30
2 + 0 = 2 decimal places

18. Additional Example 3 Continued
To find your weight on another planet, multiply the relative gravitational pull of the planet and your weight. The relative gravitational pull on Mars is What would a person who weighs 85 pounds on Earth weigh on Mars?
Estimate
0.5 • 80 = 40
32.30 is a reasonable answer.
The person would weigh pounds on Mars. 18

19. Check It Out: Example 3A
On average, people ages 13 to 15 years old sleep 9.5 hours a day. How many hours does the average teenager spend sleeping in a year?
1825
hours
 9.5
365

20. 20 days × 2 rides per day = 40 rides per month
Check It Out: Example 3B
Maria commutes to and from work on the train 20 days each month. Her train ride each way lasts 1.2 hours. How many hours does she spend commuting to work each month?
20 days × 2 rides per day = 40 rides per month
 40
1.2
48.0 hours 20

21. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 21

22. 5. Dennis runs 7.2 miles per day. How far does he run in 5 days? 6.3
Lesson Quiz
Multiply.
1. 9 · 0.7
2. (1.5)2
Multiply. Estimate to check whether each answer is reasonable · 4.1
· (–5.4)
5. Dennis runs 7.2 miles per day. How far does he run in 5 days?
6.3
2.25
13.94; Estimate: 3 • 4 = 12
–41.148; Estimate: 8 • (–5) = –40
36 miles 22

23. Lesson Quiz for Student Response Systems
1. Multiply.
7 · 0.5
A. 35
B. 3.5
C. 0.35 D 23

24. Lesson Quiz for Student Response Systems
2. Simplify.
(4.5)2
A. 9 B C
D. 25 24

25. Lesson Quiz for Student Response Systems
3. Multiply and then estimate to check whether the answer is reasonable.
2.4 · 3.2
A. 12; estimate: 4 · 3 = 12
B. 7.68; estimate: 2 · 3 = 6
C. 6.8; estimate: 2 · 3 = 6
D. 6; estimate: 2 · 3 = 6 25

26. Lesson Quiz for Student Response Systems
4. Multiply and then estimate to check whether the answer is reasonable.
8.53 · (–6.3)
A. –47.891; estimate: 8 · (–6) = –48
B. –48.739; estimate: 8 · (–6) = –48
C. –53.739; estimate: 9 · (–6) = –54
D. –54.891; estimate: 9 · (–6) = –54 26

27. Lesson Quiz for Student Response Systems
5. Kenneth travels 4.5 miles per day. How much does he travel in 6 days?
A. 30 miles
B. 28 miles
C. 27 miles
D. 24 miles 27