1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up in Spiral Estimate by rounding to the nearest integer.
– 7.47 –
Multiply. 8 1 6 18
 76
63,992
6. 1,240  83
102,920
 712
584,552
 15
4,530

3. Standards California Extension of NS2.3
Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.
(Also a review of 5th grade NS2.1)
California
Standards

4. One of the coolest summers on record in the Midwest was in 1992
One of the coolest summers on record in the Midwest was in The average summertime temperature that year was 66.8°F. Normally, the average temperature is 4°F higher than it was in 1992.
To find the normal average summertime temperature in the Midwest, you can add 66.8°F and 4°F.

5. 66.8 + 4.0 70.8 Use zero as a placeholder so that
both numbers have the same number
of digits after their decimal points.
70.8
Add each column just as you would
add integers.
Line up the decimal points.
The normal average summertime temperature in the Midwest is 70.8°F.

6. Additional Example 1A: Adding and Subtracting Decimals
Add. Estimate to check whether the answer is
reasonable.
4.55
Line up the decimal points.
Use zero as a placeholder.
15.85
Add.
Estimate
= 16
15.85 is a reasonable answer.

7. Additional Example 1B: Adding and Subtracting Decimals
Subtract. Estimate to check whether the answer is reasonable.
28 –
28.000
Use zeros as placeholders.
–15.911
Line up the decimal points.
12.089
Subtract.
Estimate
28 – 16 = 12
is a reasonable answer.

8. Check It Out! Example 1A
Add. Estimate to check whether the answer is
is reasonable.
6.78
Line up the decimal points.
Use zero as a placeholder.
19.98
Add.
Estimate
= 20
19.98 is a reasonable answer.

9. Subtract. Estimate to check whether the answer is reasonable.
Check It Out! Example 1B
Subtract. Estimate to check whether the answer is reasonable.
34 –
34.000
Use zeros as placeholders.
–12.462
Line up the decimal points.
21.538
Subtract.
Estimate
34 – 12 = 22
is a reasonable answer.

10. 7  8 56 0.7  0.8 0. 56 1 decimal place 1 decimal place
To multiply decimals, multiply as you would with integers, and then place the decimal point. The product should have the same number of decimal places as the sum of the 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

11. Additional Example 2A: Multiplying Decimals
Multiply. Estimate to check whether the answer is reasonable.
2.4  2
2.4
 2
1 decimal place
0 decimal places
4.8
1 + 0 = 1 decimal place
Estimate
2  2 = 4
4.8 is a reasonable answer.

12. Additional Example 2B: Multiplying Decimals
Multiply. Estimate to check whether the 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.

13. Check It Out! Example 2A
Multiply. Estimate to check whether the answer is reasonable.
3.2  1.6
3.2
 1.6
1 decimal place
1 decimal place
1 92
+ 3 20
5.12
1 + 1 = 2 decimal places
Estimate
3  2 = 6
5.12 is a reasonable answer.

14. Check It Out! Example 2B
Multiply. Estimate to check whether the answer is reasonable.
–2.96  0.7
–2.96
 0.7
2 decimal places
1 decimal place
–2.072
2 + 1 = 3 decimal places
Estimate
–3  1 = –3
–2.072 is a reasonable answer.

15. 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
The person would weigh 32.3 pounds on Mars.

16. Check It Out! Example 3
Jet fuel weighs approximately 6.2 pounds
per gallon. If a plane was serviced with 1,012 gallons of fuel, how many pounds of fuel were used?
 6.2
1,012
0 decimal places
1 decimal place
202 4
6274.4
1 + 0 = 1 decimal place
A plane would use 6,274.4 pounds of fuel.

17. Lesson Quiz
Add, subtract, or multiply. Estimate to check whether your answer is reasonable. 1.
21.25; Estimate: = 21
6.72 – 4.16 2.
2.56; Estimate: 7 – 4 = 3
 4.1
 (–5.4)
5. Dennis runs 7.2 miles per day. How far does he run in 5 days?
13.94; Estimate: 3 • 4 = 12
–41.148; Estimate: 8 • (–5) = –40
36 miles