Course 2

4-1 Estimate with Decimals4-1 Estimate with Decimals

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 2

4-1 Estimate with Decimals

Warm UpEstimate.

1. 27 • 30

2. 85 • 92

3. 12 • 28

4. 185 • 201

900

8,100

300

40,000

Course 2

4-1 Estimate with Decimals

Problem of the Day

I am a two-digit decimal greater than 0.25 and less than . My hundredthsdigit is 3 times my tenths digit. What number am I?0.26 or 0.39

52

Course 2

4-1 Estimate with Decimals

Learn to estimate decimal sums, differences, products, and quotients.

Course 2

4-1 Estimate with Decimals

Vocabulary

compatible numbers

Course 2

4-1 Estimate with Decimals

Jessie earned $26.00 for baby-sitting. She wants to use the money to buy a ticket to a water park for $14.75 and a souvenir T-shirt for $13.20.

To find out if Jessie has enough money to buy both items, you can use estimation. To estimate the total cost of the ticket and the T-shirt, round each price to the nearest dollar, or integer. Then add the rounded values.

Course 2

4-1 Estimate with Decimals

$14.757 7 > 5, so round to $15 $15

$13.202 2 < 5, so round to $13 $13+$28

The estimated cost is $28, so Jessie does not have enough money to buy both items.

To estimate decimal sums and differences,round each decimal to the nearest integerand then add or subtract.

Course 2

4-1 Estimate with Decimals

To round to the nearest integer, look at the digit in the tenths place. If it is greater than or equal to 5, round to the next integer. If it is less than 5, keep the same integer.

Remember!

Course 2

4-1 Estimate with Decimals

Estimate by rounding to the nearest integer.

4.5 + 8.9

5 5 ≥ 5, so round to 5.9 > 5, so round to 9.

4.5+8.9

14 Estimate+9

Additional Example 1A: Estimating Sums and Differences of Decimals

Course 2

4-1 Estimate with Decimals

Estimate by rounding to the nearest integer.

28.3 – 11.728 3 < 5, so round to 28.

7 > 5, so round to 12.28.3

–11.716 Estimate

–12

Additional Example 1B: Estimating Sums and Differences of Decimals

Course 2

4-1 Estimate with Decimals

Estimate by rounding to the nearest integer.

57.2 + (–23.72)57 2 < 5, so round to 57.

7 > 5, so round to –24. 57.2

+ (–23.72)33 Estimate

+ (–24)

Additional Example 1C: Estimating Sums and Differences of Decimals

Course 2

4-1 Estimate with Decimals

Estimate by rounding to the nearest integer.

6.7 + 4.97 8 ≥ 5, so round to 7.

9 > 5, so round to 5.6.8

+4.912 Estimate+5

Check It Out: Example 1A

Course 2

4-1 Estimate with Decimals

Estimate by rounding to the nearest integer.

19.2 – 13.619 2 < 5, so round to 19.

6 > 5, so round to –14.5 Estimate

–14

Check It Out: Example 1B

19.2–13.6

Course 2

4-1 Estimate with Decimals

Estimate by rounding to the nearest integer.

61.3 + (–18.84)61 3 < 5, so round to 61.

8 > 5, so round to –19. 61.3

+ (–18.84)42 Estimate

+ (–19)

Check It Out: Example 1C

Course 2

4-1 Estimate with Decimals

Compatible numbers are numbers that replace the numbers in the problem and are easier to use.

You can use compatible numbers when estimating.

Course 2

4-1 Estimate with Decimals

Guidelines for Using Compatible Numbers

When multiplying. . .

round numbers to the nearest nonzero integer or to numbers that are easy to multiply.

When dividing. . .

round numbers so that they divide without leaving a remainder.

Course 2

4-1 Estimate with Decimals

Use compatible numbers to estimate.

45.99 · 2.31

50Round to the nearest multiple of 10.

100 Estimate

2

Additional Example 2A: Estimating Products and Quotients of Decimals

3 < 5, so round to 2.45.99

2.31

Course 2

4-1 Estimate with Decimals

Use compatible numbers to estimate.

51.33 ÷ (–7.98)

51.33 48 51 is prime, so round to 48.

–8 –8 divides into 48 without a remainder.

–7.98

Estimate

Additional Example 2B: Estimating Products and Quotients of Decimals

48 ÷ –8 = –6

A prime number has exactly two factors. 1 and itself. So the factors of 51 are 1 and 51.

Remember!

Course 2

4-1 Estimate with Decimals

Use compatible numbers to estimate.

39.62 · 4.99

40Round to the nearest multiple of 10.

200 Estimate

5

Check It Out: Example 2A

9 > 5, so round to 5.39.62

4.99

Course 2

4-1 Estimate with Decimals

Use compatible numbers to estimate.

19.42 ÷ (–4.88)

19.42 20 19 is prime, so round to 20.

–5 –5 divides into 20 without a remainder.

–4.88

Estimate

Check It Out: Example 2B

20 ÷ –5 = –4

Course 2

4-1 Estimate with Decimals

Cara spent $58.80 on 4.8 pounds of lobster. Use estimation to check whether it is reasonable to spend $12 per pound on lobster.

$58.80 $60 Round to the nearest multiple of 10.

5 4.85

Estimate

Additional Example 3: Application

60 ÷ 5 = 12

8 > 5, so round to 5.

The estimate is the same as Cara’s calculation, so $12 per pound for lobster is a reasonable answer.

Course 2

4-1 Estimate with Decimals

Clem spent $18.43 on 11.7 pounds of apples. Use estimation to check whether it is reasonable to spend about $4 per pound on apples?

18.43 $20Round to the nearest multiple of 10.

10 11.7

Estimate

Check It Out: Example 3

20 ÷ 10 = 2

10 divides evenly into 20 without a remainder.

The estimate is more than Clem’s calculation, so it is not reasonable to spend $4 per pound of apples.

Course 2

4-1 Estimate with Decimals

Lesson Quiz: Part I

Estimate by rounding to nearest integer.

1. 68.4 + 29.5

2. 7.24 + (–10.5)

Use compatible numbers to estimate.

3. 48.27 4.67

4. 54.37 5.67

–4

98

250

9

Possible answers:

Course 2

4-1 Estimate with Decimals

Lesson Quiz: Part II

Use compatible numbers to estimate.

5. Ray is catering a party for 60 people. He needs to have 30 pounds of potato salad. He has made 6.21 pounds and 22.68 pounds. Estimate to check whether he has enough for the party?

No; The estimate is 29 pounds.