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4-1. Estimate with Decimals. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 4-1. Estimate with Decimals. Course 2. Warm Up Estimate. 1. 2 7 • 30 2. 85 • 92 3. 12 • 28 4. 185 • 201. 900. 8,100. 300. 40,000. 4-1. Estimate with Decimals. Course 2.

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4-1

Estimate with Decimals

Course 2

Warm Up

Problem of the Day

Lesson Presentation

4-1

Estimate with Decimals

Course 2

Warm Up

Estimate.

1. 27 • 30

2.85• 92

3. 12 • 28

4. 185 • 201

900

8,100

300

40,000

4-1

Estimate with Decimals

Course 2

Problem of the Day

I am a two-digit decimal greater than 0.25 and less than . My hundredths

digit is 3 times my tenths digit. What number am I?

2

5

0.26 or 0.39

4-1

Estimate with decimals

Course 2

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

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Vocabulary

compatible numbers

4-1

Estimate with Decimals

Course 2

Jessie earned \$27.00 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.

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

\$14.75

7

7 > 5, so round to \$15

\$15

\$13

\$13.20

2

2 < 5, so round to \$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 integer

4-1

Estimate with Decimals

Remember!

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.

Course 2

Insert Lesson Title Here

4-1

Estimate with Decimals

4.5

+8.9

+9

Course 2

Insert Lesson Title Here

Additional Example 1A: Estimating Sums and Differences of Decimals

Estimate by rounding to the nearest integer.

A. 4.5 + 8.9

5

5 ≥ 5, so round to 5.

9 > 5, so round to 9.

Estimate

14

4-1

Estimate with Decimals

28.3

–11.7

–12

Course 2

Insert Lesson Title Here

Additional Example 1B: Estimating Sums and Differences of Decimals

Estimate by rounding to the nearest integer.

B. 28.3 – 11.7

28

3 < 5, so round to 28.

7 > 5, so round to 12.

Estimate

16

4-1

Estimate with Decimals

57.2

+ (–24)

+ (–23.72)

Course 2

Insert Lesson Title Here

Additional Example 1C: Estimating Sums and Differences of Decimals

Estimate by rounding to the nearest integer.

C. 57.2 + (–23.72)

57

2 < 5, so round to 57.

7 > 5, so round to –24.

33

Estimate

4-1

Estimate with Decimals

6.8

+4.9

+5

Course 2

Insert Lesson Title Here

Try This: Example 1A

Estimate by rounding to the nearest integer.

A. 6.7 + 4.9

7

8 ≥ 5, so round to 7.

9 > 5, so round to 5.

Estimate

12

4-1

Estimate with Decimals

19.2

–13.6

–14

Course 2

Insert Lesson Title Here

Try This: Example 1B

Estimate by rounding to the nearest integer.

B. 19.2 – 13.6

19

2 < 5, so round to 19.

6 > 5, so round to –14.

Estimate

5

4-1

Estimate with Decimals

61.3

+ (–19)

+ (–18.84)

Course 2

Insert Lesson Title Here

Try This: Example 1C

Estimate by rounding to the nearest integer.

C. 61.3 + (–18.84)

61

3 < 5, so round to 61.

8 > 5, so round to –19.

42

Estimate

4-1

Estimate with Decimals

Course 2

You can use compatible numbers when estimating.

Compatiblenumbers are numbers that

replace the numbers in the problem and

are easier to use.

4-1

Insert Lesson Title Here

Course 2

4-1

Estimate with Decimals

45.99

 2.31

 2

Course 2

Insert Lesson Title Here

Additional Example 2A: Estimating with Decimals

Use compatible numbers to estimate.

A. 45.99 · 2.31

Round to the nearest multiple of 10.

50

3 < 5, so round to 2.

100

Estimate

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Additional Example 2B: Estimating with Decimals

Use compatible numbers to estimate.

B. 51.33 ÷ (–7.98)

51 is prime, so round to 49.

51.33

49

–7.98

–7 divides into 49

without a remainder.

–7

49 ÷ –7 = –7

Estimate

4-1

Estimate with Decimals

39.62

 4.99

 5

Course 2

Insert Lesson Title Here

Try This: Example 2A

Use compatible numbers to estimate.

A. 39.62 · 4.99

Round to the nearest multiple of 10.

40

9 > 5, so round to 5.

200

Estimate

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Try This: Example 2B

Use compatible numbers to estimate.

B. 19.42 ÷ (–4.88)

19 is prime, so round to 20.

19.42

20

–4.88

–5 divides into 20

without a remainder.

–5

20 ÷ –5 = –4

Estimate

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Cara spent \$58.80 on 4.8 pounds of lobster and

calculated that she spent about \$12 per pound of

lobster. Use estimation to check whether her

calculation is reasonable.

\$60

\$58.80

Round to the nearest

multiple of 10.

8 > 5, so round to 5.

5

4.85

60 ÷ 5 = 12

Estimate

The estimate is the same as Cara’s calculation. The lobster cost about \$12 per pound.

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Try This: Example 3

Clem spent \$18.43 on 11.7 pounds of apples. Is it reasonable to say that Clem spent about \$2 per pound on apples?

Round to the nearest

multiple of 10.

\$20

18.43

10 divides evenly into 20 without a remainder.

10

11.7

20 ÷ 10 = 2

Estimate

The estimate is the same as Clem’s calculation. The apples cost about \$2 per pound.

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Lesson Quiz: Part 1

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

98

–4

250

9

4-1

Estimate with Decimals

Course 2

Insert Lesson Title Here

Lesson Quiz: Part 2

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. Does he have enough for the party?

no