math gr4 ch15

Chapter 15Decimals: Addition and Subtraction

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Chapter 15Decimals: Addition and Subtraction

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1515Decimals: Addition and Subtraction

Lesson 15-1 Round Decimals

Lesson 15-2 Estimate Decimal Sums and Differences

Lesson 15-3 Problem-Solving Strategy: Work Backward

Lesson 15-4 Add Decimals

Lesson 15-5 Problem-Solving Investigation: Choose a Strategy

Lesson 15-6 Subtract Decimals



Five-Minute Check (over Chapter 14)

Main Idea

California Standards

Example 1

Example 2

Example 3

15-115-1 Round Decimals



• I will round decimals.



Standard 4NS2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.


About 2.93 million people live in San Diego County, California. How many people live in San Diego County when rounded to the nearest whole number?




One Way: Use a Number Line

2.93 is between 2 and 3.It is closer to 3.

So, round 2.93 to 3.



Another Way: Use Rounding Rules

Use the same process that you use with rounding whole numbers.

Answer: To the nearest whole number, 2.93 rounds to 3.

2.93



Round 4.65 to the nearest whole number.

A. 3

B. 4

C. 5

D. 6


Round 46.45 to the nearest whole number. Use the rounding rules.

Answer: To the nearest whole number, 46.45 rounds to 46.


46.45




A. 89

B. 88

C. 87

D. 86


A golfer had an average score of 72.84 in one season. Round this score to the nearest tenth. Use rounding rules.

Answer: To the nearest tenth, 72.84 rounds to 72.8.


72.84



Round 92.37 to the nearest tenth.

A. 92.2

B. 92.3

C. 92.4

D. 92.5


Five-Minute Check (over Lesson 15-1)

Main Idea


Key Concept: Estimate Decimal Sums

Key Concept: Estimate Decimal Differences

Example 1

Example 2

15-215-2 Estimate Decimal Sums and Differences



• I will use rounding to estimate sums and differences.



Standard 4NS2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places.


Martina is going white water rafting with her family. During their first day, they will travel 6.5 miles before lunch and 8.75 miles after lunch. About how far will they travel on their first day?


To estimate the sum of decimals, you can round each decimal to the nearest whole number and then add.


Belkis rides her bike 4.6 miles on Saturday and 6.25 miles on Sunday. About how many miles does she ride her bike altogether on both days?

4.6

Answer: So, Belkis rode her bike about 11 miles.


+ 6.255

+ 6Round 4.6 to 5 Round 6.25 to 6

You need to estimate 4.6 + 6.25. Round each addend to the nearest whole number. Then add.

11



Adriano ran 2.3 miles on Friday and 3.45 miles on Saturday. About how many miles did he run altogether on both days?

A. 3

B. 4

C. 5

D. 6



Jairo has $38.55. If he buys a CD that costs $16.99, about how much money will he have left?

You need to estimate $38.55 – $16.99. Round each decimal to the nearest whole number. Then subtract.



Answer: So, Jairo will have about $22 left.

$39 – $17

$22

$38.55 – $16.99

$39 – $17

Round $38.55 to $39. Round $16.99 to $17.



Sonia has $42.67. If she buys a pair of shoes for $24.99, about how much money will she have left?

A. $18

B. $19

C. $20

D. $21



Main Idea


Example 1: Problem-Solving Strategy

15-315-3 Problem-Solving Strategy: Work Backward



• I will solve problems by working backward.



Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.



Standard 4NS3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.


Rey has lacrosse practice in the evenings. He gets home from school and eats a snack for 15 minutes. Then he spends 1 hour doing his homework. It takes him 15 minutes to get to practice. Practice is at 5 P.M. What time does Rey get home from school?



Understand

What facts do you know?

• Rey eats a snack for 15 minutes.

• He works on homework for 1 hour.

• It takes 15 minutes to get to practice at 5 P.M.

What do you need to find?

• What time Rey gets home from school.



Plan

Work backward to solve the problem.



SolveStart with the end result. Then work backward one step at a time.


5 P.M. – 15 minutes = 4:45 P.M.

practice starts

time to get to practice

4:45 P.M. – 1 hour = 3:45 P.M.

time spent on homework


Solve


3:45 P.M. – 15 minutes = 3:30 P.M.

time spent eating

Answer: So, Rey got home from school at 3:30 P.M.


Check

Look back at the problem. 15 + 1 hour + 15 minutes = 1 hour and 30 minutes. If he gets home at 3:30 P.M., one hour and 30 minutes later would be 5 P.M. The answer is correct.




Main Idea


Example 1

Example 2

15-415-4 Add Decimals

Addition of Decimals



• I will add decimals.




Standard 4MR2.1 Use estimation to verify the reasonableness of calculated results.


Odina slept 8.3 hours on Monday night and 7.66 hours on Tuesday night. How many hours did she sleep on the two nights combined?


Estimate 8.3 + 7.66 8 + 8 = 16

Step 1 Line up the decimal points.

8.30 + 7.66

Write a 0 in the hundredths place as a placeholder.



Step 2 Add.

Add the digits in each place value. Then bring the decimal point straight down in the sum. 15.96

8.30 + 7.66

Answer: So, Odina slept a total of 15.96 hours.



Check for Reasonableness.

Since 15.96 is close to the estimate of 16, the answer is reasonable.



Meredith studied for 2.4 hours on Tuesday night and 1.83 hours on Wednesday night. How many hours did she spend studying on the two nights combined?

A. 3.23

B. 4.23

C. 4.33

D. 5.23



Kate spent $1.25 for a juice box and $1.79 for yogurt. How much did she spend in all?

Estimate $1 + $2 = $3


$1.25 + $1.79

You need to find $1.25 + $1.79.



Step 2 Add.

Add the digits in each place value. Regroup if necessary.

$3.04

$1.25 + $1.79

11

Answer: So, Kate spent $3.04.




The sum of $3.04 is close to the estimate of 3, so the answer is reasonable.



Jerome spent $2.55 on a sandwich and $1.75 on a bottle of juice. How much did he spend in all?

A. $3.20

B. $4.20

C. $4.30

D. $4.75



Main Idea


Example 1: Problem-Solving Investigation

15-515-5 Problem-Solving Investigation: Choose a Strategy



• I will choose the best strategy to solve a problem.



Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.



Standard 4SDAP1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.


Jennifer: My friends and I have pets. We all have different kinds of pets. Among the three of us, we have a lizard, a cat, a gerbil, and a snake. I do not have a cat. Rondell’s pet is not a gerbil or a snake. Lorena’s two pets are not lizards. My pet does not begin with the letters s or g.



YOUR MISSION: Find with person owns each pet.



Understand

What facts do you know?

• You know the clues for each person’s pet.

What do you need to find?

• You need to find which person owns each pet.



Plan

Make a table to show what you know. Then use logical reasoning to find which person owns each pet.



Solve

Make a table. Write a yes or no for each fact that you are given. Once you write yes in the table, you can write no in the rest of the boxes in that row and column.



Solve

Answer: So, Jennifer owns a lizard. Lorena owns a gerbil and a snake. Rondell owns a cat.



Check

Look back at the problem. The solution matches the facts given in the problem. So, the answer is correct.




Main Idea


Example 1

Example 2

15-615-6 Subtract Decimals

Subtraction of Decimals



• I will subtract decimals.




Standard 4MR2.1 Use estimation to verify reasonableness of calculated results.



A fruit stand sells a bag of grapes for $1.70 and a bunch of bananas for $1.19. What is the difference in price?


$1.70 – $1.19

Estimate $1.70 – $1.19 $1.7 – $1.2 = $0.50



Step 2 Subtract. Regroup if needed.

Bring the decimal point straight down in the sum.

Answer: So, the difference in price is $0.51.

$1.70 – $1.19

$0.51

106




Since the answer of $0.51 is close to the estimate of $0.50, the answer is reasonable.



Find the difference between 2.25 and 1.4.

A. 1.85

B. 0.85

C. 0.05

D. 0.80



Arati is 52.5 inches tall and her sister is 48.8 inches tall. How much taller is Arati than her sister?


52.5 – 48.8

Estimate 52.5 – 48.8 53 – 49 = 4



Step 2 Subtract.

Subtract the digits in each place value. Regroup if necessary.

Answer: So, Arati is 3.7 inches taller than her sister.

151

52.5 – 48.8

114

3.7




The answer 3.7 is close to the estimate of 4. So, the answer is reasonable.

You can also add to check.

48.8 + 3.7

52.5

So, the answer is correct.



Find the difference between 78.2 and 55.1.

A. 231

B. 2.31

C. 23.1

D. 0.231



Five-Minute Checks

Addition of Decimals

Subtraction of Decimals


Lesson 15-1 (over Chapter 14)

Lesson 15-2 (over Lesson 15-1)






(over Chapter 14)

A. <

B. >

C. =

Compare. Write <, >, or =.

6 7 310


(over Chapter 14)

A. <

B. >

C. =


5.6 5


(over Chapter 14)

A. <

B. >

C. =


2 2.1110


(over Chapter 14)

A. <

B. >

C. =


4.7 4.07


(over Chapter 14)

Use a number line to order from greatest to least.

11 , 11.9, 11 , 11.2538100

12

A. 11.9, 11.25, 11 , 11 38100

12

B. 11 , 11.9, 11.25, 1138100

12

C. 11.9, 11 , 11 , 11.25 38100

12

D. 11 , 11.9, 11 , 11.25 38100

12


(over Chapter 14)

Use a number line to order from greatest to least.

A. 3.2, 3 , 4 , 4.6245

510

3 , 4.62, 3.2, 445

510

B. 4 , 4.62, 3 , 3.2 45

510

C. 4.62, 4 , 3.2, 3 45

510

D. 4.62, 4 , 3 , 3.2 45

510


(over Lesson 15-1)


A. 1.5

B. 1

C. 2

D. 0



A. 26

B. 20

C. 27

D. 30

(over Lesson 15-1)



A. 53

B. 50

C. 53.5

D. 54

(over Lesson 15-1)



A. 67

B. 70

C. 60

D. 68

(over Lesson 15-1)



A. 3.1

B. 3

C. 0

D. 3.2

(over Lesson 15-1)



A. 9.3

B. 9

C. 9.4

D. 10

(over Lesson 15-1)



A. 49

B. 48.5

C. 48

D. 48.1

(over Lesson 15-1)



A. 92.7

B. 93

C. 92.1

D. 92.6

(over Lesson 15-1)


(over Lesson 15-2)

Estimate. Round to the nearest whole number.

A. 4

B. 4.5

C. 5

D. 4.9

1.5+ 3.4


(over Lesson 15-2)


A. 49

B. 50.5

C. 50

D. 51

37.61+ 12.84


(over Lesson 15-2)


A. 21

B. 38

C. 22

D. 20.8

28.90 – 8.27


(over Lesson 15-2)


A. 47.7

B. 45

C. 46

D. 46.8

66.3 – 19.51


(over Lesson 15-2)


A. 19

B. 19.6

C. 20

D. 15.2

2.18 + 17.4


(over Lesson 15-2)


A. 52

B. 53

C. 52.6

D. 51

22.78 + 29.82


(over Lesson 15-2)


A. $8.00

B. $7.50

C. $12.52

D. $7.00

$52.25 – $44.77


(over Lesson 15-3)

Solve. Use the Work Backward strategy. A number is added to 2. Next, the sum is divided by 3. Then, 1 is subtracted from the quotient. The result is 3. What is the number?

A. 2

B. 7

C. 10

D. 12


(over Lesson 15-4)

Add. Use estimation to check for reasonableness.

A. 0.12

B. 12

C. 1.2

D. 1.4

0.8+ 0.4


(over Lesson 15-4)


A. 9.6

B. 10.66

C. 9.12

D. 9.66

8.20+ 1.46


(over Lesson 15-4)


A. 12.72

B. 13.82

C. 11.82

D. 13.72

4.35+ 9.47


(over Lesson 15-4)


A. $13.96

B. $12.86

C. $12.96

D. $12.97

$6.07+ $6.89


(over Lesson 15-4)


A. 58.30

B. 68.30

C. 58.29

D. 57.20

24.38+ 33.92


(over Lesson 15-4)


A. 85.90

B. 74.81

C. 75.91

D. 84.91

45.23+ 39.68


(over Lesson 15-4)


A. $71.02

B. $82.02

C. $82.12

D. $81.02

$62.50 + $19.52


(over Lesson 15-4)


A. 8.82

B. 3.05

C. 8.92

D. 4.15

5.3 + 2.47 + 1.15


(over Lesson 15-5)

Use any problem-solving strategy to solve. Finn, Malik, and Kwag are all wearing different colored shirts. Their shirts are red, blue, or green. Malik’s shirt is not blue. Finn’s shirt color doesn’t start with an “r” or a “g”. Kwag’s shirt is green. What color shirt is each boy wearing?

A. Finn: red; Malik: blue; Kwag: green

B. Finn: blue; Malik: green; Kwag: red

C. Finn: yellow; Malik: red; Kwag: green

D. Finn: blue; Malik: red; Kwag: green

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math gr4 ch15

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