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![Page 1: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/1.jpg)
Chapter 6Multiplying and Dividing Decimals and Fractions
Click the mouse or press the space bar to continue.
Chapter 6Multiplying and Dividing Decimals and Fractions
Click the mouse or press the space bar to continue.
![Page 2: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/2.jpg)
66Multiplying and Dividing Decimals and Fractions
Lesson 6-1 Multiplying Decimals by Whole Numbers
Lesson 6-2 Multiplying Decimals
Lesson 6-3 Problem-Solving Strategy: Reasonable Answers
Lesson 6-4 Dividing Decimals by Whole Numbers
Lesson 6-5 Dividing by Decimals
Lesson 6-6 Problem-Solving Investigation: Choose the Best Strategy
Lesson 6-7 Estimating Products of Fractions
Lesson 6-8 Multiplying Fractions
Lesson 6-9 Multiplying Mixed Numbers
Lesson 6-10 Dividing Fractions
Lesson 6-11 Dividing Mixed Numbers
![Page 3: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/3.jpg)
Five-Minute Check (over Chapter 5)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
Example 4
Example 5
6-16-1 Multiplying Decimals by Whole Numbers
![Page 4: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/4.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
• I will estimate and find the product of decimals and whole numbers.
• scientific notation
![Page 5: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/5.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.
![Page 6: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/6.jpg)
Find 18.9 × 4.
6-16-1 Multiplying Decimals by Whole Numbers
One Way: Use estimation.
Round 18.9 to 19.18.9 × 4 19 × 4 or 76
18.9× 4
6
Since the estimate is 76, place the decimal point after the 5.
33
57 .
![Page 7: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/7.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Another Way: Count decimal places.
18.9× 4
6
33
57 .
![Page 8: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/8.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Find 12.7 × 5.
A. 64
B. 63.5
C. 60.35
D. 63.35
![Page 9: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/9.jpg)
Find 0.56 × 7.
6-16-1 Multiplying Decimals by Whole Numbers
One Way: Use estimation.
Round 0.56 to 1.0.56 × 7 1 × 7 or 7
0.56× 7
2
Since the estimate is 7, place the decimal point after the 3.
43
93.
![Page 10: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/10.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Another Way: Count decimal places.
0.56× 7
2
43
93.
![Page 11: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/11.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Find 0.47 × 8.
A. 8
B. 5
C. 4.76
D. 0.392
![Page 12: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/12.jpg)
Find 3 × 0.016.
6-16-1 Multiplying Decimals by Whole Numbers
0.016× 3
8
1
40.0
![Page 13: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/13.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Find 0.026 × 2.
A. 0.052
B. 0.52
C. 0.0052
D. 0.502
![Page 14: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/14.jpg)
ALGEBRA Evaluate 5g if g = 0.0091.
6-16-1 Multiplying Decimals by Whole Numbers
0.0091× 5
5
4
504
5g = 5 × 0.0091 Replace g with 0.0091.
0.
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6-16-1 Multiplying Decimals by Whole Numbers
ALGEBRA Evaluate 3h if h = 0.0054.
A. 1.62
B. 0.162
C. 0.00162
D. 0.0162
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The average distance from Earth to the Sun is 1.5 × 108 kilometers. Write the distance in standard form.
6-16-1 Multiplying Decimals by Whole Numbers
One Way: Use order of operations.
Evaluate 108 first.Then multiply.
1.5 × 108 = 1.5 × 10,000,000= 150,000,000 kilometers
![Page 17: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/17.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
Another Way: Use mental math.
Move the decimal point to the right the same number of places as the exponent of 10, or 8 places.
1.5 × 108 = 1.50000000
= 150,000,000
![Page 18: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/18.jpg)
6-16-1 Multiplying Decimals by Whole Numbers
The average distance from the Sun to the planet Jupiter is 58.8 × 107 kilometers. Choose the answer showing the distance written in standard form.
A. 588,000,000 kilometers
B. 58,000,000 kilometers
C. 5,880,000,000 kilometers
D. 5,800,000 kilometers
![Page 20: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/20.jpg)
Five-Minute Check (over Lesson 6-1)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
6-26-2 Multiplying Decimals
![Page 22: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/22.jpg)
6-26-2 Multiplying Decimals
Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.
![Page 23: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/23.jpg)
6-26-2 Multiplying Decimals
Estimate 8.3 × 2.9 8 × 3 or 24
×8.32.9747
+ 16624.07
Find 8.3 × 2.9.
one decimal placeone decimal place
two decimal places
Answer: So, the product is 24.07.
![Page 24: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/24.jpg)
6-26-2 Multiplying Decimals
Check for Reasonableness
Compare 24.07 to the estimate. 24.07 is about 24.
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Find 0.12 × 5.3.
6-26-2 Multiplying Decimals
Estimate 0.12 × 5.3 0 × 5 or 0
×0.12
5.336
+ 600.636
two decimal placesone decimal place
three decimal places
Answer: So, the product is 0.636.
![Page 27: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/27.jpg)
6-26-2 Multiplying Decimals
Check for Reasonableness
Compare 0.636 to the estimate. 0.636 is about 0.
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6-26-2 Multiplying Decimals
Find 0.14 × 3.3.
A. 0.636
B. 0.543
C. 0.462
D. 0.723
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ALGEBRA Evaluate 1.8r if r = 0.029.
6-26-2 Multiplying Decimals
1.8r = 1.8 × 0.029 Replace r with 0.029.
×0.029
1.8232
+ 290.0522
one decimal place
Annex a zero to make four decimal places.
Answer: So, the product is 0.0522.
three decimal places
![Page 30: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/30.jpg)
6-26-2 Multiplying Decimals
ALGEBRA Evaluate 2.7x if x = 0.038.
A. 2.738
B. 0.1026
C. 0.0126
D. 0.2106
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Carmen earns $14.60 per hour as a painter’s helper. She worked a total of 15.75 hours one week. How much money did she earn?
6-26-2 Multiplying Decimals
×$14.60
15.757300
10220
229.9500
two decimal placestwo decimal places
73001460+
Estimate 14.60 × 15.75 15 × 16 or 240.
![Page 32: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/32.jpg)
Compare $229.95 to the estimate. $229.95 is about $240.
Answer: So, Carmen earned $229.95.
6-26-2 Multiplying Decimals
Check for Reasonableness
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6-26-2 Multiplying Decimals
Alex went shopping for 6.5 hours and spent $32.50 per hour. How much did she spend?
A. $211.25
B. $225
C. $250.25
D. $211.50
![Page 35: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/35.jpg)
Five-Minute Check (over Lesson 6-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
6-36-3 Problem-Solving Strategy: Reasonable Answers
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6-36-3 Problem-Solving Strategy: Reasonable Answers
• I will solve problems by determining reasonable answers.
![Page 37: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/37.jpg)
6-36-3 Problem-Solving Strategy: Reasonable Answers
Standard 5MR3.1 Evaluate the reasonableness of the solution in the context of the original situation.
Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.
![Page 38: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/38.jpg)
6-36-3 Problem-Solving Strategy: Reasonable Answers
For their science project, Stephanie and Angel need to know about how much more a blue whale weighs in pounds than a humpback whale.
They have learned that there are 2,000 pounds in one ton. While doing research, they found a table that shows the weights of whales in tons.
![Page 39: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/39.jpg)
Understand
What facts do you know?
• There are 2,000 pounds in one ton.
• A blue whale weighs 151.0 tons.
• A humpback whale weighs 38.1 tons.
What do you need to find?
• A reasonable estimate of the difference in the weight of a blue whale and a humpback whale.
6-36-3 Problem-Solving Strategy: Reasonable Answers
![Page 40: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/40.jpg)
Plan
Estimate to find the weight of each whale in pounds and then subtract to find a reasonable estimate of the difference.
6-36-3 Problem-Solving Strategy: Reasonable Answers
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Solve
Blue whale:
Answer: A reasonable estimate for the difference in the weight of a blue whale and a humpback whale is 220,000 pounds.
6-36-3 Problem-Solving Strategy: Reasonable Answers
Humpback whale:
2,000 × 151
2,000 × 38.1
2,000 × 150
2,000 × 40
300,000 80,000
300,000 – 80,000 = 220,000
![Page 42: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/42.jpg)
Check
6-36-3 Problem-Solving Strategy: Reasonable Answers
Look back at the problem. A blue whale weighs about 150 – 40 or 110 more tons than a humpback whale. This is equal to 110 × 2,000 or 220,000 pounds. So the answer is reasonable.
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Five-Minute Check (over Lesson 6-3)
Main Idea
California Standards
Example 1
Example 2
Example 3
6-46-4 Dividing Decimals by Whole Numbers
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6-46-4 Dividing Decimals by Whole Numbers
• I will divide decimals by whole numbers.
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6-46-4 Dividing Decimals by Whole Numbers
Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.
![Page 47: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/47.jpg)
6-46-4 Dividing Decimals by Whole Numbers
Standard 5NS2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.
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Find 7.2 ÷ 3.
6-46-4 Dividing Decimals by Whole Numbers
Estimate 7.2 ÷ 3 7 ÷ 3 or about 2.
3 7.22 4.
– 61 2
– 1 20 7.2 ÷ 3 = 2.4 Compared to the estimate,
the quotient is reasonable.
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6-46-4 Dividing Decimals by Whole Numbers
Find 6.4 ÷ 4.
A. 8
B. 16
C. 1.6
D. 0.8
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Find 6.6 ÷ 15.
6-46-4 Dividing Decimals by Whole Numbers
Estimate 6.6 ÷ 15 7 ÷ 15 or about 0.5.
15 6.60 4.
– 06 6
– 6 06
6.6 ÷ 15 = 0.44 Compared to the estimate, the quotient is reasonable.
40
0– 60
0
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6-46-4 Dividing Decimals by Whole Numbers
Find 8.8 ÷ 16.
A. 5.5
B. 0.55
C. 0.22
D. 2.2
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During a science experiment, Nita measured the mass of four unknown samples. Her data is shown below.
6-46-4 Dividing Decimals by Whole Numbers
Sample 1: 6.22 g
Sample 2: 6.00 g
Sample 3: 6.11 g
Sample 4: 6.11 g
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First, add all the data together.
Answer: So, the mean mass of Nita’s samples is 6.11 grams.
6-46-4 Dividing Decimals by Whole Numbers
+
6.226.006.116.11
24.44
Divide by the number of addends to find the mean mass.
4 24.446.11
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6-46-4 Dividing Decimals by Whole Numbers
Greta bought 4 pairs of socks for $25.36. If each pair of socks costs the same amount, how much was each pair?
A. $6.34
B. $6.00
C. $4.63
D. $3.64
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Five-Minute Check (over Lesson 6-4)
Main Idea
California Standards
Example 1
Example 2
Example 3
Example 4
6-56-5 Dividing by Decimals
Dividing Decimals
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6-56-5 Dividing by Decimals
Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.
![Page 59: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/59.jpg)
6-56-5 Dividing by Decimals
Standard 5NS2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.
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Find 21.44 ÷ 6.4.
Estimate 21 ÷ 7 = 3
6-56-5 Dividing by Decimals
64 214.43 3.
– 19222 4
–
0
3 2–
0
6.4 21.444
19 20
3 20
Divide as with whole numbers.
Annex a zero to continue.
Place the decimal point.
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21.44 divided by 6.4 is 3.34.
6-56-5 Dividing by Decimals
Compare to the estimate.
3.34 × 6.4 = 21.44
Check
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Find 72 ÷ 0.4.
6-56-5 Dividing by Decimals
4 720.18 .
– 432
–00
–0
0.4 72.00
32
0
Place the decimal point.
Answer: So, 72 ÷ 0.4 = 180.
Check 180 × 0.4 = 72
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Find 0.024 ÷ 2.4.
6-56-5 Dividing by Decimals
24 0.240 0.
– 002
–24
–0
2.4 0.0241
0
24
Place the decimal point.
Answer: So, 0.024 ÷ 2.4 = 0.01.
Check 0.01 × 2.4 = 0.024
24 does not go into 2, so write a 0 in the tenths place.
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Ioviana bought a stock at $42.88 per share. If she spent $786.85, how many shares did she buy? Round to the nearest tenth.
6-56-5 Dividing by Decimals
42.88 786.85
Find 786.85 ÷ 42.88.
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6-56-5 Dividing by Decimals
42.88 78685.008 3.
– 428835805
–1501 0
5
34304
Answer: So, to the nearest tenth, 786.85 ÷ 42.88 = 18.4. So, Ioviana bought about 18.4 shares.
1
1286 4–2146 02144 0–
20
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6-56-5 Dividing by Decimals
Oprah bought televisions for everyone in her audience at $245.75 per TV. If she spent $21,773.45 about how many people were in the audience? Round to the nearest whole number.
A. 88.6 people
B. 88 people
C. 89 people
D. 90 people
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Five-Minute Check (over Lesson 6-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
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6-66-6 Problem-Solving Investigation: Choose the Best Strategy
• I will choose the best strategy to solve a problem.
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6-66-6 Problem-Solving Investigation: Choose the Best Strategy
Standard 5MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; . . . and verify the reasonableness of results.
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MIGUEL: At the store, I saw the following items: a batting glove for $8.95, roller blades for $39.75, a can of tennis balls for $2.75, and weights for $5.50. I have $15 and I would like to buy more than one item.
YOUR MISSION: Find which items Miguel can buy and spend about $15.
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
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Understand
What facts do you know?
• You know the cost of the items and that Miguel has $15 to spend.
What do you need to find?
• You need to find which items Miguel can buy.
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
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Plan
Make an organized list to see the different possibilities and use estimation to be sure he spends about $15.
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
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Solve
Since the roller blades cost more than $15, you can eliminate the roller blades. The batting glove is about $9, the weights are about $6, and the can of tennis balls is about $3.
Start with the batting glove:
• 1 glove + 1 weights ≈ $9 + $6 or $15
• 1 glove + 2 cans of tennis balls ≈ $9 + $6 or $15
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
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Solve
List other combinations that contain the weights:
• 2 weights + 1 can of tennis balls ≈ $12 + $3 or $15
• 1 weights + 3 cans of tennis balls ≈ $6 + $9 or $15
List the remaining combinations that contain only tennis balls:
• 5 cans of tennis balls ≈ $15
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
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Check
6-66-6 Problem-Solving Investigation: Choose the Best Strategy
Check the list to be sure that all of the possible combinations of sporting good items that total no more than $15 are included.
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Five-Minute Check (over Lesson 6-6)
Main Idea and Vocabulary
California Standards
Example 1
Example 2
Example 3
6-76-7 Estimating Products of Fractions
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6-76-7 Estimating Products of Fractions
• I will estimate products of fractions using compatible numbers and rounding.
• compatible numbers
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6-76-7 Estimating Products of Fractions
Standard 5MR2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
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6-76-7 Estimating Products of Fractions
Find a multiple of 5 that is close to 16.
× 1615
× 16 means of 16. 15
15
Estimate × 16.15
× 1515
× 15 = 315
Answer: So, × 16 is about 3.15
15 and 5 are compatible numbers since 15 ÷ 5 = 3
15 ÷ 5 = 3
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6-76-7 Estimating Products of Fractions
A. 2
Estimate × 19.19
B. 3
C. 212
D. 214
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6-76-7 Estimating Products of Fractions
Find a multiple of 4 that is close to 23.
× 2314
Estimate × 23 first. 14
Estimate × 23.34
× 2414
× 24 = 614
Use 24 since 24 and 4 are compatible numbers.
24 ÷ 4 = 6
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6-76-7 Estimating Products of Fractions
Answer: So, of 23 is about 18.34
If of 24 is 6, then of 24 is 6 × 3 or 18.34
14
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6-76-7 Estimating Products of Fractions
Estimate × 29.35
B. 18
C. 17
A. 1725
D. 20
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6-76-7 Estimating Products of Fractions
×45
1 × 16
Estimate × .45
16
16
1 × 16
= 16
Answer: So, × is about .45
16
16
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6-76-7 Estimating Products of Fractions
Estimate × .56
23
B. 2
C. 1
A. 113
D. 213
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6-76-7 Estimating Products of Fractions
Estimate the area of the rectangle.
Round each mixed number to the nearest whole number.
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6-76-7 Estimating Products of Fractions
× 7 × 2 = 14
Answer: So, the area is about 14 square inches.
786
142
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6-76-7 Estimating Products of Fractions
Estimate the area of a rectangle with a width of
9 in. and a length of 3 in.45
18
A. 30 sq. in.
B. 27 sq. in.
C. 40 sq. in.
D. 36 sq. in.
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Five-Minute Check (over Lesson 6-7)
Main Idea
California Standards
Key Concept: Multiply Fractions
Example 1
Example 2
Example 3
Example 4
6-86-8 Multiplying Fractions
Multiplying Fractions
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6-86-8 Multiplying Fractions
Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
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6-86-8 Multiplying Fractions
Find × .15
16
15
× 16
=1 × 1 5 × 6
=1
30
Multiply the numerators.Multiply the denominators.
Simplify.
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6-86-8 Multiplying Fractions
Find × 7.58
58
× 7
=5 × 7 8 × 1
=358
Multiply.
Simplify.
Estimate × 7 = 3 .12
12
=58
× 71
Write 7 as . 71
or 438
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6-86-8 Multiplying Fractions
Find × .37
29
37
× =3 × 2 7 × 9
=6
63
Multiply.
Simplify.
Estimate × 0 = 0.12
or
29
221
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6-86-8 Multiplying Fractions
ALGEBRA Evaluate pq if p = and q = .34
23
=3 × 2 4 × 3
The GCF of 2 and 4 is 2. The GCF of 3 and 3 is 3. Divide the numerator and the denominator by 2 and 3.
pq = ×34
23
Replace p with and q with .34
23
1
1
1
2
=12
Simplify.
Answer: So, × = .34
23
12
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6-86-8 Multiplying Fractions
ALGEBRA Evaluate gh if g = and h = .25
510
B. 15
A. 12
C. 1050
D. 5
50
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Five-Minute Check (over Lesson 6-8)
Main Idea
California Standards
Key Concept: Multiply Mixed Numbers
Example 1
Example 2
Example 3
6-96-9 Multiplying Mixed Numbers
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6-96-9 Multiplying Mixed Numbers
Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
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6-96-9 Multiplying Mixed Numbers
Find × 3 .38
13
38
× 3 13
Estimate Use compatible numbers × 3 = 112
12
3 × 10 8 × 3
=
Write 3 as . 13
103=
38
× 103
=54
or 114
Divide 10 and 8 by their GCF, 2. Divide 3 and 3 by their GCF, 3.
Simplify. Compare to the estimate.
5
4 1
1
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6-96-9 Multiplying Mixed Numbers
Find × 2 .45
23
C. 3
A. 2 2
15
12D. 3
B. 2 12
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6-96-9 Multiplying Mixed Numbers
Belinda lives 1 times farther from school than
Elena does. If Elena lives 4 miles from school,
how far from school does Belinda live?
12
15
Elena lives 4 miles from school. Multiply 4 × 1 .15
12
15
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6-96-9 Multiplying Mixed Numbers
4 × 115
12
21 × 3 5 × 2
=
First, write mixed numbers as improper fractions.
=32
×215
Then, multiply the numerators and multiply the denominators.
Simplify.= or 66310
310
Answer: So, Belinda lives 6 miles from school.310
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6-96-9 Multiplying Mixed Numbers
Mariah is making 4 times the recipe for crispy
treats. If the recipe calls for 1 cups of butter, how
much butter will she need?
14
14
A. 8516
B. 5 15
C. 5 5
16
D. 2516
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6-96-9 Multiplying Mixed Numbers
ALGEBRA If y = 3 and w = 2 , what is the value
of wy?
34
45
=Divide the numerator and denominator by 2 and 5.
Simplify.
7
2 1
3
wy = 2 × 3 45
34 Replace w with 2 and y with 3 .
45
34
154 ×
145
= or 10 12
212
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6-96-9 Multiplying Mixed Numbers
ALGEBRA If m = 4 and n = 2 , what is the value of mn?
58
67
C. 13 3
14
D. 13
A. 18514
B. 18014
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Five-Minute Check (over Lesson 6-9)
Main Idea and Vocabulary
California Standards
Key Concept: Divide Fractions
Example 1
Example 2
Example 3
Example 4
Example 5
6-106-10 Dividing Fractions
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6-106-10 Dividing Fractions
Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
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Find the reciprocal of 8.
6-106-10 Dividing Fractions
Since, 8 × = 1, the reciprocal of 8 is .18
18
Answer: 18
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6-106-10 Dividing Fractions
Find the reciprocal of 6.
A. 6
B. 0.6
C. 61
D. 16
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6-106-10 Dividing Fractions
Answer: 53
Find the reciprocal of .35
Since, × = 1, the reciprocal of is .35
53
35
53
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6-106-10 Dividing Fractions
C. 22
D. 33
Find the reciprocal of .23
A. 32
B. 23
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6-106-10 Dividing Fractions
13
÷ 56
1 × 6 3 × 5
=
Multiply by the reciprocal .65
=25
Divide 3 and 6 by the GCF, 3.
Multiply numerators. Multiply denominators.
2
1
Find ÷ .13
56
=13
× 65
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6-106-10 Dividing Fractions
5 ÷ 16 Multiply by the reciprocal .
61
Simplify.
Find 5 ÷ .16
=51
× 61
= or 30301
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6-106-10 Dividing Fractions
A relay race is of a mile long. There are 4 runners
in the race. What portion of a mile will each racer
run?
34
Divide into 4 equal parts.34
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6-106-10 Dividing Fractions
Answer: So, each runner ran of a mile.316
= Multiply.
Simplify. = 316
÷ 434 Multiply by the reciprocal.=
34
× 14
34
× 14
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A. 34
B. 1
12
6-106-10 Dividing Fractions
C. 18
D. 24
Three ladies decided to knit the world’s longest
scarf. It was of a mile long. If each lady knit the
same amount, what portion of a mile did each lady
knit?
14
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Five-Minute Check (over Lesson 6-10)
Main Idea
California Standards
Key Concept: Dividing by Mixed Numbers
Example 1
Example 2
Example 3
6-116-11 Dividing Mixed Numbers
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6-116-11 Dividing Mixed Numbers
Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.
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6-116-11 Dividing Mixed Numbers
Find 6 ÷ 2 .14
12
6 ÷ 214
12
Estimate 6 ÷ 3 = 2
Write mixed numbers as improper fractions.=
254
÷ 52
Multiply by the reciprocal.=
254
× 25
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6-116-11 Dividing Mixed Numbers
Divide 2 and 4 by the GCF, 2, and 25 and 5 by the GCF, 5.=
254
× 25
1
2
5
1
Simplify. = or 2 1
252
Check for Reasonableness 2 is about 3.12
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6-116-11 Dividing Mixed Numbers
Find 3 ÷ 1 .34
12
C. 2
34D. 2
B. 2 12
A. 26
12
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6-116-11 Dividing Mixed Numbers
ALGEBRA Find a ÷ b if a = 2 and b = .58
23
a ÷ b
Write the mixed number as an improper fraction.=
218
÷ 23
= 2 ÷58
23
Multiply by the reciprocal.=218
× 32
Replace a with 2 and b with . 58
23
Simplify.=6316
or 31516
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6-116-11 Dividing Mixed Numbers
ALGEBRA Find f ÷ g if f = 3 and g = .23
58
D. 216
A. 535
C. 5 1315
B. 2 7
24
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6-116-11 Dividing Mixed Numbers
Estimate 180 ÷ 4 = 45
180 ÷ 3 34
Write mixed numbers as improper fractions.
A team took 3 days to complete 180 miles of an
adventure race consisting of hiking, biking, and river
rafting. How many miles did they average each day?
34
= ÷1801
154
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= 48
6-116-11 Dividing Mixed Numbers
Multiply by the reciprocal.= ×1801
415
Simplify.=72015
Compare to the estimate.
Answer: So, the team averaged 48 miles each day.
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6-116-11 Dividing Mixed Numbers
A cross country skier took 4 days to travel 240
miles. How many miles did he average each day?
23
D. 52 miles12
A. 51 miles37
B. 51 miles6
14
C. 50 miles 34
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66Multiplying and Dividing Decimals and Fractions
Five-Minute Checks
Dividing Decimals
Multiplying Fractions
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66Multiplying and Dividing Decimals and Fractions
Lesson 6-1 (over Chapter 5)
Lesson 6-2 (over Lesson 6-1)
Lesson 6-3 (over Lesson 6-2)
Lesson 6-4 (over Lesson 6-3)
Lesson 6-5 (over Lesson 6-4)
Lesson 6-6 (over Lesson 6-5)
Lesson 6-7 (over Lesson 6-6)
Lesson 6-8 (over Lesson 6-7)
Lesson 6-9 (over Lesson 6-8)
Lesson 6-10 (over Lesson 6-9)
Lesson 6-11 (over Lesson 6-10)
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66Multiplying and Dividing Decimals and Fractions
(over Chapter 5)
Find 6 – 2 .14
34
C. 4 12
D. 4
A. 3 12
B. 8 34
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66Multiplying and Dividing Decimals and Fractions
(over Chapter 5)
Find 5 – 3 .13
59
C. 8 69
A. 2 49
B. 1 79
D. 269
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66Multiplying and Dividing Decimals and Fractions
(over Chapter 5)
Find the value of n.
n + 1 = 835
A. 625
B. 6
D. 5
C. 4 35
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66Multiplying and Dividing Decimals and Fractions
(over Chapter 5)
Find the value of n.
C. 25
A. 3
B. 5
13
D. 1 56
n + 10 = 1212
13
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-1)
Find 3.8 × 2.
A. 5.8
B. 7.6
C. 5.6
D. 5
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66Multiplying and Dividing Decimals and Fractions
Find 0.6 × 25.
A. 15
B. 25
C. 10
D. 4
(over Lesson 6-1)
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66Multiplying and Dividing Decimals and Fractions
Find 0.038 × 15.
A. 0.63
B. 1.35
C. 0.57
D. 1
(over Lesson 6-1)
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66Multiplying and Dividing Decimals and Fractions
Find 0.0003 × 17.
A. 0.0021
B. 0.0034
C. 0.0051
D. 0.21
(over Lesson 6-1)
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66Multiplying and Dividing Decimals and Fractions
Mercury is approximately 3.6 × 107 miles from the Sun. How far is this?
A. 360 mi
B. 1,800,000 mi
C. 36,000,000 mi
D. 3,000,000 mi
(over Lesson 6-1)
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-2)
Find 75.4 × 2.9.
A. 150.36
B. 77.36
C. 125
D. 218.66
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-2)
Find 0.05 × 0.123.
A. 0.15
B. 0.00615
C. 0.00506
D. 1
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-2)
Evaluate 2.5y if y = 4.8.
A. 4.8
B. 10.48
C. 8.5
D. 12
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-2)
Selam makes $6.75 an hour. Last week, she worked 12.4 hours. How much did she earn?
A. $36.75
B. $48.55
C. $48.50
D. $83.70
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-3)
Determine a reasonable answer. Mr. Nieto has 63.75 yards of fencing. How many feet of fencing is that?
A. 127.50 ft
B. 191.25 ft
C. 255 ft
D. 33.75 ft
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66Multiplying and Dividing Decimals and Fractions
Cafeteria workers made 23.5 gallons of punch for an awards banquet. They are serving the punch in 1-quart pitchers. How many containers do they need for all the punch? (1 gal = 4 qt)
A. 11.75 pitchers
B. 40 pitchers
C. 4 pitchers
D. 94 pitchers
(over Lesson 6-3)
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-4)
Find 27.09 ÷ 9. Round to the nearest tenth if necessary.
A. 7.09
B. 4
C. 3.01
D. 7
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-4)
Find 378.5 ÷ 5. Round to the nearest tenth if necessary.
A. 75.7
B. 75
C. 35.5
D. 102
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-4)
Find 247.52 ÷ 7. Round to the nearest tenth if necessary.
A. 35.4
B. 24
C. 35.04
D. 23.5
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-4)
Find the mean for the following set of data: 7.8, 9.02, 2.62.
A. 4.5
B. 4.45
C. 6.48
D. 5.55
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-5)
Find 24.36 ÷ 4.2.
A. 5.8
B. 5.66
C. 4
D. 6.18
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-5)
Find 15.39 ÷ 0.05.
A. 128.5
B. 3
C. 12
D. 307.8
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-5)
Find 0.648 ÷ 0.12.
A. 0.85
B. 1.48
C. 5.4
D. 5.6
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-5)
Find 0.782 ÷ 3.4.
A. 0.023
B. 0.015
C. 4
D. 12
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-6)
Choose the best strategy to solve the problem. The sum of three consecutive numbers is 42. What are the three numbers?
A. 12, 14, 16
B. 15, 12, 9
C. 13, 14, 15
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66Multiplying and Dividing Decimals and Fractions
C. 1 × 36 = 6
(over Lesson 6-7)
Estimate the product.
A. × 38 = 816
× 3816
B. × 36 = 616
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-7)
Estimate the product.
A. 1 × 45 = 45
C. × 45 = 3023
× 4423
B. × 45 = 4523
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-7)
Estimate the product.
B. × 45 = 3038
× 38
45
C. × 45 = 1712
A. × 1 = 12
12
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-7)
B. 25 × 40 = 1,000 ft2
C. 26 × 40 = 1,040 ft2
A. 25 × 40 = 975 ft2
A pool is 25 feet wide and 39 feet long.
Estimate the area.
14
56
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-8)
Multiply. Write in simplest form.
× 23
910
13B.
C. 9
10
D. 35
A. 45
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-8)
Multiply. Write in simplest form.
× 45
56
45B.
D. 25
A. 23
C. 113
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-8)
Evaluate n if n = . Write each product in
simplest form.
89
34
B. 13
D. 39
A. 45
C. 23
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-8)
Evaluate 10n if n = . Write each product in
simplest form.
34
B. 423
D. 13
A. 7 12
C. 79
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-9)
Multiply. Write in simplest form.
× 1 23
910
B. 2 23
D. 2
C. 1 12
A. 3 35
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-9)
Multiply. Write in simplest form.
B. 24 12
C. 21 12
A. 10 15
5 × 4 56
15
D. 31 12
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-9)
The length of a square sandbox is 4 feet. What is
the area of the sandbox?
23
B. 23 ft2 59
C. 21 ft2 59
A. 21 ft2 79
![Page 188: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/188.jpg)
66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-9)
ALGEBRA If a = 4 and t = 1 , what is the value
of at?
45
116
C. 5 35
D. 6
A. 5 5
16
B. 3
16
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-10)
Divide. Write in simplest form.
÷ 45
110
D. 8
C. 4
B. 12
A. 5
10
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-10)
÷ 78
14
Divide. Write in simplest form.
B. 4
D. 2
C. 3
A. 3 12
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66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-10)
6 ÷ 23
Divide. Write in simplest form.
B. 3
D. 9
C. 8
A. 23
![Page 192: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/192.jpg)
66Multiplying and Dividing Decimals and Fractions
(over Lesson 6-10)
÷ 12
34
Divide. Write in simplest form.
C. 1
A. 23
B. 12
D. 13
![Page 193: Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing.](https://reader037.fdocuments.us/reader037/viewer/2022102801/56649e685503460f94b65100/html5/thumbnails/193.jpg)
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