Numeracy: The Basics Workbook – Set L: Dividing...

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Companion Workbook to Numeracy: The Basics Video Series

NUMERAC Y:The Basics Workbook

Set L: Dividing Decimals

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i Set L: Dividing Decimals

Workplace Education Manitoba would like to express appreciation to the following for supporting the development of this curriculum:

The Government of Canada Human Resource Skills Development Canada (HRSDC)

and

The Manitoba Government

Industry Workforce Development (IWD), Entrepreneurship, Training and Trade (ETT)

Workplace Education Manitoba would also like to thank the individuals from across Manitoba who provided consultation, content, and feedback.

For more information, visit www.wem.mb.ca

or contact the Project Coordinator Lindsay Laidlaw at [email protected]

Workplace Education Manitoba

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©Workplace Education Manitoba, 2012 All rights reserved; no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopying, recording, or otherwise without prior written permission of the Publishers. This manual may not be lent, resold, hired out or otherwise disposed by way of trade in any form of binding or cover than that which it is published, without the prior consent of the Publishers.

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mailto:[email protected]

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NUMERACY: The Basics Workbook Set L: Dividing Decimals

INTRODUCTION What is Numeracy: The Basics Workbook?

This workbook is intended to accompany Workplace Education Manitoba’s (WEM) Numeracy: The Basics Video Series, a set of 50 videos that explain essential numeracy concepts. The refresher videos cover 25 critical numeracy topics, each broken into concept and practice. The video series and accompanying downloadable workbooks can be found on the WEM website at http://www.wem.mb.ca/learning_on_demand.aspx These Numeracy: The Basics workbooks provide an opportunity for additional skill-building practice. Numeracy: The Basics topics are:

Order of Operations 1 Order of Operations 2 Adding & Subtracting Fractions 1 Adding & Subtracting Fractions 2 Multiplying & Dividing Fractions Mixed & Improper Fractions Operations with Mixed Fractions 1 Operations with Mixed Fractions 2 Operations with Mixed Fractions 3 Adding & Subtracting Decimals Multiplying Decimals Dividing Decimals Order of Operations & Decimals Decimals, Fractions & Percent 1 Decimals, Fractions & Percent 2 Imperial Conversions Metric Conversions Metric and Imperial Conversions Geometry 1 – Perimeter Geometry 2 – Area Geometry 3- Volume Solving Equations 1 Solving Equations 2 Ratio & Proportion Averages

http://www.wem.mb.ca/learning_on_demand.aspx

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DIVIDING DECIMALS This workbook contains five skill-building practice sections. Solutions can be found at the end of the workbook. Practice Section A

Calculate the following. Stop dividing if you get more than 5 decimal places in your answer. 1. 4.4 2 = 2. 5.4 3 = 3. 3.5 4 = 4. 8.5 2.5 = 5. 9.3 1.5 = 6. 0.054 0.003 = 7. 3.8 0.5 = 8. 5.7 0.25 = 9. 13.34 5.8 = 10. 12.3 1.6 = 11. 9.3 1.8 = 12. 12.9 3.3 = 13. 9.8 2.7 = 14. 12.97 1.5 = 15. 14.87 (1.5 0.5) =

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Practice Section B

Calculate the following. Stop dividing if you get more than 5 decimal places in your answer. 1. 0.375 0.125 = 2. 53.3 2.05 = 3. 14.8 2.5 = 4. 15.3 2.4 = 5. 20.41 2.5 = 6. 21.525131 6.1 = 7. 4 0.48 = 8. 5.28 1.8 = 9. 3.6 3.7 = 10. 12.28 2.4 = 11. 12.9 6.6 = 12. 17.88 1.44 = 13. 684 40.5 = 14. 21.63 1.8 = 15. 0.875 0.52 =

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Practice Section C

Calculate the following. 1. 2254 4.6 = 2. 190.875 0.625 = 3. 12.9 3.3 0.05 = 4. 144.48 2.2 = 5. 456.8 3 0 =

Practice Section D

In this section, solutions for the practice questions contain commonly-made errors. For each question, circle the error(s) and give a correct solution. 1. Samuel says “when you divide any whole number by a decimal, the original number always gets

larger.” Leslie disagrees and responds by saying “I am convinced that any whole number divided by a decimal can result in a number smaller or larger than the original.” Would you support Samuel or Leslie? Defend your choice.

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2. Below is a possible solution to a question that contains some error(s). Circle the error(s) and present a correct solution.

Calculate: 164.5 0.47 Solution:

164.5 0.4735

47 1645

141235235

(0)

Practice Section E

Challenge Question. If you can do this one, then you get an A+. 1. a) Based on your knowledge of decimals, give an approximation of the

answer to the question 946324.5897 358.48 . Explain the rationale for your best approximation.

b) Calculate: 946324.5897 358.48 Round to the nearest whole number. c) How does your answer in (b) compare to your approximation in (a)?

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NUMERACY: The Basics Workbook

SOLUTIONS

Set L Dividing Decimals

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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions

DIVIDING DECIMALS

Practice Section A

1. Solution:

4.4 22.2

2 4.4

4

044

0

2. Solution:

5.4 31.8

3 5.4

3

2424

0

3. Solution:

3.5 40.875

4 3.500

0

3532

3028

2020

0

4. Solution:

8.5 2.53.4

25 85.0

75

100100

(0)

5. Solution:

9.3 1.56.2

15 93.0

90

3030

0

6. Solution:

0.054 0.00318

3 54

3

2424

0

8



7. Solution:

3.8 0.57.6

5 38.0

35

3030

0

8. Solution:

5.7 0.2522.8

25 570.0

50

7050

200200

0

9. Solution:

13.34 5.82.3

58 133.4

116

174174

0

10. Solution:

12.3 1.67.6875

16 123.0000

112

11096

140128

120112

8080

0

11. Solution:

9.3 1.85.166

18 93.000 5.16

90

3018

120108

120108

120

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12. Solution:

12.9 3.33.9090

33 129.0000 3.9090

99

300297

300297

3

13. Solution:

9.8 2.73.629

27 98.000 3.629

81

170162

8054

260243

170

14. Solution:

12.97 1.58.646

15 129.700 8.646

120

9790

7060

10090

100

15. Solution:

1.5 0.53

5 15

15

0

14.87 34.956

3 14.870 4.956

12

2827

1715

2018

20

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Practice Section B

1. Solution:

0.375 0.1253

125 375

375

0

2. Solution:

53.3 2.0526

205 5330

410

12301230

0

3. Solution:

14.8 2.55.92

25 148.0

125

230225

5050

0

4. Solution:

15.3 2.46.375

24 153.00000

144

9072

180168

120120

0

5. Solution:

20.41 2.58.164

25 204.100

200

4125

160150

100100

0

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6. Solution:

21.525131 6.13.52871

61 215.25131

183

322305

175122

531488

433427

6161

(0)

7. Solution:

4 0.488.33

48 400.00 8.3

384

160144

160

8. Solution:

5.28 1.82.933

18 52.800 2.933

36

168162

6054

60

9. Solution:

3.6 3.70.972

37 36.000 2.972

333

270259

11074

360

10. Solution: 12.28 2.4

5.116624 122.8000 5.116

120

2824

4024

160144

160

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11. Solution:

12.9 6.61.95454

66 129.00000 1.954

66

630594

360330

300264

360330

30

12. Solution:

17.88 1.4412.4166

144 1788.0000 12.416

144

348288

600576

240144

960864

960

13. Solution:

684 40.516.88

405 6840.00 16.8

405

27902430

36003240

36003240

360

14. Solution:

21.63 1.812.0166

18 216.3000 12.016

18

3636

030

3018120108

120

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15. Solution:

0.875 0.521.68269

52 87.50000

52

355312

430416

140104

360312

480468

12

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Practice Section C

1. Solution: 3. Solution:

2254 4.6490

46 22540

184

414414

00

0

12.9 3.33.9090

33 129.0000 3.90

99

300297

300297

30

3.90 0.0578.181

5 390.909 78.18

35

4040

954040

95

4

2. Solution: 4. Solution:

190.875 0.625305.4

625 190875.0

1875

3370

33753125

25002500

0

144.48 2.265.672

22 1444.80000 65.672

132

124110

148132160154

6044160

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5. Solution: There is no need to do the first division ( 456.8 3 ) because you can NEVER divide by 0! It is impossible to divide something (i.e. 456.8 3 ) by nothing (i.e. 0 ), therefore this question has no solution.

Practice Section D

1. Solution: The answer to this question depends on the definition of decimal. It is true that a decimal greater than 0 and less than 1 would make Samuel correct as in the example 12 0.5 24 . Really though, a decimal is defined as any number with a decimal point, for example12 1.5 8 . Therefore, 0.5 and 1.5 are both considered decimal numbers and so Leslie is correct.

2. Solution: There is one error in line 1. The decimal was moved 2 places to the right on the 0.47 , but only moved 1 decimal place to the right on the 164.5 . The correct solution is:

164.5 0.47350

47 16450

141235235

00

(0)

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Practice Section E

1. a) Solution: To find a good estimate, pick some ‘nice’ numbers to divide: Some good estimates would be: 920000 400 2300 950000 400 2375 1000000 400 2500 The best estimate from the list would be 2500.

b) Solution:

946324.5897 358.482639.825

35848 94632458.970

71696

229364215088142765107544

352218322632

295869286784

9085771696

191610179240

12370

The result of the division, rounded to the nearest whole number, is 2640.

c) Solution: The estimated and the actual answer are close, although no estimates were over the actual result.

Numeracy: The Basics Workbook – Set L: Dividing...

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