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Companion Workbook to Numeracy: The Basics Video Series
NUMERAC Y:The Basics Workbook
Set L: Dividing Decimals
AC
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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
1000 Waverley Street Winnipeg, MB, R3T 0P3
©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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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
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NUMERACY: The Basics Workbook Set L: Dividing Decimals
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals
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
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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
15. Solution:
0.875 0.521.68269
52 87.50000
52
355312
430416
140104
360312
480468
12
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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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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NUMERACY: The Basics Workbook Set L: Dividing Decimals Solutions
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.
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