N U M E R A C Y:
The Basics Workbook
Set L: Dividing Decimals
Companion Workbook to Numeracy: The Basics Video Series
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Set L: Dividing Decimals
i
Set L: Dividing Decimals
NUMERACY: The Basics Workbook
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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1
Set L: Dividing Decimals
NUMERACY: The Basics Workbook
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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2
Set L: Dividing Decimals
NUMERACY: The Basics Workbook
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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3
Set L: Dividing Decimals
NUMERACY: The Basics Workbook
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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4
Set L: Dividing Decimals
2.
NUMERACY: The Basics Workbook
Below is a possible solution to a question that contains some error(s).
Circle the error(s) and present a correct solution.
Calculate:
Solution:
164.5 0.47
164.5 0.47
35
47 1645
141
235
235
(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 W orkbook
SOLUTIONS
Set L
Dividing Decimals
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6
Set L: Dividing Decimals Solutions
NUMERACY: The Basics Workbook
DIVIDING DECIMALS
Practice Section A
1.
Solution:
4.4 2
4.
2.2
2 4.4
Solution:
8.5 2.5
3.4
25 85.0
4
75
04
4
100
100
(0)
0
2.
Solution:
5.4 3
1.8
3 5.4
5.
Solution:
9.3 1.5
6.2
15 93.0
3
24
24
90
30
30
0
3.
0
Solution:
3.5 4
0.875
4 3.500
0
6.
Solution:
0.054 0.003
18
3 54
35
32
30
28
20
20
3
24
24
0
0
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Set L: Dividing Decimals Solutions
7.
Solution:
3.8 0.5
NUMERACY: The Basics Workbook
7.6
5 38.0
Solution:
12.3 1.6
7.6875
16 123.0000
35
112
10.
110
30
30
96
140
0
128
8.
120
Solution:
5.7 0.25
22.8
25 570.0
112
80
80
50
0
70
50
200
200
0
9.
Solution:
13.34 5.8
2.3
58 133.4
11.
Solution:
9.3 1.8
5.166
18 93.000
5.16
90
30
18
120
108
116
174
174
0
120
108
120
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8
Set L: Dividing Decimals Solutions
12.
Solution:
12.9 3.3
3.9090
33 129.0000
NUMERACY: The Basics Workbook
14.
Solution:
12.97 1.5
8.646
15 129.700
3.9090
120
99
300
97
90
297
300
70
297
60
3
13.
8.646
100
90
100
Solution:
9.8 2.7
3.629
27 98.000
81
170
162
15.
3.629
Solution:
1.5 0.5
3
5 15
15
80
54
260
243
170
0
14.87 3
4.956
3 14.870
4.956
12
28
27
17
15
20
18
20
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Set L: Dividing Decimals Solutions
NUMERACY: The Basics Workbook
Practice Section B
1.
Solution:
0.375 0.125
3
125 375
4.
Solution:
15.3 2.4
6.375
24 153.00000
144
375
90
0
72
2.
180
Solution:
53.3 2.05
168
120
26
205 5330
120
410
0
1230
1230
0
3.
Solution:
14.8 2.5
5.92
25 148.0
125
230
225
50
50
5.
Solution:
20.41 2.5
8.164
25 204.100
200
41
25
160
150
100
100
0
0
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Set L: Dividing Decimals Solutions
6.
Solution:
21.525131 6.1
NUMERACY: The Basics Workbook
8.
3.52871
61 215.25131
183
2.933
36
322
305
168
162
175
122
60
54
531
488
60
9.
433
427
61
61
259
110
74
8.3
360
384
160
144
160
2.972
270
Solution:
4 0.48
8.33
48 400.00
Solution:
3.6 3.7
0.972
37 36.000
333
(0)
7.
Solution:
5.28 1.8
2.933
18 52.800
10.
Solution:
12.28 2.4
5.1166
24 122.8000
5.116
120
28
24
40
24
160
144
160
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11
Set L: Dividing Decimals Solutions
11.
Solution:
12.9 6.6
NUMERACY: The Basics Workbook
13.
1.95454
66 129.00000 1.954
Solution:
684 40.5
16.88
405 6840.00 16.8
66
405
630
2790
2430
594
3600
360
330
3240
3600
300
264
3240
360
360
330
30
12.
Solution:
17.88 1.44
12.4166
144 1788.0000 12.416
144
348
288
600
576
240
144
960
864
14.
Solution:
21.63 1.8
12.0166
18 216.3000 12.016
18
36
36
03
0
30
18
120
108
120
960
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Set L: Dividing Decimals Solutions
15.
NUMERACY: The Basics Workbook
Solution:
0.875 0.52
1.68269
52 87.50000
52
355
312
430
416
140
104
360
312
480
468
12
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13
Set L: Dividing Decimals Solutions
NUMERACY: The Basics Workbook
Practice Section C
1.
Solution:
3.
Solution:
3.90 0.05
2254 4.6
78.181
5 390.909 78.18
12.9 3.3
490
46 22540
3.9090
33 129.0000
184
35
3.90
99
414
414
0
0
40
40
300
9
297
300
5
40
297
40
30
0
9
5
4
2.
Solution:
190.875 0.625
305.4
625 190875.0
1875
4.
Solution:
144.48 2.2
65.672
22 1444.80000
65.672
132
124
337
110
148
0
3375
3125
2500
2500
0
132
160
154
60
44
160
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Set L: Dividing Decimals Solutions
5.
NUMERACY: The Basics Workbook
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 example 12 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 0.47
350
47 16450
141
235
235
0
0
(0)
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Set L: Dividing Decimals Solutions
NUMERACY: The Basics Workbook
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 358.48
2639.825
35848 94632458.970
71696
229364
215088
142765
107544
352218
322632
295869
286784
90857
71696
191610
179240
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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16