Table Of ContentBUSINESS ARITHMETIC
Business Arithmetic
HAROLD WARD
M
© Harold Ward 1977
All rights reserved. No part of this publication may be
reproduced or transmitted, in any form or by any means,
without permission.
First published 1977 by
THE MACMILLAN PRESS L TO
London and Basingstoke
Associated companies in Delhi Dublin
Hong Kong Johannesburg Lagos Melbourne
New York Singapore and Tokyo
ISBN 978-0-333-19790-5 ISBN 978-1-349-03028-6 (eBook)
DOI 10.1007/978-1-349-03028-6
The paperback edition of this book is sold subject to the
condition that it shall not, by way of trade or otherwise,
be lent, resold, hired out, or otherwise circulated without
the publisher's prior consent, in any form of binding or
cover other than that in which it is published and without
a similar condition including this condition being im
posed on the subsequent purchaser.
Contents
Preface
1 Addition and Subtraction
2 Multiplication and Division. Whole numbers, decimals, contracted
methods 6
3 Factors and multiples. H.C.F., L.C.M., square roots 19
4 Fractions. Decimals. Multiplication and division. Brackets 24
5 Ratio and Proportion. Compound ratios, Inverse and compound
proportion. Partnerships 36
6 Percentages and their application. Commission. Discounts 48
7 Rates and Taxes. Insurance. Bankruptcy. Income tax 61
8 Metric System and Foreign Exchange 76
9 Indices and Logarithms 86
10 Simple Interest. Instalments 101
11 Compound interest and its applications. Depreciation. Sinking
funds. Annuities. Freehold and Leasehold 109
12 Mensuration-Areas and Volumes. Pythagoras's theorem 124
13 Problems of distance, time and speed. Graphs 134
14 Banking and Finance. Bills of Exchange. Average due date.
Trading, Profit and Loss Accounts. Turnover and Outlay 142
15 Stocks and Shares. Types of capital and shares. Stock Exchange.
Income and Yield. Business documents 151
16 Averages and Index Numbers. Arithmetic Mean. Median. Mode 164
17 Pictorial representation. Pie diagrams. Bar charts. Graphs 171
Answers to Progress Tests 179
Suggested answers to Past Examination Questions 185
v
Preface
An arithmetical textbook should ideally cater for several different kinds of
reader.
There are those students whose early introduction to the subject was not
blessed with success and who are, in consequence, dismissed as having no head
for figures.
Others, who are working alone, and whose schooldays are perhaps long
behind them, find that they have forgotten many of the basic principles. Even
those who feel at home with figures sometimes find that what they learned at
school is oflittle immediate help when they enter the world of business, either
because they cannot apply their knowledge or because they are not sufficiently
acquainted with the organisation and practices of modern commerce.
I have tried to overcome these difficulties and diversities of outlook in the
following ways:
I For the student of limited numeracy this book begins by taking him
systematically through the basic processes of arithmetic which, right from the
start, are applied to practical business problems.
2 For the student working alone there is an introduction to the practical
problems of business. The successive stages of difficulty are explained with a
wealth of worked, step-by-step examples, and self-examination questions,
with answers, enable him to test his progress as he goes along.
The more numerate student might very well skip the first four chapters but,
thereafter, he will find himself introduced to all the facets of the business
world, and each one is explained with a variety of example and practical detail.
Teachers will welcome the break -down of the text into a series of working
units, each followed by a progress test, and answers.
The coverage is wide, and should be adequate for most professional
examinations in Arithmetic, up to the advanced level. There is also an
introductory treatment of commonly used Statistical processes. Students
working for the examinations of the principal Public Bodies will find a
selection of past examination questions with answers.
It should be pointed out that these answers are the ones suggested by the
author, and are not to be regarded as 'official' answers of the appropriate
Examining Body.
In conclusion the author gratefully acknowledges permission to quote from
the past examination questions of the following bodies:
Union of Lancashire and Cheshire Institutes (U .L.C!.); the Royal Society of
Arts (R.S.A.); the London Chamber of Commerce and Industry (L.CC).
HAROLD WARD
1 Addition and Subtraction
UNIT A ADDITION
Speed and accuracy can be attained if the following principles are used:
I Try to get a rough estimate of the answer as a check on your working. This
principle applies to everything in arithmetic, and will often draw attention to
some obvious error such as a misplaced decimal. To get an estimate, simply
·round off' the numbers involved, e.g. adding 139 and 41.3 is roughly the sum
of 140 and 41, so the answer is about 181.
2 Add both up and down, and look for 'ten groups', i.e. when two or more
numbers, not too far apart, add up to 10, couple them together, and register
them mentally as 10, e.g. 1 + 4 + 6 + 9+l should be mentally registered (going
from right to left) as 10, 20, 21.
3 Be sure to place units, tens, hundreds, etc., in their correct position, with
the units, etc., exactly under each other.
Example 1
The figures below give the weekly collections of rubber (in kg) on a small
plantation. Find the total.
5765 M ental steps adding upwards.
1875 Col. 1 10; 20; 26; write down 6, carry 2 to next column.
4336 2 10; 20; 26; " " 6,,, 2" "
"
1232 3 10; 20; 28; ,,8, 2 "
"
2658 4 4; 5; 15;" 15.
"
15866
Note in the last column we grouped 3 numbers.
Repeating the addition, going downwards, we would say:
Col. 1 10; 20; 26; write down 6, carry 2 to next column.
" 2 8; 18; 21; 26; " " 6, " 2" "
,,3 12; 22; 28; " ,,8, 2""
,,4 12; 13; 15; " ,,15.
Note. Some students find it helpful to write down the 'carrying figure' below
the next column, so that they do not forget it.
Horizontal and Vertical Addition
Consider the following sales in 4 departments of a store, for a period of 4
weeks.
Dept 1 Dept 2 Dept 3 Dept 4 Total
weekly
£ £ £ £ sales
Week 1 3716 134 968 2042 6860
Week 2 4324 204 1132 2350 8010
Week 3 3681 172 874 2618 7345
Week 4 3427 133 935 2175 6670
Total sales
per Dept 15148 643 3909 9185 28885
GRAND TOTAL
Adding horizontally, we get totals of all 4 departments for the week in
question. (Method: add right to left, looking for 10 groups. Then, as a check,
add left to right.)
Adding vertically (using the method of Example 1), we get total sales for
each department separately, and if we add these sub-totals horizontally, we get
total sales for the whole store, for the whole period. This is the grand total.
Notes. I This should be the same result as adding the end column totals,
which give weekly sales of all departments.
2 When adding horizontally, be careful to remember the position of the
digits you are adding, i.e. be sure they are all units, or tens or hundreds, etc.
Progress Test 1A
1 The attendance at a football match was recorded at each entrance as
follows: 2976; 1864; 3031; 1219; 1133. What was the total atten
dance?
2
2 Complete the following table to show meals served in a cafe.
Mon. Tues. Wed. Thurs. Fri. Sat. Totals
Week I 63 147 138 72 95 215
Week 2 87 163 142 98 115 235
Week 3 124 166 127 113 181 269
Week 4 146 164 115 185 123 277
Totals
3 The daily sales during a certain week (in tonnes) of a produce merchant are
as follows:
Mon. Tues. Wed. Thurs. Fri. Sat. Totals
Coffee 17 23 34 38 42 66
Cocoa 23 27 26 24 22 28
Rice 146 164 135 175 118 182
Wheat 74 76 73 77 94 116
Totals
Complete the totals to show his sales break-down.
UNIT B SUBTRACTION
The simplest way is known as 'complementary addition' and is the method
used in shops when giving change.
If you bought something for 27p and gave a 50p piece, you could say
50p - 27p = 23p = the change, but the shopkeeper, in counting this out, would
start with the price paid (27p) and in handing out the change, would build up
(or add) the various coins, until he reached 50p (the original number).
Example 2
7832
-5947
1885
Step 1 Units. 7 and 5 are 12. Put down 5 and carry 1 ten.
Step 2 Tens. 1 and 4 are 5, 5 and 8 are 13. Put down 8 and carry 1 hundred.
Step 3 Hundreds. 1 and 9 are 10, 10 and 8 are 18. Put down 8 and carry I
thousand.
Step 4 Thousands. 1 and 5 are 6, 6 and I are seven. Put down 1.
3
