Elwes, richard the math handbook everyday math made simple quercus (2011)
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The Math Handbook
Everyday Math Made Simple
Richard Elwes
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New York ã London
â 2011 by Richard Elwes
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Contents
Introduction
The language of mathematics
Addition
Subtraction
Multiplication
Division
Primes, factors and multiples
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Negative numbers and the number
line
Decimals
Fractions
Arithmetic with fractions
Powers
The power of 10
Roots and logs
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Percentages and proportions
Algebra
Equations
Angles
Triangles
Circles
Area and volume
Polygons and solids
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Pythagoras’ theorem
Trigonometry
Coordinates
Graphs
Statistics
Probability
Charts
Answers to quizzes
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Index
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Introduction
“I was never any good at
mathematics.”
I must have heard this sentence
from a thousand different people.
I cannot dispute that it may be
true: people do have different
strengths and weaknesses, different
interests and priorities, different
opportunities and obstacles. But,
all the same, an understanding of
mathematics is not something
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anyone is born with, not even
Pythagoras himself. Like all other
skills, from portraiture to computer
programming, from knitting to
playing cricket, mathematics can
only be developed through
practice, that is to say through
actually doing it.
Nor, in this age, is mathematics
something anyone can afford to
ignore. Few people stop to worry
whether they are good at talking or
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good at shopping. Abilities may
indeed vary, but generally talking
and shopping are unavoidable
parts of life. And so it is with
mathematics. Rather than trying to
hide from it, how about meeting it
head on and becoming good at it?
Sounds intimidating? Don’t panic!
The good news is that just a
handful of central ideas and
techniques can carry you a very
long way. So, I am pleased to
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present this book: a no-nonsense
guide to the essentials of the
subject, especially written for
anyone who “was never any good
at mathematics.” Maybe not, but
it’s not too late!
Before we get underway, here’s a
final word on philosophy.
Mathematical education is split
between two rival camps.
Traditionalists brandish rusty
compasses and dusty books of log
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tables, while modernists drop
fashionable buzzwords like
“chunking” and talk about the
“number line.” This book has no
loyalty to either group. I have
simply taken the concepts I
consider most important, and
illustrated them as clearly and
straightforwardly as I can.
Many of the ideas are as ancient as
the pyramids, though some have a
more recent heritage. Sometimes a
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modern presentation can bring a
fresh clarity to a tired subject; in
other cases, the old tried and tested
methods are the best.
Richard Elwes
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The language of
mathematics
• Writing mathematics
• Understanding what the various
mathematical symbols mean, and
how to use them
• Using BEDMAS to help with
calculations
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Let’s begin with one of the
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commonest questions in any
mathematics class: “Can’t I just
use a calculator?” The answer is
… of course you can! This book is
not selling a puritanical brand of
mathematics, where everything
must be done laboriously by hand,
and all help is turned down. You
are welcome to use a calculator
for arithmetic, just as you can use
a word-processor for writing text.
But handwriting is an essential
skill, even in
today’s hi-tech
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world. You can use a dictionary or
a spell-checker too. All the same,
isn’t it a good idea to have a
reasonable grasp of basic spelling?
There may be times when you don’t
have a calculator or a computer to
hand. You don’t want to be
completely lost without it! Nor do
you want to have to consult it
every time a few numbers need to
be added together. After all, you
don’t get out your dictionary every
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time you want to write a simple
phrase.
So, no, I don’t want you to throw
away your calculator. But I would
like to change the way you think
about it. See it as a labor saving
device, something to speed up
calculations, a provider of handy
shortcuts.
The way I don’t want you to see it
is as a mysterious black box which
performs near-magical feats that
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