Complete Mathematics

A step by step introduction to the mathematical essentials

Trevor Johnson, Hugh Neill

• Publisher: Teach Yourself
• Year: 2010
• Topic: Mathematics
• eBook ISBN:
  9781444130980
• Subtopic: Mathematics General
• Index: Mathematics

Are you looking for a clear, accessible guide to mathematics that can help you brush up your skills and rediscover the key concepts and techniques? Complete Mathematics provides an invaluable, step-by-step introduction to the subject. Packed full of worked examples and useful exercises, it will guide you through the essentials quickly and easily, giving you the knowledge you need to gain maths confidence.NOT GOT MUCH TIME?One, five and ten-minute introductions to key principles to get you started.
AUTHOR INSIGHTSLots of instant help with common problems and quick tips for success, based on the author's many years of experience.
TEST YOURSELFTests in the book and online to keep track of your progress.
EXTEND YOUR KNOWLEDGEExtra online articles at www.teachyourself.com to give you a richer understanding of psychology.
FIVE THINGS TO REMEMBERQuick refreshers to help you remember the key facts.
TRY THISInnovative exercises illustrate what you've learnt and how to use it.

1

Number

In this chapter you will learn:

• about place value

• about the four operations of arithmetic

• about the order in which arithmetic operations should be carried out

• about some special numbers.

1.1 Introduction – place value

Over the centuries, many systems of writing numbers have been used. For example, the number which we write as 17 is written as XVII using Roman numerals.

Our system of writing numbers is called the decimal system, because it is based on ten, the number of fingers and thumbs we have.

The decimal system uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The place of the digit in a number tells you the value of that digit.

When you write a number, the value of the digit in each of the first four columns, starting from the right, is

Thus, in the number 3652, the value of the 2 is two units and the value of the 6 is six hundreds.

The decimal system uses zero to show that a column is empty. So 308 means three hundreds and eight units; that is, there are no tens. The number five thousand and twenty-three would be written 5023, using the zero to show that there are no hundreds.

Extra columns may be added to deal with larger numbers, the value of each column being ten times greater than that of the column on its immediate right. It is usual, however, to split large numbers up into groups of three digits.

You read 372 891 as three hundred and seventy-two thousand, eight hundred and ninety-one.

In words, 428 763 236 is four hundred and twenty-eight million, seven hundred and sixty-three thousand, two hundred and thirty-six.

Exercise 1.1

1 What is the value of the 5 in each of the following numbers?

(a) 357

(b) 598

(c) 5842

(d) 6785

2 Write these numbers in figures.

(a) seventeen

(b) seventy

(c) ninety-seven

(d) five hundred and forty-six

(e) six hundred and three

(f) eight hundred and ten

(g) four hundred and fifty

(h) ten thousand

(i) eight thousand, nine hundred and thirty-four

(j) six thousand, four hundred and eighty

(k) three thousand and six

3 Write these numbers completely in words.

(a) 52

(b) 871

(c) 5624

(d) 980

(e) 7001

(f) 35 013

(g) 241 001

(h) 1 001 312

4 Write down the largest number and the smallest number you can make using

(a) 5, 9 and 7

(b) 7, 2, 1 and 9.

5 Write these numbers completely in words.

(a) 342 785

(b) 3 783 194

(c) 17 021 209

(d) 305 213 097

6 Write these numbers in figures.

(a) five hundred and sixteen thousand, two hundred and nineteen

(b) two hundred and six thousand, and twenty-four

(c) twenty-one million, four hundred and thirty-seven thousand, eight hundred and sixty-nine

(d) seven million, six hundred and four thousand, and thirteen

1.2 Arithmetic – the four operations

In this book, the authors assume that you have access to a calculator, and that you are able to carry out simple examples of the four operations of arithmetic – addition, subtraction, mul...

Table of contents

• Cover 
• Title
• Contents 
• Welcome to Complete Mathematics!
• Introduction
• 1 Number
• 2 Angles
• 3 Fractions
• 4 Two-dimensional shapes
• 5 Decimals
• 6 Statistics 1
• 7 Directed numbers
• 8 Graphs 1
• 9 Measurement
• 10 Perimeter and area
• 11 Algebraic expressions
• 12 Approximation
• 13 Equations 1
• 14 Percentages
• 15 Formulae
• 16 Circles
• 17 Probability
• 18 Three-dimensional shapes
• 19 Ratio and proportion
• 20 Pythagoras’ theorem and trigonometry
• 21 Indices and standard form
• 22 Statistics 2
• 23 Graphs 2
• 24 Equations 2
• Answers
• Taking it further
• Copyright