Mathematics: A Complete Introduction

The Easy Way to Learn Maths

Hugh Neill, Trevor Johnson

• Publisher: Teach Yourself
• Year: 2018
• Print ISBN: 9781473678378
• eBook ISBN: 9781473678361
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

Maths does not have to be difficult. This book, complete with exercises and answers, forms a course which will take you from beginner or intermediate level to being a confident mathematician. This book includes: simple step-by-step explanations, to help you grasp new topics or those that have previously confused you; practice questions throughout, to help you embed your learning and improve your confidence; and end of chapter summaries, to help you remember the key points you've learned - all in one great-value book, so you don't need any separate workbooks or coursebooks.Chapters include: number; angles; fractions; two-dimensional shapes; decimals; statisticsl directed numbers; graphs; measurement; perimeter and area; algebraic expressions; approximations; equations; percentages; formulae; circles; probability; three-dimensional shapes; ratio and proportion; pythagoras' theorem and trigonometry; indices and standard form. ABOUT THE SERIES
The Complete Introduction series from Teach Yourself is the ultimate one-stop guide for anyone wanting a comprehensive and accessible entry point into subjects as diverse as philosophy, mathematics, psychology, Shakespeare and practical electronics. Loved by students and perfect for general readers who simply want to learn more about the world around them, these books are your first choice for discovering something new.

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) 35013

(g) 241001

(h) 1001312

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) 342785

(b) 3783194

(c) 17021209

(d) 305213097

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, multiplication and division – either in your head or on paper. If you have difficu...

Table of contents

• Cover 
• Title
• Contents 
• Welcome to Mathematics: A complete introduction!
• 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