Summary Guides - Maths 7 - Sample Pages

Summary guides 

Maths 

Uncorrected 

7 

Sample Pages 

Dean Findlay

Summary Guides 

Maths 7 

Dean Findlay 

Uncorrected 

Sample Pages

Table of Contents 

Introduction 

1. Number 

1.1 Place value 

1.2 Number symbols 

1.3 Addition and subtraction of whole numbers 

1.4 Multiplication of whole numbers 

1.5 Division of whole numbers 

1.6 Order of operations 

1.7 Estimation 

2. Fractions 

Answers 

2.1 Types of fractions 

2.2 Equivalent fractions 

2.3 Simplifying fractions 

2.4 Addition and subtraction of fractions 

2.5 Multiplication of fractions 

2.6 Division of fractions 

3. Decimals 

Answers 

Uncorrected 

3.1 Place value of decimals 

3.2 Comparing decimals 

3.3 Rounding decimals 


3.4 Addition and subtraction of decimals 

3.5 Multiplying decimals by multiples of ten 

3.6 Multiplying decimals by decimals 

3.7 Division with decimals 

3.8 Decimals and fractions 

Answers 

Copyright © Insight Publicaons Summary Guides – Maths 7

4. Percentages, money, and time 

4.1 Decimals and percentages 

4.2 Percentage of an amount 

4.3 Fractions, decimals, and percentages 

4.4 Financial mathematics 

4.5 Time 

Answers 

5. Negative numbers 

5.1 Integers 

5.2 Comparing and ordering integers 

5.3 Addition and subtraction of integers 

5.4 Multiplication and division of integers 

5.5 Powers of integers 

5.6 Negative fractions 

5.7 Negative decimals 

Answers 

6. Factors, multiples, squares, and roots. 

6.1 Multiples 

6.2 Factors 

6.3 Divisibility 

6.4 Powers and roots 

6.5 Prime and composite numbers 

Answers 

7. Rates, ratios, and proportions 

7.1 Rates 

7.2 Ratios 

Uncorrected 

7.3 Proportions 

7.4 Combined applications 

Answers 



8. Algebra 

8.1 Introduction to algebra 

8.2 Creating algebraic expressions 

8.3 Substitution 

8.4 Like terms 

8.5 Expanding 

8.6 Application of algebraic problems 

Answers 

9. Solving equations 

9.1 Introduction to equations 

9.2 Equivalent equations 

9.3 Solving equations algebraically 

9.4 Creating and solving equations 

9.5 Applications of equations 

Answers 

10. Patterns, rules, tables, and graphs 

10.1 Number patterns 

10.2 Spatial patterns 

10.3 Rules and tables 

10.4 Cartesian coordinates 

10.5 Transformations 

Answers 

11. Measurement 

11.1 Units of length 

11.2 Perimeter 

11.3 Area 

Uncorrected 


11.4 Area of composite shapes 

11.5 Volume of rectangular prisms 

Answers 


12. Geometry 

12.1 Geometric notation 

12.2 Angles at a point 

12.3 Parallel lines 

12.4 Polygons 

12.5 Triangles 

12.6 Quadrilaterals 

12.7 Solids and nets 

12.8 Circle geometry 

Answers 

13. Statistics 

13.1 Numerical data 

13.2 Dot plots and column graphs 

13.3 Line graphs 

13.4 Stem and leaf plots 

13.5 Pie charts 

14. Probability 

Answers 

14.1 Introduction to probability 

14.2 Theoretical probability 

14.3 Experimental probability 

15. Algorithms 

Uncorrected 

Answers 



Introduction 

The series, Summary Guides – Maths, has been written by practising teachers with 

years of classroom experience, who are passionate about creating user-friendly, 

accessible guides on mathematics. 

The explanations and exercises in these guides develop core numeracy skills for 

personal, work and civic life, and provide the base knowledge for the professional 

applications of maths as well as mathematical specialisations. Maths is part of your daily 

life no matter what you choose to do as an adult – it is important for thinking critically 

and making sense of the world. 

This book summarises key concepts in a clear and comprehensive way. It includes 

examples with worked solutions and step-by-step explanations, as well as exercises for 

you to complete. The best way to use this book is to make a habit of it – regularly 

working through the exercises and examples, and comparing your answers against those 

provided. Whether you commit to a daily, weekly or fortnightly routine, this consistent 

practice is the key to your success. 

The content of this book is based on years of experience in the classroom, making 

maths comprehensible and achievable for students. Through using this guide, you will be 

able to practise your skills and grow in confidence. We hope this resource will help you 

reap the rewards of maths. 

Dean Findlay and Insight Publications 

Uncorrected 



Chapter 1 - Number 

Chapter 1 - Number 

Numbers are made up of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. 

We use them every day for all types of mathematics. 

1.1 Place value 

The position of a digit in a number gives a different value to the digit. 

Here is an example of a place value chart for the number of people who attended the tennis 

on a day over the summer: 30 516 

Number 3 0 5 1 6 

Place Value 

Example 

Ten 

Thousands 

In the number 256, determine the place value of 

Thousands Hundreds Tens Ones 

a. the 2. b. the 5. c. the 6. 

Solution 

Working 

Explanation 

a. Hundreds The 2 in the whole number 256 is in the 

hundreds place. 

b. Tens The 5 in the whole number 256 is in the 

tens place. 

c. Ones The 6 in the whole number 256 is in the 

ones place. 

Exercise 1.1 

Uncorrected 

Note: it is common to also see the ‘ones’ 

places called ‘units’ 


Determine the place value of each digit in brackets for the numbers listed. 

a. 23 045 (2) b. 562 021 (6) c. 803 096 (8) d. 451 382 (8) 

e. 12 538 (5) f. 837 036 (6) g. 34 789 (7) h. 89 123 (9) 


Chapter 1 – Number 

1.2 Number symbols 

There are different mathematical symbols that are used to compare numbers. 

Equal to Not equal to Greater than 

Greater than 

or equal to 

Less than 

Less than or 

equal to 

Example 

= ≠ > ≥ < ≤ 

Complete the following number sentences by placing the correct symbol in each box. 

a. b. c. c. 

Solution 

Working 

Explanation 

a. Looking at the hundreds column, 300 is less 

than 500. 

b. Looking at the tens column, they are equal. 

Then look at the digits in the ones column, 9 

is greater than 6. 

c. Reading from left to right, the digits are 

equal until the tens column where 17 is less 

than 44. 

Exercise 1.2.1 

Uncorrected 


a. b. c. c. 


d. e. e. f. 





a. b. c. 

d. e. f. 

1.3 Addition and subtraction of whole numbers 

Addition and subtraction of whole numbers requires a good understanding of place value 

from the previous section. Remember that sum means to add together, and difference means 

subtraction. 

There are many ways to add and subtract in mathematics. In this study guide we are going 

to explore two approaches: mental strategies and the addition and subtraction algorithms. 

Example 

Find the sum and difference of the following using mental strategies. 

a. 37 + 38 b. 54 + 22 c. 126 + 125 

d. 94 − 49 e. 88 − 43 f. 100 − 42 

Solution 

a. 37 + 38 

40 + 40 = 80 

80 − 5 = 75 

Working 

b. 50 + 4 and 20 + 2 

50 + 20 = 70 

4 + 2 = 6 

Explanation 

Round both up to 40 and calculate the sum. 

Uncorrected 

37(+3) and 38(+2) 

Then subtract the amount we rounded both 

up by. 


Separate 54 and 22 into their place value. 

Add the tens and ones separately. 

54 + 22 = 76 

Combine for the final answer. 



c. 125 + 1 + 125 

Read 126 as 125 + 1 

125 × 2 + 1 = 251 

d. 95 − 50 

Double 125, then add 1. 

94 − 49 is difficult to think about. So, add 1 

to both numbers. 

= 45 

e. 80 + 8 and 40 + 3 

80 − 40 = 40 

8 − 3 = 5 

88 − 43 = 45 

f. 100 − 40 − 2 

= 58 

Example 

The difference will stay the same. 

Separate 88 and 43 into their place values. 

Subtract the tens and ones separately. 

Combine for the final answer. 

100 is easy to work with, so separate the 42 

into tens and ones. 

Subtract in parts. 

Find the sum of 28 and 34 using the addition algorithm. 

Solution 

Step 1. 

Step 2. 

Step 3. 

Uncorrected 

Working 

Explanation 

Set up the equation vertically with each digit 

lining up with the corresponding place value. 

Starting from the right (the ones), add the 

digits together. 


The sum of the ones is larger than 9, so 

write down the value of the ones and carry 

the tens to step 3. 

Then add the digits in the tens column. 

Remember to add the one from the previous 

step. 



Example 

Find the difference of 174 and 28 using the subtraction algorithm. 

Solution 

Working 

Explanation 

Step 1. 

Step 2. 

Step 3. 

Exercise 1.3 

Set up the equation vertically with each digit 

lining up with the corresponding place value. 

Starting from the right (the ones), subtract 

the bottom digit from the top. 

Since 8 is more than 4, we must ‘borrow’ 

from the tens column. 

We can then subtract 8 from 14. 

Then subtract the digits in the tens column, 

remembering the 7 tens are now 6 tens. 

Since there are no other hundreds, carry it 

down to the answer. 

Use an appropriate strategy to solve the following sum and difference problems. 

Uncorrected 

a. 95 + 12 b. 26 + 32 c. 145 + 143 d. 98 + 88 

e. 47 − 19 f. 76 − 13 g. 200 − 33 h. 457 − 112 




Answers 

Exercise 1.1 

a. ten thousands b. ten thousands c. hundred thousands 

d. tens e. hundreds f. ones 

g. hundreds h. thousands 


a. 21 < 25 b. 234 > 226 c. 44 557 > 44 516 

d. 87 > 78 e. 190 381 > 190 234 f. 879 < 889 


a. b. c. 

d. e. f. 

Exercise 1.3 

a. 107 b. 58 c. 288 d. 186 

e. 28 f. 63 g. 167 h. 345 

Exercise 1.4 

a. 108 b. 255 c. 111111 d. 22222222 

e. 111111 f. 333333 g. 11111111 h. 55555555 

Exercise 1.5 

a. 12 b. 11 c. 90 d. 1728 

e. 54 f. 48 g. 26 h. 57 

Exercise 1.6 

Uncorrected 


a. 38 b. 0 c. 19 d. 2 

e. 360 f. 58 g. 58 h. 29

Summary Guides - Maths 7 - Sample Pages

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?