#### Chapters

Chapter 2 - Linear Equations in One Variable

Chapter 3 - Understanding Quadrilaterals

Chapter 4 - Practical Geometry

Chapter 5 - Data Handling

Chapter 6 - Squares and Square Roots

Chapter 7 - Cubes and Cube Roots

Chapter 8 - Comparing Quantities

Chapter 9 - Algebraic Expressions and Identities

Chapter 10 - Visualising Solid Shapes

Chapter 11 - Mensuration

Chapter 12 - Exponents and Powers

Chapter 13 - Direct and Inverse Proportions

Chapter 14 - Factorisation

Chapter 15 - Introduction to Graphs

Chapter 16 - Playing with Numbers

## Chapter 16 - Playing with Numbers

#### Pages 255 - 256

Find the values of the letters in each of the following and give reasons for the steps involved.

3 A

+ 2 5

-------

B 2

-------

Find the values of the letters in the following and give reasons for the steps involved.

4 A

+ 9 8

------

C B 3

------

Find the value of the letter in the following and give reasons for the steps involved.

1 A

x A

------

9 A

------

Find the values of the letters in the following and give reasons for the steps involved.

A B

+ 3 7

------

6 A

------

Find the values of the letters in the following and give reasons for the steps involved

A B

x 3

-------

C A B

-------

Find the values of the letters in the following and give reasons for the steps involved.

A B

x 5

-------

C A B

-------

Find the values of the letters in the following and give reasons for the steps involved.

A B

x 6

-------

B B B

-------

Find the values of the letters in the following and give reasons for the steps involved.

A 1

+ 1 B

-------

B 0

-------

Find the values of the letters in the following and give reasons for the steps involved.

2 A B

+ A B 1

---------

B 1 8

----------

Find the values of the letters in the following and give reasons for the steps involved.

1 2 A

+ 6 A B

---------

A 0 9

---------

#### Page 260

If 21*y*5 is a multiple of 9, where *y* is a digit, what is the value of *y*?

If 31*z*5 is a multiple of 9, where *z* is a digit, what is the value of *z*? You will find that there are two answers for the last problem. Why is this so?

If 24*x* is a multiple of 3, where *x* is a digit, what is the value of *x*?

(Since 24*x* is a multiple of 3, its sum of digits 6 + *x* is a multiple of 3; so 6 + *x* is one of these numbers: 0, 3, 6, 9, 12, 15, 18…. But since *x* is a digit, it can only be that 6 + *x* = 6 or 9 or 12 or 15. Therefore, *x* = 0 or 3 or 6 or 9. Thus, *x* can have any of four different values)

If 31*z*5 is a multiple of 3, where *z* is a digit, what might be the values of *z*?