The document provides explanations of various math concepts for 8th grade students in Term 1. It covers the commutative, associative, and distributive properties, order of operations (BODMAS), factors, primes, multiples, percentages, squares and cubes of integers, simple interest formula, hire purchase, integers, and equivalent fractions. Key definitions and rules are given for adding, subtracting, multiplying, and dividing integers. Examples are provided to illustrate percentage calculations and working with fractions.

1. Maths Explanations
Grade 8
Term 1

2. Commutative Property
• 5 + 7 7 + 5
= 12 or = 12
• 2 x 3 3 x 2
= 6 or = 6

3. Associative Property
• 5 + 3 + 6 5 + 3 + 6
= 5 + (3 + 6) OR = (5 + 3) + 6
= 5 + 9 = 8 + 6
= 14 = 14
• 2 x 3 x 11
= 2 x (3 x 11) OR = (2 X 3) X 11
= 2 x 33 = 6 X 11
= 66 = 66

4. Distributive Property
• 3 x ( 2 + 5 )
= (3 x 2) + (3 x 5) OR 3(2) + 3(5)
= 6 + 15 6 + 15
= 21 = 21

5. BODMAS
B = Brackets
O = Of (x)
D = Division
M = Multiplication
A = Addition
S = Subtraction

6. Definitions
Factors : Numbers that divide equally into another number with no
. Remainder
Prime Factors : Prime Numbers that divide equally in another
. Number
Multiples : The product of a number and any whole number
(times tables)

7. Percentages
How to find the Percentage of a number
(a) 36 of 48
= 75
= 36 / 48 x 100
(b) 25 of 15
= 166,67
= 25/15 x 100

8. Percentage of an Amount
How to find the Percentage of an Amount
(a) 25% of 120
30
= 25/100 x 120
(b) 150% of R45
R 67,50
= 150/100 x 45

9. Squares And Cubes Of
Integers

10. Squares Of Integers
(Positive)2 = Positive
(Negative)2 = Positive

11. Cubes Of Integers
(Positive)3 = Positive
(Negative)3 = Negative

12. Simple Interest
Formular
S = Simple Interest
P = Principle / Initial Amount
I = Interest
N = Number of Years S = P X I X N
OR
S = (P)(I)(N) Ways to write formular
OR
S = (P) X (I) X (N)

13. Hire Purchase
First find your total purchase price
Then divide total purchase price by the time period (years converted to months)
Your answer goes here …

14. Introduction To
Integers

15. What are integers
All the positive and negative whole numbers
(-) Negative Numbers (+) Positive Numbers
Decrease Increase
- 8 - 7 - 6 -5 -4 - 3 -2 -1 0 1 2 3 4 5 6 7 8

16. Adding Integers (Rules)
 Positive + Positive = Positive
 Negative + Negative = Negative
 Positive + Negative = Sign of biggest number
OR VISE-VERSA

17. What is Additive Inverse
Additive Inverse is any two numbers that cancel out and end up adding to 0
Examples
1. (-2) + 2
= 0
* If there is additive inverse in any sum, you can strike it off *
2. (-5) + 6 + 7 + 5
= 10 + 6
= 16

18. Subtracting Integers (Rules)
 Negative – Negative = Positive
Negative sign outside is multiplied by number
in the inside

19. Multiplying Integers (Rules)
 Negative x Negative = Positive
Positive x Negative = Positive
Negative x Positive = Negative

20. Dividing Integers
Positive ÷ Positive = Positive
Negative ÷ Negative = Positive
Positive ÷ Negative = Negative
Negative ÷ Positive = Negative

21. Equivalent Fractions
Examples
Denominator of 30
4
5𝑐
30
5
= 6
*Multiply numerator + denominator by 6
4 = 4 x 6 = 24
5 5 x 6 = 30