math explain

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