Back to: MATHEMATICS JSS 2
Welcome to JSS2!
We are eager to have you join us in class!!
In today’s class, We will be discussing Basic Operation of Integers. We hope you enjoy the class!
- Definition
- Indices
- Laws of Indices
Definition of Integer
An integer is any positive or negative whole number
Example:
Simplify the following
I. (+8) + (+3) ii. (+9) – (+4)
Solution
I. (+8) + (+3) = +11 ii (+9) – (+4) = 9-4 = +5 or 5
Self Evaluation
Simplify the following
i. (+12) –(+7) ii. 7-(-3)-(-2)
Indices
The plural of index is indices
10 x 10 x 10= 103 in index form, where 3 is the index or power of 10.
P5 =p x p x p x p x p. 5 is the power or index of p in the expression P5.
Laws of Indices
- Multiplication law:
ax x ay = ax+y
E.g. a5xa3 = a x a x a x a x a x a x a x a =a8
y1 x y4 = y 1+4 = y5
a3 x a5 = a3 + 5 = a8
4c4 x 3c2
= 4 x 3 x c4 x c2 = 12 x c4+2 =12c6
Classwork
Simplify the following
(a) 103 x 104 (b) 3 x 106 x 4 x 102 (c) p3 x p (d) 4f3 x 5f7
- Division law
(1) ax ÷ ay = ax ÷ ay = ax-y
Example
Simplify the following
(1) a7÷a3=a x a x a x a x a x a x a ÷ a x a x a
a7-3 = a4
(2) 106÷103=106÷103=106-3=103
(3) 10a7÷2a2=10a7÷2a2=5a7-2=5a5
Classwork
Simplify the following
A. 105÷103 B. 51m9÷3m C. 8×109÷4×106
- By division law
ax-x=a0
a0=1
E.g. 1000 =1
500=1
- Zero indexes
ax ÷ ax =
- Negative index
a0 ÷ ax = 1/ax
But by division law, a0-x=a-x
Therefore, a-x=1/ax
Example
- Simplify (i) b-2 (ii) 2-3
Solution
b-2 = 1/ b2 (ii) 2-3 = 1/23 = 1/2x2x2 = 1/8
Class work
(1) 10-2 (2) d0 x d4 x d-2 (3) a-3÷a-5 (4) (1/4)-2
- Power of index
[am]n = amxn =
E.g. [a2]4= x a2 x a2 x a2 = a x a x a x a x a x a x a x a=a8
Therefore. a2×4=a8.
(6) [mn] a=m ax na = mana. e.g. [4+2x] 2 = 42+22xx2 =
16+4x2 = 4[4+1xx2] = 4[4+x2].
- Fractional indexes
am/n = a1/n xm= n√ am
Example
- (a1/2)2 = a2/2 = a1 =a
- (√a)2 = √a x √a = √a x a = √a2 = a e.g. 321/5= 5√321
- 323/5 = 5√323 = 5√25×3 = 23 = 2x2x2 = 8
- 272/3 = 3√272 = 32 = 3x3x3 = 9
- 4-3/2 = √(1/4)3= 1/23
- (0001)3 =1×10-3 = (10-3)3=10-3×3=10-9 = =0.000000001
- (am)p/q = amp = √(a)p
- (162)3/4 = √ (162)3 = (22)3 = (4)3=4x4x4 = 64
- The Equator of power for equal base
Ax =Ay , That is x = y
READING ASSIGNMENT
New General Mathematics, UBE Edition, chapter 2 Pages 24-26
Essential Mathematics by A J S Oluwasanmi, Chapter 3 pages 27-29
WEEKEND ASSIGNMENT
- Simplify (+13) – (+6)
(a)7 (b) -7 (c) 19 (d) 8
- Simplify (+11) – (+6) – (-3)
(a)7 (b)8 (c)9 (d)10
- Simplify 5x3 x 4x7 (a) 20x4 (b) 20x10 (c) 20x7 (d) 57x10
- Simplify 10a8 ÷ 5a6 (a) 2a2 (b) 50a2 (c) 2a14 (d) 2a48
- Simplify r7 ÷ r7 (a) 0 (b) 1 (c) r14 (d) 2r7
THEORY
- Simplify
- 5y5 x 3y3
- 24 x 8
- 6x
- Simplify (1/2)-3
We have come to the end of this class. We do hope you enjoyed the class?
Should you have any further question, feel free to ask in the comment section below and trust us to respond as soon as possible.
In our next class, we will be talking about Whole Numbers and Decimal Numbers. We are eager to meet you there.
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I love this lesson
You are trying
Seriously
How can I download this pdf
How Do you mark the self Evaluation? how ever here is my answer of only the first one
I) (+12)_(+7)=5or+5.I really love using the class notes thanks
I don’t understand the multiplication law classwork (b) compared with the examples is confusing. Please help me
well done