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= 10^{3} in index form, where 3 is the index or power of 10.

P^{5 }=p x p x p x p x p. 5 is the power or index of p in the expression P^{5}.

** **

**Laws of Indices**

**Multiplication law:**

a^{x} x a^{y} = a^{x+y}

E.g. a^{5}xa^{3 }= a x a x a x a x a x a x a x a =a^{8}

y^{1 }x y^{4 }= y^{ 1+4} = y^{5}

a^{3 }x a^{5 }= a^{3 + 5 }= a^{8}

4c^{4 }x 3c^{2}

= 4 x 3 x c^{4 }x c^{2 }= 12 x c^{4+2 }=12c^{6}

** **

**Classwork **

Simplify the following

**(a)** 10^{3 }x 10^{4 }**(b)** 3 x 10^{6 }x 4 x 10^{2 }**(c)** p^{3 }x p **(d)** 4f^{3 }x 5f^{7 }

^{ }

**Division law**

(1) a^{x }÷ a^{y }= a^{x }÷ a^{y }= a^{x-y}

** **

**Example**

Simplify the following

**(1) **a^{7}÷a^{3}=a x a x a x a x a x a x a ÷ a x a x a

a^{7-3 }= a^{4}

**(2)** 10^{6}÷10^{3}=10^{6}÷10^{3}=10^{6-3}=10^{3}

**(3)** 10a^{7}÷2a^{2}=10a^{7}÷2a^{2}=5a^{7-2}=5a^{5}

** **

**Classwork**

Simplify the following

**A.** 10^{5}÷10^{3} **B.** 51m^{9}÷3m **C.** 8×10^{9}÷4×10^{6 }

**By division law**

a^{x-x}=a^{0}

a^{0}=1

E.g. 100^{0 }=1

50^{0}=1

**Zero indexes**

a^{x }÷ a^{x }= ${a}^{x\u2013x}={a}^{0}=1$

** **

**Negative index**

a^{0 }÷ a^{x }= 1/a^{x}

But by division law, a^{0-x}=a^{-x}

Therefore, a^{-x}=1/a^{x}

**Example**

- Simplify (i) b
^{-2}(ii) 2^{-3}

**Solution**

b^{-2} = 1/ b^{2 } (ii) 2^{-3} = 1/2^{3 }= 1/2x2x2 = 1/8

** **

**Class work**

(1) 10^{-2} (2) d^{0 }x d4 x d^{-2 }(3) a^{-3}÷a^{-5} (4) (1/4)^{-2}

- Power of index

[a^{m}]^{n }= a^{mxn }= ${a}^{mn}$

E.g. [a^{2}]^{4}= x a^{2 }x a^{2 }x a^{2 }= a x a x a x a x a x a x a x a=a^{8}

Therefore. a^{2×4}=a^{8.}

(6) [mn]^{ a}=m ^{a}x n^{a }= m^{a}n^{a}. e.g. [4+2x]^{ 2 }= 4^{2}+2^{2}xx^{2}_{ }=

16+4x^{2 }= 4[4+1xx^{2}] = 4[4+x^{2}].

**Fractional indexes**

a^{m/n} = a^{1/n }x^{m}= ^{n}√ am

Example

- (a
^{1/2})^{2}= a^{2/2 }= a^{1 }=a - (√a)
^{2 }= √a x √a = √a x a = √a^{2 }= a e.g. 32^{1/5}=^{5}√32^{1} - 32
^{3/5 = }^{5}√32^{3 }^{= 5}√2^{5×3 }= 2^{3 }= 2x2x2 = 8 - 27
^{2/3 }=^{3}√27^{2 }= 3^{2 }= 3x3x3 = 9 - 4
^{-3/2 }= √(1/4)^{3}= 1/2^{3} - (0001)
^{3 }=1×10^{-3 }= (10^{-3)3=}10^{-3×3=}10^{-9 }=__$\frac{1}{1000000000}$ =0.000000001__ - (a
^{m})^{p/q }= a^{mp }= √(a)^{p} - (16
^{2})^{3/4 }= √ (16^{2})^{3 }= (2^{2})^{3 = }(4)^{3=}4x4x4 = 64

** **

**The Equator of power for equal base**

A^{x }=A^{y} , 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 5x
^{3}x 4x^{7 }(a) 20x^{4 }(b) 20x^{10 }(c) 20x^{7}(d) 57x^{10} - Simplify 10a
^{8}÷ 5a^{6}(a) 2a^{2}(b) 50a^{2 }(c) 2a^{14 }(d) 2a^{48} - Simplify r
^{7}÷ r^{7}(a) 0 (b) 1 (c) r^{14 }(d) 2r^{7}

** **

**THEORY **

**Simplify**

- 5y
^{5}x 3y^{3} - 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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LyahI love this lesson

LyahYou are trying

MelaSeriously

MallamHow can I download this pdf

seannazuHow 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

Kalu Kalu ChinonsoI don’t understand the multiplication law classwork (b) compared with the examples is confusing. Please help me

KYKelaniwell done