Form 1 Unit 7 :Lesson 4 – Multiplication and Division of Directed Numbers

FORM 1 UNIT 7 Form 1 Unit 7 :Lesson 4 – Multiplication and Division of Directed Numbers

Objective

At the end of this lesson, students should be able to multiply and divide directed numbers.

The rules for multiplying and dividing two directed number are as follows;

Example 1

Solution

Example

Simplify:

a) (–2)(–3)(–4) b) (–1)(–2)(–1)(–3)(–4)(–2)(–1)

Solution

Exponents

Example 1

Simplify: a) (–3)²b) –3²

Solution

a) (–3)²= (–3)(–3) = +9 (– x – = +)
b) –3²= –(3)(3) = (–1)(9) = –9 (– x + = –) Note the difference between the above examples.

In the example b) the square “to the power 2” was only on the 3; it was not on the minus sign. Parentheses or brackets makes all the difference in the two examples.

Example 2

Simplify

1) a) (–5)³ b) (–2)⁴

1) a) (–5)³ = (–5)(–5)(–5)
= (25)(–5)
= –125

b) (–2)⁴ = (–2)(–2)(–2)(–2)
= + 4 x + 4

= (4)(4)
= 16

Example 3

a = –2 and b = –6

Work out the following

a) a²b)a²+ b² c) b³– a² d) (a – b)²

Solution

a) a²

= –2 × –2

= 4

b) a²+ b²

= (–2 × – 2)+( –6 × –6)

= 4 + 36 = 40

c) b²– a²

= (–6 × –6) – (–2 × –2)

= 36 – 4

= 32

d) (a – b)²

= (–2 – –6)²

= (–2 + 6)

= (4)²

= 16

BODMAS

Example 1

Simplify the following.

Solution

In this problem you can see all the different operations. When there is more than one operation involved in a problem, we have to follow the order of operations.

(a) 23 – (5– –7)

(First, carry out the operations inside the brackets, – – = +)

= 23 – (5 + 7)

= 23 – (12) (next, remove the brackets )

= 11

(b) 5 × – 4 + –8 (Remember the order, × before +)

= –20 + –8 (+ – = –)

= – 20 – 8

= –28

(In this problem, ( )brackets are inside the [ ] brackets, so first you have to solve the inner brackets before and the outer brackets.)

= – 25 ÷ [5 × –2 – (–15)] (–3 ×5 = –15 )

= – 25 ÷ [–10 – (–15) ] (5 × –2 = –10)