# MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS

## MULTIPLICATION AND DIVISION OF DIRECTED NUMBERS

Revision on addition and subtraction of directed numbers

Note that:

Â (a). + + = + OR – – = + (Replacing the same signs that apprear together by a positive sign

(b). +Â  –Â  = – OR – + = – (Replacing two different signs that appear together by a negative sign

Example 1: Find the values of the following:

(a). + 7Â  + (+8) (b) +13 â€“ (+6)

Solution:

(a).Â  + 7 + (+8) = 7 + 8 = 15

(b). + 13 â€“ (+6) = 13 â€“ 6 = 7

Example 2 : Calculate the following (a) 25 â€“ (+3) (b) 12 â€“ (-9)

Solution

(a). 25Â  – (+3) = 25 â€“ 3 = 22

(b). 12 –Â  (-9) = 12 + 9 = 21

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## MULTIPLICATION OF DIRECTED NUMBERS

RULES:

• + Â * Â – = –Â  OR – * + = – (If different signs are multiplied the answer is NEGATIVE).
• + Â * + = + ORÂ  – * –Â  =Â  + ( If the same signs are multiplied the answer is positive).

Example1: Simplify the following (a) (+12) * (+5) (b) (-3) * (-8)

Solution:

(a). 12 * 5 = 60

(b). -3 * -8 = + 24

Example 2: Find the values of the following (a) -4 * -2 * -2 * -2 * -2Â Â  (b) 7 * (-3) * (-1) * (-1) * 20

Solution:

( a). -4 *Â  -2 * -2 * -2 * -2 = – 64 ( rules, we have equal signs to give positive while different sign gives negative)

(b). 7 * (-3) * (-1) * (-1) * 20 = 7*-3 = -21 *-1 * -1 = -21*20 = – 420

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## DIVISION OF DIRECTED NUMBERS

RULES:

+ Ã· + = + OR – Ã· – = + ( If the sign are divided the answer is positive)

+ Ã· + = – OR – Ã· + = =- (Ie the sign are different theanswer is negative).

Eample 1: work out the following (a) (+80) Ã· (-10)Â Â Â  (b) (-25) Ã· (-5)

Solution:

• (+80) Ã· (-10) = – 8 (because the signs are different)
• (-25) Ã· (-5) = + 5(because the signs are the same)

DO THESE:

Simplify the following

(b) (-25) Ã· (-5)

(a). 3 x 5 x 2 x 15 (-9)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (b). -8 x (-11) x 9 x (-5)

Â Â Â Â Â Â Â Â Â  -5 x 25 x 3Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Â Â Â Â Â Â Â Â Â Â Â Â  2 x (-33) x (-3)