Multlipication and Division of Directed Number – JSS2 Mathematics Lesson Note (First Term)

 Multiplication and division of directed numbers

Revision on addition and subtraction of directed numbers

Note that:

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

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

Example 1: Find the values of the following:

(a). + 7  + (+8) (b) +13 – (+6)

Solution:

(a).  + 7 + (+8) = 7 + 8 = 15

(b). + 13 – (+6) = 13 – 6 = 7

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

Solution

(a). 25  – (+3) = 25 – 3 = 22

(b). 12 –  (-9) = 12 + 9 = 21

Multiplication of directed numbers

RULES:

(i)     +  *  – = –  OR – * + = – (If different signs are multiplied the answer is NEGATIVE).

(ii)   +  * + = + OR  – * –  =  + ( 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 * -2   (b) 7 * (-3) * (-1) * (-1) * 20

Solution:

( a). -4 *  -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

Division of directed numbers

RULES:

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

+ ÷ + = – OR – ÷ + = =- ( the sign is different the answer is negative).

Example 1: work out the following (a) (+80) ÷ (-10) (b) (-25) ÷ (-5)

Solution:

(a)    (+80) ÷ (-10) = – 8 (because the signs are different)

(b)   (-25) ÷ (-5) = + 5(because the signs are the same)

Do these:

Simplify the following

(b) (-25) ÷ (-5)

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

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