MULTIPLICATION OF DIRECTED NUMBERS Archives

ADDITION AND SUBTRACTION OF DIRECTED NUMBERS Directed numbers are the positive and negative numbers in any given number line e.g -4 -3 -2 -1 0 1 2 3 4 The (+) and (-) signs show the direction from the origin (o). To add a positive number move to the right on the number line Addition -2 -1 0 +1 +2 +3 +4 To subtract a positive number, move to the left on the number line Subtraction -2 -1 0 +1 +2 +3 +4 Worked examples Simplify the following (-2_+(-4) (-6)+(+6)+0 iii. 6-(-3)-(-4) Solution 1) (-2)+(-4)2+4-6 -6 -5 -4 -3 -2 -1 +1 +2 (-6)+(-6)+0 6+6+0 - 0 -6 -5 -4 -3 -2 -1 0 +1 +2 +3 -(-3)-(-4) 6+3+4 - 13 -1 0 +1 +2 +4 +5 +6 +7 +8 +9 +10 +11 +12 +13 EVALUATION Simplify the following (+6)-(+10) 12-(+3)-8 (-5)+(-5)+(-5) (-8)-(-2)+(-2) MULTIPLICATION OF DIRECTED NUMBERS Multiplication is a short way of writing repeated addition e.g. 3x44+4+4 12. When directed numbers are multiplied together, two like signs give a positive result, while two unlike signs give a negative result in general (i) (+a) x (-b) +ab (ii) (-a) x (-b) +ab (iii) (+a) x(-b)-ab (iv) (-a) x (+b) -ab Worked examples Simplify the following (a) (+1/2) x (+1/4) +1/8 (b) (+17) x (-3) -51 (c ) (- 91/3) x (+2/5) -56/15 -311/15 DIVISION OF DIRECTED NUMBERS The rules of multiplication of directed numbers also apply to the division of directed numbers (+a) ÷ (+b)+(a/b) (-a) ÷ (-b)+(a/b) iii. (+a) ÷ (-b) -(a/b) (-a)÷(+b) -(a/b) Class work Simplify the following (-36) ÷ (+4) (-4) ÷(-12) (-6) x (-5) -10 x 3 Complete the following (+6) + (5) (+6) + (9) (-6) + (5) (+7) + (4) (+8) - (+6) WEEKEND ASSIGNMENT Simplify 12 - (+3) - 8 ____ a) -1 (b) +1 (c)-2 (d)+2 Simplify (-3) (-1) ____ a) -2 (b) -1 (c)+1 (d) +2 Simplify (+15) x (-4) ____ a) -20 (b) -60 (c)+20 (d) +60 Divide -18 by -3 ____ a) -6 (b) +6 (c)-21 (d) +15 Divide -5 by -15 ____ a) +1/3 (b) -1/3 (c) +1/5 (d) -1/5 THEORY 1a). Simplify 4/9 of (-2 4) b) Simplify (-2) + (-7) using number lines. 2 Simplify a) 7 x (-6.2) b) -112 ÷ -4 See also APPROXIMATION OF NUMBERS ROUNDING SIMPLE INTEREST FRACTIONS H.C.F & L.C.M AND PERFECT SQUARES WHOLE NUMBERS AND DECIMAL NUMBERS