Directed Number Using Negative Numbers Objective To able

Directed Number Using Negative Numbers

Objective • To able to – Add & Subtract negative numbers – Multiply & Divide negative numbers

A Directed Number… • Is one which has a + or – sign attached • To show its direction +2 -2 Positive & Negative numbers Yes! NOT Plus & Minus numbers NO!

From 0 on a number line +5 -5 5 to right +3 5 to left -6 -5 -4 -3 -2 -1 0 1 3 to right 2 3 4 5 6

Adding numbers +3 + +2 = +5 +5 +3 -6 -5 -4 -3 -2 -1 0 1 +2 2 3 4 5 6

Adding numbers 3 + -2 2 3 = -5 -5 -2 -6 -5 -4 -3 -3 -2 -1 0 1 4 5 6

Adding numbers +5 + -2 = +3 +3 +5 -6 -5 -4 -3 -2 -1 0 1 2 -2 3 4 5 6

Adding numbers +2 + -5 2 3 = -3 -3 -5 -6 -5 -4 -3 -2 -1 0 +2 1 4 5 6

Try these a) + b) +6 + -3 c) -2 + -4 + d) 1 + 6 +3 -6 -5 -7 -4 -3 Think of 1 st number as a starting point -4 +3 -6 +5 -2 -1 Think of 2 nd number as a move left or right 0 1 2 3 4 5 6

Subtracting numbers +5 - +2 = +3 +2 +5 +3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Subtracting numbers +5 - +2 = +3 +3 +5 - +2 is just -2 -6 -5 -4 -3 -2 -1 -2 0 1 2 3 4 5 6

Subtracting numbers +3 - +5 = -2 -2 -5 -6 -5 -4 -3 -2 -1 0 +3 1 2 3 4 5 6

4 Volunteers with WHITEBOARDS • How good a teacher am I? • Give a mark between 1 and 10 • Hold up your boards – show class SUBTRACT a NEGATIVE means ADD

Subtract a NEGATIVE number +3 + -2 = +1 = +3 So +1 -6 -5 - -2 -4 -3 -2 -1 +1 +30 1 2 2 3 4 5 6

Try these a) +3 - -2 b) +1 - -3 c) -2 - +4 -6 -5 -4 -3 Think of 1 st number as a starting point Think of 2 nd number as a move left or right +5 +4 -6 -2 -1 Think of SUBTRACT as a REVERSE of DIRECTION 0 1 2 3 4 5 6

Basic Rules ADD a POSITIVE means ADD + +3 = + 3 ADD a NEGATIVE means SUBTRACT + -3 = - 3 SUBTRACT a POSITIVE means SUBTRACT - +3 = - 3 SUBTRACT a NEGATIVE means ADD - -3 = + 3

Sometimes Textbooks give a number in a bracket 5 - (+2) = 5 - +2 Sometimes Textbooks give the sign NOT raised 5 - (+2) =5 - + ( 2) =5 - +2

Task • AQA Intermediate Text [Green] – Page 36 Exercise 4. 3 – Write Questions and answers

Multiply & Divide with Negative numbers

Multiplication +3 x +2 = +6 +2 -6 -5 -4 -3 -2 -1 0 1 +2 2 3 +2 4 5 6

Multiplication +3 -2 -6 -5 x -2 -2 -4 -3 = -6 -2 -2 -1 0 1 2 3 4 5 6

Multiplication -3 x -2 = +6 +2 +2 +2 -2 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

Rule for Multiplication POSITIVE x POSITIVE = POSITIVE +2 x +3 = +6 POSITIVE x NEGATIVE = NEGATIVE +2 x -3 = -6 NEGATIVE x POSITIVE = NEGATIVE -2 x + 3 = -6 NEGATIVE x NEGATIVE = POSITIVE -2 x -3 = + 6 If SAME SIGN, answer is POSITIVE

Rule for Division Inverse of Multiplication POSITIVE ÷ POSITIVE = POSITIVE +18 ÷ +3 = +6 POSITIVE ÷ NEGATIVE = NEGATIVE +18 ÷ -3 = -6 NEGATIVE ÷ POSITIVE = NEGATIVE -18 ÷ + 3 = -6 NEGATIVE ÷ NEGATIVE = POSITIVE -18 ÷ -3 = + 6 If SAME SIGN, answer is POSITIVE

Task • Exercise 4. 4 page 38 • Review Exercise

Puzzle • Can you complete this puzzle? Click Here

Using negative numbers in formulae • We call putting a number into an expression Substitution

Examples t=f+7 If t = f + 7 If f = 5 t=5+7 If f = -5 t = -5 + 7 t = 12 t=2

Examples t = 3 q + 4 If q = 5 t = 3 x 5 + 4 3 q = 3 x q t = 15 + 4 t = 19 If q = -5 t = 3 x-5 + 4 t = -11 NOT t = 35 + 4 = 39

Examples S = t 2 = t x t If t = 5 S = 5 x 5 If t = -5 S = -5 x-5 S = 25

Exercises • Referring to your notes on negatives • Attempt Exercises in Keymaths 8/3 page 126 onwards – 6: 5 – 6: 6 – 6: 7 – 6: 8