Operations with Signed Numbers

Operations with Signed Numbers

Addition

SAME SIGNS DIFFERENT SIGNS

ADD the numbers and KEEP the sign. SUBTRACT the numbers and keep the sign of the LARGER number.

Do Now:

1) 11 + 15 2) -11 + (-15) 3) 11 + (-15) 4) -11 +15

Subtraction

K (keep) C (change) O (opposite)

All subtraction problems can be changed to addition problems by changing the “ – “ to “ + “ and changing the sign of the number that follows the subtraction sign. Then you just follow the rules of addition.

Example: 25 – 10 = 15 34 – (-10) = 44

25 – 10 = 34 – (-10) =

K C O K C O

25 + (-10) = 34 + (+10) =

15 44

Do Now:

5) 12 - 15 6) 12 - (-15) 7) -12 – 15 8) - 12 – (-15)

Multiplication and Division

SAME SIGNS DIFFERENT SIGNS

Product or Quotient is POSITIVE Product or Quotient is NEGATIVE

Do Now:

9) 8 ∙ ¾ 10) – 8 ∙ ¾ 11) 8 ∙ - ¾ 12) -8 ∙ - ¾

13) 15 ÷ ⅝ 14) -15 ÷ ⅝ 15) 15 ÷ - ⅝ 16) -15 ÷ - ⅝

Part I:
1) 28 + (-31) = 2)-41.4 + (-19.8) =

3) 23.8 - (-38.3)= 4) -45.07 - (-46.2) =

5) (-7 ½)(5 ⅓)= 6) (-6 ¾)(- 4 ½ )=

7) (2 ½ ) ÷ (-3 ⅛)= 8) -16 ÷ (- 5 ¼ )=

9) 100- 122 · (- ½) + (8)(-2) = 10) x= -5:3x2 ÷(35 - 4x)+x =

11) a = 5 b = -6 c = -3 12) x =-10 y =4 z =- 2

[2b2 - a3 ÷ (8c - 1)] ÷ (-2a - 1) 4y2 - 8x ÷ (2z) + 6

12c2 + 12b– 2a - 42x2 + 15z - 10y- 55

Part II:
1) 24 - 12 · 3 + 6 =

a) 6 b) 42 c) -6 d) – 192

2) 36 + 33÷ (1/9) - 8 · (12) =

a) 130 b) 171 c) 183 d) 4,764

3) Evaluate: 52÷ (-22 + 32) + 24 · (1/4) =

4) Evaluate: 122 - 42÷ (-1/2) + 2 · (-3)2 =

5) a = -3 b = 7

5a - 12b + 9 · 3=

2b - 3a + 1

6) Evaluate 3y2 + 8x = , when x = 3 and y= -2

a) 12 b) 36 c) 60 d) 0

7) (112 + 20 ∙ ¾ ) ÷ 4 – 5 ∙ 7 =

8) Evaluate when a = -5, b = 4, and c = -2

3b – 16 ÷ 2c + 3a .

(2a2 + 9c) ÷ 4b