Operations with Signed Numbers
Addition
SAME SIGNS
ADD the numbers and KEEP the sign.
Do Now:
1) 11 + 15
2) -11 + (-15)
DIFFERENT SIGNS
SUBTRACT the numbers
and keep the sign of the
LARGER number.
3) 11 + (-15)
4) -11 +15
Subtraction
K
C (change)
(keep)
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:
Do Now:
5) 12 - 15
25 – 10 = 15
34 – (-10) = 44
25 – 10 =
K C O
25 + (-10) =
15
34 – (-10) =
K C O
34 + (+10) =
44
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) =
3) 23.8 - (-38.3) =
5) (-7 ½)(5 ⅓) =
7) (2 ½ ) ÷ (-3 ⅛) =
2) -41.4 + (-19.8) =
4) -45.07 - (-46.2) =
6) (-6 ¾)(- 4 ½ ) =
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)
12c2 + 12b – 2a – 4 + c
4y2 - 8x ÷ (2z) + 6
2x2 + 15z - 10y- 55
Part II:
1) 24 - 12 · 3 + 6 =
a) 6
b) 42
c) -6
d) – 192
c) 183
d) 4,764
2) 36 + 33 ÷ (1/9) - 8 · (12) =
a) 130
3) Evaluate:
b) 171
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
7) (112 + 20 ∙ ¾ ) ÷ 4 – 5 ∙ 7 =
8) Evaluate when a = -5, b = 4, and c = -2
3b – 16 ÷ (2c) + 3a .
(2a2 + 9c) ÷ 4b
d) 0
DO NOT DO ON SHEET! DO IN NB!!
1) 256 – 46 · 3 – 11=
2) 24 ÷ (6 – 3 · 4) · 13 =
3) 100 - 122 · ¼ + (6)(-2) =
4) 112 – 3· 42 ÷ (⅔) - 72 =
5) Substitute and Evaluate:
y = -5
3y3 - 2y2 ÷ 10 + 379 =
6) Substitute and Evaluate:
x = -4
5x2 ÷ (½) - 12x
7) Substitute and Evaluate:
b = 7 and c = -2
bc2 ÷ (42 – 4b) – 11c =
8) Evaluate when a = -4, b = 5, and c = 2
6c2 ÷ (c2 – ab) - 6a .
6a2 – 8b ÷ (-2c) - 6
10) Evaluate when a = -8, b = -3, and c = 9
4b3 + ac – ab - 1
c – 16b ÷ a + 8a + 2b
2
9) Evaluate when x = -6, y = 3, and z = -2
2x2 – (yz – 10y) - 18 .
3z2 – 12x ÷ (4y) – 4z + 4
Q1 Quiz 3 Review:
Do the following problems in your NB:
1) Evaluate:
2) a = -4
225 ÷ (51 - 62) - 32 ÷ (-4/9) =
b=9
3a2 – (8b ÷ a) + (5)(-6) _
ba2 ÷ [9a ÷ (2b)]
3) Evaluate when a = -3, b = 5, and c = -7
6b – 56 ÷ (2c) + 3a .
(2c + 10a) ÷ (b – 1) – 7
2
4) Evaluate when a = -8, b = -3, and c = 9
4b3 + ac – ab - 1
c2 – 16b ÷ a + 4a - 2
5) Evaluate when a = -2, b = -5, and c = 6
4a3 ∙ (22 + bc) – 2a
3b2 – 4c + 10a + b
6) x = -4 and y = 7
yx3 - xy2 + 11xy
7) x = -3
12x2 – 2x3 ÷ (2x + 12) + 6x
8) Evaluate when x = 4 y = -8 and z = 6
xyz - 2y2 ÷(- ½) - 3xz _
( z2 + x2 – y2 + 2) ÷ (⅔) + 1
9) f = 9
3 - 4f 2 ÷ 27 + f =
Q1 Quiz 4 Review Answer Key:
1) 87
2) - ½ (numerator= 36, denominator = -72)
3) 2 ½ (numerator= 25, denominator = 10)
4) -5 (numerator= -205, denominator = 41)
5) 10 (numerator= 260, denominator = 26)
6) -560
7) 99
8) 4/7 (numerator= -8, denominator = -14)
9) 0