# Operations with Signed Numbers Addition ```Operations with Signed Numbers
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
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 ∙ &frac34;
10) – 8 ∙ &frac34;
11) 8 ∙ - &frac34;
12) -8 ∙ - &frac34;
13) 15 &divide; ⅝
14) -15 &divide; ⅝
15) 15 &divide; - ⅝
16) -15 &divide; - ⅝
Part I:
1) 28 + (-31) =
3) 23.8 - (-38.3) =
5) (-7 &frac12;)(5 ⅓) =
7) (2 &frac12; ) &divide; (-3 ⅛) =
2) -41.4 + (-19.8) =
4) -45.07 - (-46.2) =
6) (-6 &frac34;)(- 4 &frac12; ) =
8) -16 &divide; (- 5 &frac14; ) =
9) 100 - 122 &middot; (- &frac12;) + (8)(-2) =
10) x= -5: 3x2 &divide;(35 - 4x)+x =
11) a = 5 b = -6 c = -3
12) x = -10 y = 4 z = - 2
[2b2 - a3 &divide; (8c - 1)] &divide; (-2a - 1)
12c2 + 12b – 2a – 4 + c
4y2 - 8x &divide; (2z) + 6
2x2 + 15z - 10y- 55
Part II:
1) 24 - 12 &middot; 3 + 6 =
a) 6
b) 42
c) -6
d) – 192
c) 183
d) 4,764
2) 36 + 33 &divide; (1/9) - 8 &middot; (12) =
a) 130
3) Evaluate:
b) 171
52 &divide; (-22 + 32) + 24 &middot; (1/4) =
4) Evaluate: 122 - 42 &divide; (-1/2) + 2 &middot; (-3)2 =
5) a = -3
b=7
5a - 12b + 9 &middot; 3
2b - 3a + 1
6) Evaluate 3y2 + 8x = , when x = 3 and y= -2
a) 12
b) 36
c) 60
7) (112 + 20 ∙ &frac34; ) &divide; 4 – 5 ∙ 7 =
8) Evaluate when a = -5, b = 4, and c = -2
3b – 16 &divide; (2c) + 3a .
(2a2 + 9c) &divide; 4b
d) 0
DO NOT DO ON SHEET! DO IN NB!!
1) 256 – 46 &middot; 3 – 11=
2) 24 &divide; (6 – 3 &middot; 4) &middot; 13 =
3) 100 - 122 &middot; &frac14; + (6)(-2) =
4) 112 – 3&middot; 42 &divide; (⅔) - 72 =
5) Substitute and Evaluate:
y = -5
3y3 - 2y2 &divide; 10 + 379 =
6) Substitute and Evaluate:
x = -4
5x2 &divide; (&frac12;) - 12x
7) Substitute and Evaluate:
b = 7 and c = -2
bc2 &divide; (42 – 4b) – 11c =
8) Evaluate when a = -4, b = 5, and c = 2
6c2 &divide; (c2 – ab) - 6a .
6a2 – 8b &divide; (-2c) - 6
10) Evaluate when a = -8, b = -3, and c = 9
4b3 + ac – ab - 1
c – 16b &divide; a + 8a + 2b
2
9) Evaluate when x = -6, y = 3, and z = -2
2x2 – (yz – 10y) - 18 .
3z2 – 12x &divide; (4y) – 4z + 4
Q1 Quiz 3 Review:
Do the following problems in your NB:
1) Evaluate:
2) a = -4
225 &divide; (51 - 62) - 32 &divide; (-4/9) =
b=9
3a2 – (8b &divide; a) + (5)(-6) _
ba2 &divide; [9a &divide; (2b)]
3) Evaluate when a = -3, b = 5, and c = -7
6b – 56 &divide; (2c) + 3a .
(2c + 10a) &divide; (b – 1) – 7
2
4) Evaluate when a = -8, b = -3, and c = 9
4b3 + ac – ab - 1
c2 – 16b &divide; 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 &divide; (2x + 12) + 6x
8) Evaluate when x = 4 y = -8 and z = 6
xyz - 2y2 &divide;(- &frac12;) - 3xz _
( z2 + x2 – y2 + 2) &divide; (⅔) + 1
9) f = 9
3 - 4f 2 &divide; 27 + f =