1
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
2
Numbers Worksheet
Part 1 – Use an integer to express the number(s) in each application below:
1) Erin discovers that she has spent $53 more than she has in her checking
account.________
2) The record high Fahrenheit temperature in the United States was 134˚ on July 10 th, 1913.
________
3) A football team gained 5 yards _________, then lost 10 yards on the next play
________
4) The shore surrounding the Dead Sea is 1348 feet below sea level. ___________
Part 2 – Tell whether each statement is true or false. (write the entire word)
5) - 2 < 4
____________
6) 6 > - 3
____________
7) - 9 < - 12 ____________
8) - 4 ≥ - 1
____________
9) - 6 ≤ 0
10) - 15 > - 5 ____________
____________
Part 3 – Write an example of a number that satisfies each given condition.
11) An integer between 3.6 and 4.6 ____________
12) A rational number between 2.8 and 2.9 ____________
13) A whole number that is not positive and is less than 1 ____________
14) A whole number that is greater than 3.5 ___________
15) A real number that is neither negative nor positive ____________
3
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
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
9) Is (9,-6) a solution for both of the
following equations?
y + 2 = -2 (x - 7)
7x – 3y = 45
10) Is ( ½ , 11) a solution for both of the
following equations?
14x - 5y = -48
y – 1 = 10(x + ½ )
11) Is (-6,-5) a solution for both of the
following equations?
y - 3 = -4 (x + 8)
6x – 12y = 24
12) Is (-8,3) a solution for both of the
following equations?
3x + 14y = 18
y – 11 = 4(x + 10)
13) Evaluate each problem in √b2 – 4ac (the entire expression is under the radical)
a) when a = 2, b= -6, and c = -8
b ) when a = -4, b= -3, and c = 7
c) when a = 3, b = 4, and c = -7
d) when a = -5, b = 1, and c = 6
4
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
c2 – 16b ÷ a + 8a + 2b
9) Evaluate when x = -6, y = 3, and z = -2
2x2 – (yz – 10y) - 18 .
3z2 – 12x ÷ (4y) – 4z + 4
5
Q1 Quiz 2 Review:
Do the following problems in your NB:
1) Evaluate:
225 ÷ (51 - 62) - 32 ÷ (-4/9) =
2) a = -4
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
c – 16b ÷ a + 4a - 2
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
8) Evaluate when x = 4 y = -8 and z = 6
12x2 – 2x3 ÷ (2x + 12) + 6x
9) f = 9
xyz - 2y2 ÷(- ½) - 3xz _
( z2 + x2 – y2 + 2) ÷ (⅔) + 1
3 - 4f 2 ÷ 27 + f =
10) Is (-3,7) a solution for both of the
following equations?
9x + 5y = 14
y – 6 = 4(x + 4)
11) Is (5,-2) a solution for both of the
following equations?
y + 9 = ½ (x + 9)
4x – 3y = 14
12) Is (⅔, -8) a solution for both of the
following equations?
12x - 5y = 48
y – 2 = 10(x + ⅓)
13) Evaluate each problem in √b2 – 4ac (the entire expression is under the radical)
a) when a = -2, b= -5, and c =7
b ) when a = 6, b= -1, and c = -5
6
Q1 Quiz 2 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
10) Yes
11) No, it is not a solution for the 2nd equation.
12) No, it is not a solution for the 2nd equation.
13) a) 9
13) b) 11