Operations with Integers
-15 + 3 = ?
12
48 / 6 + 2 =?
10
4 + (3 + 9) = (4 + 3) + 9
Associative Property of Addition
u/4 = 6
u = 24
What does PEMDAS stand for?
P- Parenthesis
E- Exponents
MD- Multiplication/Division
AS- Addition/Subtraction
25 - (-14) = ?
39
(36 - 12) / (2 + 6) = ?
3
mn + 0 = mn
Identity Property of Addition
t - 7 < 3.4
t < 10.4
What is the rule we use for subtracting integers?
Keep - Change - Flip!
(Keep the first number the same, change subtraction to addition, flip the sign of the second number)
(-7) (50) = ?
-350
5(21 - 32) = ?
60
19 x 53 = 53 x 19
Commutative Property of Multiplication
13n + 42 = 81
n = 3
When writing the answer to an inequality, what three parts do you need to have?
Variable, inequality sign, and number value
(-51)/(-3) = ?
17
(9.8 + 2.2) / (7 - 5) = ?
6
8(x + 2) = 8x + 16
Distributive Property
-8m - 6 < 10
m > -2
What is the rule we use when solving inequalities that makes them different from equations?
When we multiply or divide by a negative, we flip the inequality sign!
Ethylene Glycol is a chemical that can be added to water to lower its freezing point, the temperature at which it freezes. The freezing point of solution A, which is 1 part ethylene glycol and one part water, is -12 degrees Celsius. The freezing point of solution B, which is 2 parts ethylene glycol and 2 parts water, is -36 degrees Celsius. Which solution has the lower freezing point, and how much lower is it?
Solution B has the lower freezing point, 24 degrees Celsius lower.
In basketball, players score points by making free throws worth 1 point each, field goals worth 2 points each, and field goals worth 3 points each. A player scores 4 free throws, 7 two-point field goals, and 2 three-point field goals. How many points did the player score in total?
4(1) + 7(2) + 2(3) = 24 points.
(x + 5y) + 2 = x + (5y + 2)
Associative property of Addition
3x - 5 > 6x + 13
-6 > x OR x < -6
When solving equations and inequalities, what order do we undo the operations?
Undo addition/subtraction first, then multiplication/division.