Crusenberry 7.16.13

Algebra

Commutative Property of Addition and Multiplication / No matter the order of the numbers, the answer is that same
Associative Property of Addition and Multiplication / No matter who you group the numbers, the answer is the same
Distributive Property / Combines both addition and multiplication; add or multiply first; either way you get the same answer
Properties of Zero (0) / If you add or subtract zero (0) from any number, the value of that number has not changed
Properties of One (1) / If you multiply or divide any number by 1, the value will not be changed
Inverse Operations / Opposites – add & subtract; multiply & divide
Function / A rule that changes one value to another value
Input / When you apply the rule to a starting number
Output / The result of the rule
Unknowns or Variables / Letters that take place of numbers
Mathematical expression / Not a complete thought
Evaluate / Find the value of an expression
Expression / Shows the relationship between two terms
Equation / A mathematical sentence stating that two expressions are equal

Identifying number patterns –

84, 77, 70, _____, _____

**This pattern subtracts 7 from each number, so the blanks would house the numbers 63 then 56

10, 15, 13, 18, _____, _____

**This patterns adds 5 and then subtracts 2, so the blanks would house the numbers 16 then 21

Commutative Property –

6 + 3 = 3 + 6

Associative Property –

( 2 + 3 ) + 4 = 5 + 42 + ( 3 + 4) + 2 + 7 **both answers are 9 regardless of how they are grouped

Distributive Property –

5 ( 8 + 2 ) = ( 5 x 8 ) + ( 5 x 2 )
5 x 10 = 40 + 10
50 = 50

Properties of Zero (0) –

16 x 0 = 016 + 0 = 1616 – 0 = 16

Properties of One (1) –

35 x 1 = 3547 ÷ 1 = 47

Inverse Operations –

3 + 7 = 10, so 10 – 7 = 315 – 7 = 8, so 8 + 7 = 15

3 x 7 = 21, so 21 ÷ 7 = 345 ÷ 5 = 9, so 9 x 5 = 45

Working with functions –

Example

Input / 25 / 9 / 4 / 50
Output / 42 / 10 / 0 / 92

**The rule is: subtract 4, then multiply by 2 **Remember you work input to output (top to bottom)

Using variables to write expressions –

**Remember a variable is a letter that represents an unknown number
Examples: a number multiplied by 16 a x 16
a number increased by 12 a + 12
five times a number 5a
the difference between a number and twenty a - 20

Evaluating expressions –

X = 2Y = 6, sox + y =
2 + 6 = 8

Interpreting Expressions and Equations –

Linda spent d dollars. Then she spent 15 dollars more. How many dollars did Linda spend?

d + 15

Laurie Ann works 8 hours a day. So far today she has worded x hours. How many hours are left in her
workday?
8 - x

Solving equations –

X + 12 = 43
- 12 -12subtract 12 from each side
x = 21

Solving inequalities –

M + 5 > 8
- 5 -5 subtract 5 from each side
M > 3

25 – n < 12
+ n + nadd n to both sides
25 < 12 + n
-12 -12subtract 12 from both sides
13 < n

Writing equations and inequalities –

52 is 5 greater than a number x
52 = x + 5