Download Adding and Subtracting mixed numbers

Chapter 5: Expressions Study Guide
Writing Algebraic Expressions:
 Define your variable
 Fewer than, less than, more than -> flip the order
3 less than a number x
x –3

Quantity of = put what follows in parentheses
2 times the quantity of 5 minus a number n
2(5 – n)
Evaluating Algebraic Expressions:
 Evaluate = Solve
 Plug your value in the expression using parentheses
 Use PEMDAS to solve
Evaluate: 3x – 2w for x = 8 and w = 4
3(8) – 2(4)
** Plug in values in parentheses **
24 – 8
16
Properties:
Commutative Property of Addition: 2 + 5 = 5 + 2
Change order of numbers (or variables, if applicable)
Commutative Property of Multiplication: 3∙7 = 7∙3
Change order of numbers (or variables, if applicable)
Chapter 5: Expressions Study Guide
Associative Property of Addition: 2 + (3 + 4) = (2 + 3) + 4
Same order of numbers, different groupings (or variables, if
applicable)
Associative Property of Multiplication: 6(xy) = (6x)y
Same order of numbers, different groupings (or variables, if
applicable)
Identity Property of Multiplication (Multiplicative Identity): 7∙1 = 7
Identity Property of Addition (Additive Identity): 6 + 0 = 6
Zero Property of Multiplication (Multiplicative Property of Zero): 5∙0
=0
Distributive Property
Distributive Property = multiply each term inside the parenthesis by
the number outside the parenthesis
Example: Use the distributive property to simplify
7(3 + 12)
* Distribute
7∙3 + 7∙12
* Multiply
21 + 84
* Clean-up
105
Example: Use the distributive property to simplify
11(x - 5)
* Distribute
11∙x - 11∙5
* Multiply
11x - 55
* Clean-up
Chapter 5: Expressions Study Guide
Example: Use the distributive property to simplify
-3(x - 12)
* Distribute
(-3)∙x – (-3)∙12
* Multiply **Use Integer rules LCO
-3x + 36
* Clean-up
Example: Use the distributive property to simplify
(4x - 10)7
* Distribute
7(4x) – (7)∙10
* Multiply
28x - 70
* Clean-up
Simplifying Algebraic Expressions
3x + 5 + 2x -3
Terms: parts of an algebraic expression separated by a + or –

Negative signs must be included (positive is assumed)
If the term is x
the coefficient is 1

If the term is –x the coefficient is -1
Example: 3x, 5, 2x, -3x
Like Terms: terms that contain the same variable or just numbers
Example: 3x, 2x and 5, -3
Coefficients: number in front of the variable (letter) ~ similar to an adjective
it describes the variable
Example: 3, 2 (because it’s 3x and 2x)
Constants: a number without a variable, a plain number!
Example: 5, -3
Chapter 5: Expressions Study Guide
Simplifying algebraic expressions = no like terms or parentheses

Combine the like terms

If the term is x the coefficient is 1

If the term is –x the coefficient is -1

Replace with the combined like terms

Do not add/subtract terms together that are not alike
Example: 2x + 7 ≠ 9
Example: Write in simplest form 7u + u + 12
7u + u = 9u
* Combine like terms
12
9u + 12
Example: Write in simplest form 10z + z -5 - 9z + 2
10z + z – 9z = 11z – 9z = 2z
* Combine like terms
-5 + 2 = -3
* Combine like terms
2z + (-3) = 2z -3
Example: Write in simplest form 5a + 3b +6 – 3a + 2
5a -3a = 2a
* Combine like terms
6+2=8
* Combine like terms
3b
2a + 3b + 8
Adding Linear Expressions


Combine like terms using integer rules
Use the Distributive Property, if applicable and then combine like
terms
Chapter 5: Expressions Study Guide
Example 1: Add. (7x + 12) + (5x + 2)
Two different ways to solve, same result
Horizontally
(7x + 12) + (5x + 2)
7x + 5x = 12x
* Combine like terms
12 + 2 = 14
* Combine like terms
12x + 14
Verically
(7x + 12) + (5x + 2)
7x + 12
* Write first expression
5x + 2
* Write second expression, lining up like
terms and combine like terms
12x + 14
Example 2: Add. (12a + 5) + (-5a - 4)
Two different ways to solve, same result
Horizontally
Vertically
(12a + 5) + (-5a - 4)
(12a + 5) + (-5a - 4)
12a + -5a = 7a
12a + 5
5 + -4 = 1
7a + 1
+ -5a - 4
7a + 1
Example 3: Add. 5(6b - 3) + (-4b + 12)
* Distribute first
Horizontally
Vertically
5(6b - 3) + (-4b + 12)
5(6b - 3) + (-4b + 12)
(30b – 15) + (-4b +12)
(30b – 15) + (-4b + 12)
Chapter 5: Expressions Study Guide
30b +-4b = 26b
30b -15
-15 + 12 = -3
26b -3
-4b + 12
26b -3
Remember: Perimeter = add all sides of the shape
Subtracting Linear Expressions


Combine like terms using integer rules
Use the Distributive Property, if applicable and then combine like
terms
Example 1: Subtract. (8x + 15) - (5x + 3)
Two different ways to solve, same result
Horizontally
(8x + 15) - (5x + 3)
8x - 5x = 3x
* Combine like terms
15 - 3 = 12
* Combine like terms
3x + 12
Verically
(8x + 15) - (5x + 3)
8x + 15
+ -5x - 3
3x + 12
* Write first expression
* Add second expression using
additive inverse, lining up like
terms and combine like terms
Example 2: Subtract. (20a + 16) - (-5a - 4)
Two different ways to solve, same result
Horizontally
Vertically
Chapter 5: Expressions Study Guide
(20a + 16) - (-5a - 4)
(20a + 16) - (-5a - 4)
20a - -5a = 20a + 5a = 25a
16 - -4 = 16 + 4 = 20
20a +16
+
25a + 20
5a + 4
25a + 20
Example 3: Subtract. 4(5a - 3) - (-2a - 6)
First distribute, then solve
Horizontally
Vertically
(20a - 12) - (-2a -6)
(20a - 12) - (-2a - 6)
20a - -2a = 20a + 2a = 22a
-12 - -6 = -12 + 6 = -6
20a -12
+
22a – 6
2a + 6
22a - 6
Greatest Common Factor: GCF
 Use upside down division for numbers
 Match variables (common variables) are included in the GCF
Example1:
Find the GCF of each pair of monomials: 12 and 20
2
2
GCF = 4
| 12
20
| 6
3
10
5
Chapter 5: Expressions Study Guide
Example2:
Find the GCF of each pair of monomials: 9ab and 15abc
3
| 9ab
3ab
15abc
5abc
GCF = 3ab
Factoring Linear Expressions using GCF
 Find the GCF of each term
 Common variables are included in the GCF
 To check your factoring, use the distributing property
Examples:
Factor each linear expression using GCF:
8x + 12
5x -32
8xy + 56x
GCF = 4
GCF = 1
GCF = 8x
4(2x + 3)
cannot be factored
8x(y + 7)
Use distributive to check your answers:
√ 8x + 12
√ 5x -32
√ 8xy + 56x