1. Chapter 1-1 Variables and expressions PreAlgebrateachers.com
Unit 1
Chapter 1-1 Variables and expressions
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2. Numerical Expression Examples:
Vocabulary:
Expression-mathematical phrase that contains operations, numbers, AND/OR variables.
***Does not have an equal sign (=)
Variable – A letter that represents a value that can change or vary
2 types of expression:
Numerical Expression: Does not contain variables
Variable Expression: Contains one or more variables.
Numerical Expression Examples:
(5)
Variable Expressions Examples
𝑋 X+2
P-R N

3. Writing Variable Expression
Key Words: Total (+) Difference (-) Product (X) (•) () Quotient (÷) (-) (/) More Than (+) Fewer Than (-) Times (X) (•) () Divided By (÷) (-) (/) Increased By (+) Less Than (-) Decreased By (-)

4. Write the algebraic expression for the given verbal expression:
Ex 1: Nine more than a number Y
Ex 2: Four less than a number N
Ex 3: Five times the quantity four plus a number C
(See next slide for answers)

5. Write the algebraic expression for the given verbal expression:
Ex 1: Nine more than a number Y
9 + Y
Ex 2: Four less than a number N
N - 4
Ex 3: Five times the quantity four plus a number C
5 X (4+C) or 5(4+C)
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6. Substitution Property of Equality
If two quantities are equal, then one quantity can be replaced by the other in a mathematical expression
“Plug it in Plug it in!”
Evaluate each expression if K = 2, m=7, and X = 4.
Ex 1: 6M-2K
6(7) – 2 (2) (replace m with 7 and K with 2)
Multiply
Subtract

7. Substitution Property of Equality
Example 2:
Evaluate each expression if K = 2, m=7, and X = 4.
= 𝐾𝑀 2 (Replace k with 2 and m with 7)
= 2 (7) 2 (Multiply numerator)
= (Divide fraction) =7
Example 3:
Evaluate each expression if K = 2, m=7, and X = 4.
=3X (Replace x with 4 )
=3(4) (Multiply 3 and 4)
= (Add)
=19

8. Let’s do some practice Evaluate: 3a – 5, A=10 2) 6𝑌 2 Y=2
3) 2X + 3Y + 4Z, X=4, Y=3, Z=2
(answers on next slide)

9. Let’s check our answers!
Evaluate:
3a – 5, A=10
3 (10) – 5
30 – 5 = 25
2) 6𝑌 2 Y=2
6 (2) 2 = = 6
3) 2X + 3Y + 4Z, X=4, Y=3, Z=2
2 (4) + 3 (3) +4 (2)
= 25

10. Chapter 1-2 Order of Operations
UNIT 1
Chapter 1-2 Order of Operations

11. Evaluate an expression: find the numerical value
Vocabulary:
Evaluate an expression: find the numerical value
Order of Operations Rules:
Simplify expressions inside parenthesis ( )
Simplify any exponents
Do all multiplication and/or division from left to right
Do all addition and/or subtraction from left to right

12. Find the value of each expression:
(divide)
(simplify)
EX 2) 4 (5) – 3
20 – 3 (complete parenthesis)
17 (simplify)

13. Find the value of each expression
[2 + (6 • 8)] – 1
[ ] – 1 (complete parenthesis)
[50] (Add)
(Simplify)
Ex 4:
10 ÷ [9 – (2 • 2)]
10 ÷ [9 – ( 4)] (complete parenthesis)
10 ÷ [5] (complete parenthesis)
(simplify by dividing)

14. Let’s Practice! 53−15 17−13 Find the value of each expression:
6 (2+9) – 3 • 8
53−15 17−13

15. Let’s check our answers!
Find the value of each expression:
3 + 4 x 5
(multiply)
(simplify)
2) 6 (2+9) – 3 • 8
6 (11) – 3 • 8 (complete parenthesis)
66 – (complete each multiplication)
(simplify)
−13 = (53 +15) ÷ (17-13) (rewrite as division problem)
(68) ÷ (4) (simplify each parenthesis)
(divide)

16. UNIT 1
Chapter 1 – 2 Properties

17. Vocabulary and Properties:
Properties: statements that are true for any numbers

18. Vocabulary and Properties

19. Vocabulary and Properties

20. Name the property shown by each statement: EX 1) 3 + 5 + 9 = 9 + 5 +3
EX 2) A • (9 • 7) = (A•9) • 9
EX 3) = 15
Check answers next!

21. Name the property shown by each statement:
EX 1) = Commutative Property of Addition
EX 2) A • (9 • 7) = (A•9) • Associative Property of Multiplication
EX 3) = Additive Identity

22. You can use what you’ve learned about properties of numbers to find sums and products mentally. Group numbers mentally so that sums or products end in a zero.
Ex 1:
(4+6) (group the 4 and 6)
(simplify)
(Add mentally)
EX 2: 5 • 7 • 8
(5•8) • 7 (group the 5 and 8)
(40) • 7 (simplify)
(multiply mentally)

23. Chapter 1 – 4 Ordered Pairs
Unit 1
Chapter 1 – 4 Ordered Pairs

24. the number lines intersect
Vocabulary:
Coordinate System - used to locate points and is formed by the intersection of two numbers that meet at a right angle at their zero points (also called a coordinate plane)
Y-axis –
Vertical number line
Origin- is at (0,0), the point at which X-Axis - the horizontal number line
the number lines intersect

25. Vocabulary: An ordered pair of numbers is used to locate a point on a coordinate plane. The first number is called is the X-coordinate. The second number is called the Y-coordinate. (3, 2) The x-coordinate corresponds to a The y-coordinate corresponds to a number Number on the x-axis on the y-axis

26. Graph each ordered pair on a coordinate system (4, 2)
To graph an ordered pair, draw a dot at the point that corresponds to the ordered pair. The coordinates are your direction to locate the point.
Example 1:
Graph each ordered pair on a coordinate system
(4, 2)
Step 1: Start at origin
Step 2: Since the x-coordinate is at 4, move 4 units
to the right
Step 3: Since the y-coordinate is 2, move 1 unit up.
Draw a dot.

27. Grade the ordered pair on a coordinate system (5,0)
Example 2:
Grade the ordered pair on a coordinate system
(5,0)
Step 1: Start at the origin
Step 2: The x-coordinate is 5. So, move 5 units
to the right
Step 3: Since the y-coordinate is 0, you will
not need to move up. Place your dot directly on the x-axis

28. Write the ordered pair that names each point Ex. 1) Point C
Sometimes a point on a graph is named by using a letter. To identify its location, you can write the ordered pair that represents the point.
Write the ordered pair that names each point
Ex. 1) Point C
Step 1: Start at the origin
Step 2: Move right on the x-axis to find the
X-coordinate of point C, which is 3.
Step 3: Move up the y-axis to find the y-coordinate,
Which is 4.
The ordered pair for point C is (3,4)
Ex 2) Point G
The x-coordinate of G is 4, and the y-coordinate is 5. The ordered pair for
point G is (4,5)