1. 2-7 Variables and Algebraic Expressions Warm Up Problem of the Day
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. 2-7 Variables and Algebraic Expressions Warm Up Evaluate. 1. 5(7) – 1
Course 2
2-7
Variables and Algebraic Expressions
Warm Up
Evaluate.
1. 5(7) – 1
2. 7(18 – 11)
 8 + 3
(40 – 35)
(12 – 4) 34 49
161
111 83

3. 2-7 Variables and Algebraic Expressions Problem of the Day
Course 2
2-7
Variables and Algebraic Expressions
Problem of the Day
How much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12?
$28

4. 2-7 Learn to evaluate algebraic expressions.
Course 2
2-7
Variables and Algebraic Expressions
Learn to evaluate algebraic expressions.

5. Insert Lesson Title Here
Course 2
2-7
Variables and Algebraic Expressions
Insert Lesson Title Here
Vocabulary
variable
constant
algebraic expression
evaluate

6. 2-7 Variables and Algebraic Expressions
Course 2
2-7
Variables and Algebraic Expressions
Ron Howard was born in You can find out what year Ron turned 16 by adding the year he was born to his age.
In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be a.

7. 2-7 Variables and Algebraic Expressions
Course 2
2-7
Variables and Algebraic Expressions
The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change.
An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, a is an algebraic expression for the year Ron Howard turns a certain age.

8. Year born + age = year at age
Course 2
2-7
Variables and Algebraic Expressions
Age
Year born + age = year at age 16
1970 18
1972 21
1975 36
1990 a a
To evaluate an algebraic expression, substitute a number for the variable.

9. Additional Example 1: Evaluating Algebraic Expressions
Course 2
2-7
Variables and Algebraic Expressions
Additional Example 1: Evaluating Algebraic Expressions
Evaluate k + 9 for each value of k.
A. k = 5
k + 9
5 + 9
Substitute 5 for k. 14
Add.
B. k = 2
k + 9
2 + 9
Substitute 2 for k. 11
Add.

10. Insert Lesson Title Here
Course 2
2-7
Variables and Algebraic Expressions
Insert Lesson Title Here
Try This: Example 1
Evaluate a + 6 for each value of a.
A. a = 3
a + 6
3 + 6
Substitute 3 for a. 9
Add.
B. a = 5
a + 6
5 + 6
Substitute 5 for a. 11
Add.

11. 2-7 Variables and Algebraic Expressions Multiplication Division
Course 2
2-7
Variables and Algebraic Expressions
Multiplication and division of variables can be written in several ways, as shown in the table.
Multiplication
Division q 2
q/2
7t · t
7(t) 7  t
q ÷ 2 s r
ab a · b
s/r
a(b) a  b
s ÷ r
When evaluating expressions, use the order of operations.

12. 2-7 Variables and Algebraic Expressions
Course 2
2-7
Variables and Algebraic Expressions
Additional Example 2A: Evaluating Algebraic Expressions Involving Order of Operations
Evaluate the expression for the given value of the variable.
A. 4x – 3 for x = 2
4(2) – 3
Substitute 2 for x.
Multiply.
8 – 3 5
Subtract.

13. 2-7 Variables and Algebraic Expressions
Course 2
2-7
Variables and Algebraic Expressions
Additional Example 2B & 2C: Evaluating Algebraic Expressions Involving Order of Operations
B. s ÷ 5 + s, for s = 15
15 ÷
Substitute 15 for s.
3 + 15
Divide. 18
Add.
C. 5x2 + 3x, for x = 2
5(2)2 + 3(2)
Substitute 2 for x.
5(4) + 3(2)
Evaluate the power.
20 + 6
Multiply. 26
Add.

14. Insert Lesson Title Here
Course 2
2-7
Variables and Algebraic Expressions
Insert Lesson Title Here
Try This: Example 2A
Evaluate each expression for the given value of the variable.
A. 3x – 2 for x = 3
3(3) – 2
Substitute 3 for x.
Multiply.
9 – 2
Subtract. 7

15. Insert Lesson Title Here
Course 2
2-7
Variables and Algebraic Expressions
Insert Lesson Title Here
Try This: Example 2B & 2C
B. r ÷ 3 + r, for r = 12
12 ÷
Substitute 12 for r.
4 + 12
Divide. 16
Add.
C. 4y2 + 2y, for y = 3
4(3)2 + 2(3)
Substitute 3 for y.
4(9) + 2(3)
Evaluate the power.
36 + 6
Multiply. 42
Add.

16. 2-7 Variables and Algebraic Expressions
Course 2
2-7
Variables and Algebraic Expressions
Additional Example 3: Evaluating Algebraic Expressions with Two Variables 6 a
Evaluate
+ 4b, for a = 3 and b = 2. 6 a
+ 4b 6 3
Substitute 3 for a and 2 for b.
+ 4(2)
Divide and multiply from
left to right.
2 + 8 10
Add.

17. Insert Lesson Title Here
Course 2
2-7
Variables and Algebraic Expressions
Insert Lesson Title Here
Try This: Example 3 8 w
Evaluate
+ 2x, for w = 4 and x = 2. 8 w
+ 2x 8 4
+ 2(2)
Substitute 4 for w and 2 for x.
Divide and multiply from
left to right.
2 + 4 6
Add.

18. Insert Lesson Title Here
Course 2
2-7
Variables and Algebraic Expressions
Insert Lesson Title Here
Lesson Quiz
Evaluate n + 7 for each value of n.
1. n = n =31
Evaluate each algebraic expression for the given value of the variables
3. 6y – 5 for y = 7
4. 4x2 + 3x for x = 6
y for x = 4 and y = 3
6. The expression 7d gives the number of days in d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks? 32 38 37
162 56 x 23 84