Upload
alison-miller
View
225
Download
0
Tags:
Embed Size (px)
Citation preview
Course 2
1-7 Variables and Algebraic Expressions1-7 Variables and Algebraic Expressions
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Course 2
1-7 Variables and Algebraic Expressions
Warm UpEvaluate.
1. 5(7) – 1
2. 7(18 – 11)
3. 22 + 17 8 + 3
4. 36 + 15(40 – 35)
5. 33 + 7(12 – 4)
34
49
161
111
83
Course 2
1-7 Variables and Algebraic Expressions
Problem of the Day
If charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12?$28
Course 2
1-7 Variables and Algebraic Expressions
Learn to evaluate algebraic expressions.
Course 2
1-7 Variables and Algebraic Expressions
Vocabulary
variableconstantalgebraic expressionevaluate
Course 2
1-7 Variables and Algebraic Expressions
Ron Howard was born in 1954. You can find out what year Ron turned 16 by adding the year he was born to his age.
1954 + 16
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
1954 + a.
Course 2
1-7 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, 1954 + a is an algebraic expression for the year Ron Howard turns a certain age.
Course 2
1-7 Variables and Algebraic Expressions
To evaluate an algebraic expression, substitute a number for the variable.
Age Year born + age = year at age
16 1954 + 16 1970
18 1954 + 18 1972
21 1954 + 21 1975
36 1954 + 36 1990
a 1954 + a
Course 2
1-7 Variables and Algebraic Expressions
Evaluate k + 9 for each value of k.
Additional Example 1: Evaluating Algebraic Expressions
A. k = 5 k + 9
5 + 9
14
Substitute 5 for k.
Add.
B. k = 2 k + 9
2 + 9 Substitute 2 for k.
11 Add.
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 1
Evaluate a + 6 for each value of a.
A. a = 3 a + 6
3 + 6
9
Substitute 3 for a.
Add.
B. a = 5 a + 6
5 + 6 Substitute 5 for a.
11 Add.
Course 2
1-7 Variables and Algebraic Expressions
Multiplication and division of variables can be written in several ways, as shown in the table.
When evaluating expressions, use the order of operations.
Course 2
1-7 Variables and Algebraic Expressions
Evaluate the expression for the given value of the variable.
Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations
A. 4x – 3 for x = 2
4(2) – 3
8 – 3
5
Substitute 2 for x.
Multiply.
Subtract.
Course 2
1-7 Variables and Algebraic Expressions
Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations
B. s ÷ 5 + s, for s = 15
15 ÷ 5 + 15
3 + 15
18
C. 5x2 + 3x, for x = 2
5(2)2 + 3(2)
5(4) + 3(2)
20 + 6
26
Substitute 15 for s.
Divide.
Add.
Substitute 2 for x.
Evaluate the power.
Multiply.
Add.
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 2A
Evaluate the expression for the given value of the variable.
A. 3x – 2 for x = 3
3(3) – 2
9 – 2
7
Substitute 3 for x.
Multiply.
Subtract.
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 2
B. r ÷ 3 + r, for r = 12
12 ÷ 3 + 12
4 + 12
16
C. 4y2 + 2y, for y = 3
4(3)2 + 2(3)
4(9) + 2(3)
36 + 642
Substitute 12 for r.
Divide.
Add.
Substitute 3 for y.
Evaluate the power.
Multiply.Add.
Course 2
1-7 Variables and Algebraic Expressions
Evaluate
Additional Example 3: Evaluating Algebraic Expressions with Two Variables
6a + 4b, for a = 3 and b = 2.
6a + 4b
63 + 4(2)
2 + 8
10
Substitute 3 for a and 2 for b.
Divide and multiply from left to right.
Add.
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 3
Evaluate 8w + 2x, for w = 4 and x = 2.
8w + 2x
84 + 2(2)
2 + 4
6
Substitute 4 for w and 2 for x.
Divide and multiply from left to right.
Add.
Course 2
1-7 Variables and Algebraic Expressions
Lesson QuizEvaluate n + 7 for each value of n.
1. n = 25 2. 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
5. + 3y 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?
3832
37
162
56x 23
84