Transcript 1-7 - Montana City School

and
Algebraic
Expressions
1-7
1-7 Variables
Variables
and
Algebraic
Expressions
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
1-7 Variables and Algebraic Expressions
Warm Up
Evaluate.
1. 5(7) – 1
34
2. 7(18 – 11)
49
3. 22 + 17  8 + 3
161
4. 36 + 15(40 – 35)
111
5. 33 + 7(12 – 4)
Course 2
83
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
variable
constant
algebraic expression
evaluate
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
Age
Year born + age = year at age
16
18
21
1954 + 16
1954 + 18
1954 + 21
1970
1972
1975
36
1954 + 36
1990
a
1954 + a
To evaluate an algebraic expression,
substitute a number for the variable.
Course 2
1-7 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
14
B. k = 2
Add.
k+9
2+9
11
Course 2
Substitute 5 for k.
Substitute 2 for k.
Add.
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
B. a = 5
Add.
a+6
5+6
11
Course 2
Substitute 3 for a.
Substitute 5 for a.
Add.
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
Additional Example 2: 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
8–3
5
Course 2
Substitute 2 for x.
Multiply.
Subtract.
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
Course 2
Substitute 15 for s.
Divide.
Add.
Substitute 2 for x.
Evaluate the power.
Multiply.
Add.
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
Course 2
Substitute 3 for x.
9–2
Multiply.
7
Subtract.
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 + 6
42
Course 2
Substitute 12 for r.
Divide.
Add.
Substitute 3 for y.
Evaluate the power.
Multiply.
Add.
1-7 Variables and Algebraic Expressions
Additional Example 3: Evaluating Algebraic
Expressions with Two Variables
Evaluate 6
a + 4b, for a = 3 and b = 2.
6
a + 4b
6
+ 4(2)
3
2+8
10
Course 2
Substitute 3 for a and 2 for b.
Divide and multiply from
left to right.
Add.
1-7 Variables and Algebraic Expressions
Check It Out: Example 3
8
Evaluate w
+ 2x, for w = 4 and x = 2.
8
w + 2x
8
+ 2(2)
4
Substitute 4 for w and 2 for x.
2+4
Divide and multiply from
left to right.
6
Course 2
Add.
1-7 Variables and Algebraic Expressions
Lesson Quiz
Evaluate n + 7 for each value of n.
1. n = 25 32
2. n =31
38
Evaluate each algebraic expression for the
given value of the variables
3. 6y – 5 for y = 7
37
4. 4x2 + 3x for x = 6
162
5. 56
x + 3y for x = 4 and y = 3
23
6. The expression 7d gives the number of days in
d weeks. Evaluate 7d for d = 12. How many
days are in 12 weeks? 84
Course 2