Transcript Evaluating Algebraic Expressions PPT

Learn to evaluate algebraic expressions.
Vocabulary
variable
constant
algebraic expression
evaluate
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.
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.
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.
Ex 1: Evaluating Algebraic Expressions
Evaluate k + 9 for each value of k.
A. k = -5
k+9
-5 + 9
4
B. k = -2
Substitute 5 for k.
Add.
k+9
-2 + 9
7
Substitute 2 for k.
Add.
Example 2
Evaluate a + 6 for each value of a.
A. a = -3
a+6
-3 + 6
3
B. a = -5
Substitute -3 for a.
Add.
a+6
-5 + 6
1
Substitute -5 for a.
Add.
Multiplication and division of variables can be
written in several ways, as shown in the table.
When evaluating expressions, use the order of
operations.
Evaluating Algebraic Expressions Involving Order of
Operations
Evaluate the expression for the given value of
the variable.
3. 4x – 3 for when x = -2
4(-2) – 3
-8 – 3
-11
Substitute 2 for x.
Multiply.
Subtract.
Additional Example 2: Evaluating Algebraic
Expressions Involving Order of Operations
4. s ÷ 5 + s, for s = -15
-15 ÷ 5 + -15
-3 + (-15)
-18
5. 5x2 + 3x, for x = -2
5(-2)2 + 3(-2)
5(4) + 3(-2)
20 + (-6)
14
Substitute -15 for s.
Divide.
Add.
Substitute -2 for x.
Evaluate the power.
Multiply.
Add.
Example 6
Evaluate the expression for the given value of
the variable.
A. -3x – 2 for x = 3
-3(3) – 2
-9 – 2
-11
Substitute 3 for x.
Multiply.
Subtract.
7. r ÷ (-3) + r, for r = 12
Substitute 12 for r.
12 ÷ -3 + 12
(-4) + 12
Divide.
8
Add.
8. 4 - y2 + 2y, for y = 3
4 - (3)2 + 2(3)
4 - (9) + 2(3)
(-5) + 6
1
Substitute 3 for y.
Evaluate the power.
Multiply.
Add.
Example 9: 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
Substitute 3 for a and 2 for b.
Divide and multiply from
left to right.
Add.
Example 10
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
Add.
Evaluate n + 7 for each value of n.
1. n = -25 -18
2. n = -31 -24
Evaluate each algebraic expression for the
given value of the variables
3. -6y – 5 for y = 7
-47
4. -4x2 + -3x for x = 6
-162
5. -56
x + 3y for x = 4 and y = 3
-5
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