Transcript Holt CA Course 1

1-5
Evaluating Algebraic Expressions
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
1-5
Evaluating 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)
83
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
California
Standards
AF1.2 Write and evaluate an algebraic
expression for a given situation, using up to
three variables.
Also covered: AF1.3
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
Vocabulary
variable
constant
algebraic expression
evaluate
Holt CA Course 1
1-5
Evaluating 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 is an expression
that contains at least one variable. For
example, 1954 + a is an algebraic expression.
Holt CA Course 1
1-5
Evaluating 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.
Holt CA Course 1
1-5
Evaluating 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.
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
Additional Example 1A: Evaluating Algebraic
Expressions
The expression b + 9 represents Chad’s age
when his brother is b years old. Evaluate the
expression for each value of b, and then tell
what the value of the expression means.
b=5
b+9
5+9
14
Substitute 5 for b.
Add.
When his brother is 5, Chad is 14.
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
Additional Example 1B: Evaluating Algebraic
Expressions
The expression b + 9 represents Chad’s age
when his brother is b years old. Evaluate the
expression for each value of b, and then tell
what the value of the expression means.
b=2
b+9
2+9
11
Substitute 2 for b.
Add.
When his brother is 2, Chad is 11.
Holt CA Course 1
1-5
Evaluating 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
Holt CA Course 1
Substitute 2 for x.
8–3
Multiply.
5
Subtract.
1-5
Evaluating 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
Holt CA Course 1
Substitute 15 for s.
Divide.
Add.
1-5
Evaluating Algebraic Expressions
Additional Example 3: Evaluating Algebraic
Expressions with More than One Variable
Evaluate 6
a + 4b − c, for a = 3, b = 2, and c = 7.
6 + 4b − c
a
6 + 4(2) − 7 Substitute 3 for a, 2 for b,
3
and 7 for c.
2+8−7
3
Holt CA Course 1
Divide and multiply from
left to right.
Add and subtract from
left to right.
1-5
Evaluating Algebraic Expressions
Check It Out! Example 1B
The expression y + 7 represents Sidney’s age
when her brother is y years old. Evaluate the
expression for each value of y, and then tell
what the value of the expression means.
y=8
y+7
8+7
15
Substitute 8 for y.
Add.
When her brother is 8, Sidney is 15.
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
Check It Out! Example 2
A. 4y2 + 2y, for y = 3
4(3)2
+ 2(3)
4(9) + 2(3)
36 + 6
42
Holt CA Course 1
Substitute 3 for y.
Evaluate the power.
Multiply.
Add.
1-5
Evaluating Algebraic Expressions
Check It Out! Example 3
Evaluate 8 − x + 2z, for w = 2, x = 3, and z = 4
w
8 − x + 2z
w
8 − 3 + 2(4)
2
Substitute 2 for w, 3 for x,
and 4 for z.
4−3+8
Divide and multiply from
left to right.
9
Holt CA Course 1
Add and subtract from left
to right.
1-5
Evaluating 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 + 3y for x = 4 and y = 3
23
x
6. The expression 7d gives the number of days in
d weeks. Evaluate 7d for d = 12. How many
84
days are in 12 weeks?
Holt CA Course 1