Transcript 1.5 Evaluating Algebraic Expressions

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 CARDS
•
•
•
•
Variable
Constant
Algebraic Expression
Evaluate
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
The actor and director Ron Howard was born
in 1954.
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.
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
Teacher Example 1: 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
Student Practice 1:
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=4
y+7
4+7
11
Substitute 4 for y.
Add.
When her brother is 4, Sidney is 11.
Holt CA Course 1
1-5
Evaluating Algebraic Expressions
Teacher Example 2:
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
Student Practice 2:
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
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
Teacher Example 3: Evaluating Algebraic
Expressions Involving Order of Operations
Evaluate the expression for the given value of
the variable.
3A. 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
Student Practice 3:
Evaluate the expression for the given value of
the variable.
3A. 3x – 2 for x = 3
3(3) – 2
Holt CA Course 1
Substitute 3 for x.
9–2
Multiply.
7
Subtract.
1-5
Evaluating Algebraic Expressions
Teacher Example 3 Continued:
3B. s ÷ 5 + s, for s = 15
15 ÷ 5 + 15
3 + 15
18
Substitute 15 for s.
Divide.
Add.
3C. 5x2 + 3x, for x = 2
5(2)2 + 3(2)
Substitute 2 for x.
5(4) + 3(2)
Evaluate the power.
20 + 6
26
Holt CA Course 1
Multiply.
Add.
1-5
Evaluating Algebraic Expressions
Student Practice 3 Continued:
3B. r ÷ 3 + r, for r = 12
12 ÷ 3 + 12
4 + 12
16
Substitute 12 for r.
Divide.
Add.
3C. 4y2 + 2y, for y = 3
4(3)2 + 2(3)
Substitute 3 for y.
4(9) + 2(3)
Evaluate the power.
36 + 6
42
Holt CA Course 1
Multiply.
Add.
1-5
Evaluating Algebraic Expressions
Teacher Example 4: 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
Student Practice 4:
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
1.5 Warm-Up
1. 4x2 + 3x for x = 6
2.
3. The expression 7d gives the number of
days in d weeks. Evaluate 7d for d = 12.
How many days are in 12 weeks?
Holt CA Course 1