Transcript 1-7 - My CCSD

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
andWords
Algebraic
1-7
1-8 Variables
Translate
intoExpressions
Math
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
1-7 Variables and Algebraic Expressions
Warm Up
Evaluate each algebraic expression for the
given value of the variables.
1. 7x + 4 for x = 6
46
2. 8y – 22 for y = 9
50
3. 12x + 8 for x = 7 and y = 4
86
4. y + 3z for y = 5 and z = 6
23
y
Course 2
1-7 Variables and Algebraic Expressions
Problem of the Day
A farmer sent his two children out to
count the number of ducks and cows in
the field. Jean counted 50 heads. Charles
counted 154 legs. How many of each kind
were counted?
23 ducks and 27 cows
Course 2
1-7 Variables and Algebraic Expressions
Learn to translate words into numbers,
variables, and operations.
Course 2
1-7 Variables and Algebraic Expressions
Although they are closely related, a Great
Dane weighs about 40 times as much as a
Chihuahua. An expression for the weight of
the Great Dane could be 40c, where c is the
weight of the Chihuahua.
When solving real-world problems, you will need
to translate words, or verbal expressions, into
algebraic expressions.
Course 2
1-7 Variables and Algebraic Expressions
Operation
•
•
•
•
•
Verbal Expressions
Algebraic
Expressions
add 3 to a number
a number plus 3
the sum of a number and 3
3 more than a number
a number increased by 3
n+3
• subtract 12 from a number
• a number minus 12
• the difference of a number
and 12
• 12 less than a number
• a number decreased by 12
• take away 12 from a number
• a number less than 12
Course 2
x – 12
1-7 Variables and Algebraic Expressions
Operation
Verbal Expressions
Algebraic
Expressions
• 2 times a number
• 2 multiplied by a number
2m or 2 • m
• the product of 2 and a
number
• 6 divided into a number
÷
Course 2
• a number divided by 6
• the quotient of a number
and 6
a ÷ 6 or
a
6
1-7 Variables and Algebraic Expressions
Additional Example 1: Translating Verbal
Expressions into Algebraic Expressions
Write each phrase as an algebraic expression.
A. the quotient of a number and 4
quotient means “divide”
n
4
B. w increased by 5
increased by means “add”
w+5
Course 2
1-7 Variables and Algebraic Expressions
Additional Example 1: Translating Verbal
Expressions into Algebraic Expressions
Write each phrase as an algebraic expression.
C. the difference of 3 times a number and 7
the difference of 3 times a number and 7
3•x
–7
3x – 7
D. the quotient of 4 and a number, increased by 10
the quotient of 4 and a number, increased by 10
4 + 10
n
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 1
Write each phrase as an algebraic expression.
A. a number decreased by 10
decreased means “subtract”
n – 10
B. r plus 20
plus means “add”
r + 20
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 1
Write each phrase as an algebraic expression.
C. the product of a number and 5
the product of a number and 5
n
•5
5n
D. 4 times the difference of y and 8
4 times the difference of y and 8
y
4•
4(y – 8)
Course 2
– 8
1-7 Variables and Algebraic Expressions
When solving real-world problems, you may
need to determine the action to know which
operation to use.
Action
Course 2
Operation
Put parts together
Add
Put equal parts together
Multiply
Find how much more
Subtract
Separate into equal parts
Divide
1-7 Variables and Algebraic Expressions
Additional Example 2A: Translating Real-World
Problems into Algebraic Expressions
Mr. Campbell drives at 55 mi/h. Write an
algebraic expression for how far he can drive
in h hours.
You need to put equal parts together. This
involves multiplication.
55mi/h · h hours
Course 2
=
55h miles
1-7 Variables and Algebraic Expressions
Additional Example 2B: Translating Real-World
Problems into Algebraic Expressions
On a history test Maritza scored 50 points on the
essay. Besides the essay, each short-answer
question was worth 2 points. Write an
expression for her total points if she answered q
short-answer questions correctly.
The total points include 2 points for each shortanswer question.
Multiply to put equal parts together.
2q
In addition to the points for short-answer questions,
the total points included 50 points on the essay.
Add to put the parts together: 50 + 2q
Course 2
1-7 Variables and Algebraic Expressions
Check It Out: Example 2A
Julie Ann works on an assembly line building
computers. She can assemble 8 units an hour.
Write an expression for the number of units
she can produce in h hours.
You need to put equal parts together. This
involves multiplication.
8 units/h · h hours
Course 2
=
8h
1-7 Variables and Algebraic Expressions
Check It Out: Example 2B
At her job Julie Ann is paid $8 per hour. In
addition, she is paid $2 for each unit she
produces. Write an expression for her total
hourly income if she produces u units per
hour.
Her total wage includes $2 for each unit produced.
Multiply to put equal parts together.
2u
In addition the pay per unit, her total income
includes $8 per hour.
Add to put the parts together: 2u + 8.
Course 2
1-7 Variables and Algebraic Expressions
Lesson Quiz
Write each phrase as an algebraic expression.
1. 18 less than an number x – 18
2. the quotient of a number and 21
x
21
3. 8 times the sum of x and 15 8(x + 15)
4. 7 less than the product of a number and 5 5n – 7
5. The county fair charges an admission of $6
and then charges $2 for each ride. Write an
algebraic expression to represent the total
cost after r rides at the fair. 6 + 2r
Course 2