Transcript Evaluating Expressions and Combining Like Terms

Evaluating Expressions
R. Portteus
Order of Operations Review
How do you follow the order of
operations?
Order of Operations
1.
2.
3.
4.
( )
Exponents Ex. 3² = 3 x 3 = 9
x or ÷, from Left to Right
+ or ─, from Left to Right
Order of Operations Review
20 ÷ 4 x 23 + (5 - 8) =
A. 43
C. 1
B. 27
D. 37
20 ÷ 4 x 23 + (5 - 8) =
A. 43
B. 27
C. 1
D.37
20 ÷ 4 x 23 + (5 - 8) =
20 ÷ 4 x 23 + (-3) =
20 ÷ 4 x 8 + (-3) =
5 x 8
+ (-3) =
40
+
-3 = 37
Evaluating Expressions
• Vocabulary:
– Variable – A symbol, usually a letter of the
alphabet, such as the letter n, that is used to
represent a number.
– Variable expression (A.K.A. - Algebraic
Expression) – An expression, such as n – 5, that
consists of one or more numbers and variables
along with one or more arithmetic operations.
(Note: No equal sign)
– Evaluate a Variable Expression – write the
expression, substitute a number for each
variable, and simplify the result.
How do you describe a
variable expression?
Variable
Expression
Meaning
Operation
5x, 5·x, (5)(x)
(same as x·5)
5 times x
Multiplication
5
,5  x
x
5 divided by x Division
5 + x (same as x + 5) 5 plus x
Addition
5–x
subtraction
5 minus x
Journal Reflection
• Evaluate Expressions Video
• Write your reflection from the video.
Journal Reflection
• Let’s watch a short video
Write your reflection from the video.
How do we evaluate expressions for
each math operation, + - x ÷ ?
Evaluate a Variable Expression
with each operation
• Example 1: Evaluate each expression when
n = 4.
Simplify (means to solve the problem or perform as
many of the indicated operations as possible.)
a. n + 3
Solution:
Substitute 4 for n. Simplify
n+3=
4+3=7
b. n – 3
Substitute 4 for n. Simplify
n–3=
Solution:
4–3=1
Evaluate an Algebraic
Expression
• Example 2: Evaluate each expression if x = 8.
a. 5x
Substitute 8 for x. Simplify
5x = 5(8)
Using parenthesis is the preferred method to show
Solution:
= 40
multiplication. Additional ways to show multiplication are
5 · 8 and 5 x 8.
b. x ÷ 4
x ÷ 4 = 8 ÷ 4 Substitute 8 for x. Simplify
Solution:
=2
x
8
Recall that division problems are also
fractions – this problem could be
written as:
4

4
 2;
b eca u se
x
x4 
4
Let’s go to the next level!
What if an expression has more than
one variable?
How do I evaluate expressions with
more than one variable?
Evaluating Expressions with
more than one variable
• Example 3: Evaluate each expression if
x = 4, y = 6, and z = 24.
Substitute 4 for x; 6 for y. simplify
a. 5xy
Solution:
5xy = 5(4)(6)
= 120
Substitute 24 for z; 6 for y. Simplify.
b. z
y
Solution:
z
24

y
6
=4
Now You Try…
Evaluate each expression given that
a = 6, b = 12, and c = 3.
1.
2.
3.
4.
5.
6.
4ac
a÷c
a+b+c
ba
b–c
c÷b
A
A
A
A
A
A
You Try #1
Evaluate each expression given that
a = 6, b = 12, and c = 3.
Substitute the value for a = 6 and c = 3
1. 4ac
into the problem and multiply
4ac = 4(6)(3)
= (24)(3)
= 72
Click to return to
“You try it” slide
You Try #2
Evaluate each expression given that
a = 6, b = 12, and c = 3.
Substitute the value for a = 6 and c = 3
2. a ÷ c
into the problem and divide
a÷c=6÷3
=2
Click to return to
“You try it” slide
You Try #3
Evaluate each expression given that
a = 6, b = 12, and c = 3.
Substitute the value for a = 6, b=12,
and c = 3 into the problem, then add.
3. a + b + c
a + b + c = 6 + 12 + 3
= 18 + 3
= 21
Click to return to
“You try it” slide
You Try #4
Evaluate each expression given that
a = 6, b = 12, and c = 3.
Substitute the value for b=12 and a = 6
into the problem, then multiply.
4. ba
ba = (12)(6)
= 72
Click to return to
“You try it” slide
You Try #5
Evaluate each expression given that
a = 6, b = 12, and c = 3.
Substitute the value for b=12 and a = 3
into the problem, then subtract.
5. b - c
b – c = 12 – 3
=9
Click to return to
“You try it” slide
You Try #6
Evaluate each expression given that
a = 6, b = 12, and c = 3.
Substitute the value for c=3 and b = 12 into
6. c ÷ b
the problem, then Divide
c 3 Note: It is better to rewrite this division
Divide both
c b  
problem as a fraction.
numerator and
b 12 This fraction can now be reduced to its
denominator by
the GCF = (3) to
simplest form.
reduce this
3 3 1
fraction.

It is OK to have a fraction
12  3 4 as an answer.
Click to return to
“You try it” slide
Summary
To evaluate expressions:
1. Replace a variable with a number
2. Follow order of operations to find
the solution.
3. Follow the algorithms for integers.
Exit Ticket
5 x 6 = 30
2(8) – 4 =
16 – 4 = 12
3 x 4 = 12
9 x 5 = 45
18/3 + 18 =
6 + 18 = 24
10 ÷ 2 + 10 =
5 + 10 = 15
9(4) – 25 =
36 – 25 = 11
9 x 9 = 81
56/8 – 5 =
7– 5= 2
14 + 3(6) =
14 + 18 = 32
Homework
• Homework Evaluate Expressions 3
Terms Add/Subtract A and B here