Transcript Evaluating Expressions and Combining Like Terms

Evaluating Expressions
and Combining Like
Terms
R. Portteus
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 divided by Division
x
5 + x (same as x + 5 plus x
Addition
5
,5  x
x
5)
5–x
5 minus x
subtraction
Evaluate a Variable
Expression
• 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:
n + 3 = 4 + 3 Substitute 4 for n. Simplify
=7
b. n – 3
n – 3 = 4 – 3 Substitute 4 for n. Simplify
Solution:
=1
Evaluate an Algebraic
Expression
• Example 2: Evaluate each expression if x =
8.
Substitute 8 for x. Simplify
a. 5x
Using parenthesis is the preferred method to show
Solution:
5x = 5(8)
multiplication. Additional ways to show multiplication are
5 · 8 and 5 x 8.
= 40
Substitute 8 for x. Simplify
b. x ÷ 4
Solution:
x÷4=8÷4
x
8

that division problems are also
4
4
= 2 Recall
fractions – this problem could be
written as:
 2;
because
x4 
x
4
Evaluating More
Expressions
• 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,
3. a + b + c
and c = 3 into the problem, then add.
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
4. ba
into the problem, then multiply.
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
5. b - c
into the problem, then subtract.
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
Combining Like Terms
• Now that we have seen some algebraic
expressions, we need to know how to
simplify them.
• Vocabulary
– Like terms: In an expression, like terms are the
terms that have the same variables, raised to
the same powers (same exponents).
• i.e. 4x and -3x or 2y2 and –y2
– Coefficient: A constant that multiplies a
variable.
• i.e. the 3 in 3a or the -1 in –b
Combining Like Terms
• In algebra we often get very long
expressions, which we need to make
simpler. Simpler expressions are
easier to solve!
• To simplify an expression we collect
like terms. Like terms include letters
that are the same and numbers.
Let’s try one…
•
•
•
•
•
Step One: Write the expression.
4x + 5x -2 - 2x + 7
Collect all the terms together which are alike. Remember that
each term comes with an operation (+,-) which goes before it.
4x, 5x, and -2x
-2 and 7
Simplify the variable terms.
4x+5x-2x = 9x-2x = 7x
Simplify the constant (number) terms.
-2+7 = 5
You have a simplified expression by writing all of the results from
simplifying.
7x + 5
Another example…
• 10x – 4y + 3x2 + 2x – 2y
3x2
Remember you cannot
10x, 2x
combine terms with
the same variable but
different exponents.
-4y – 2y
• 3x2 + 12x – 6y
Now you try…
Simplify the following:
• 5x + 3y - 6x + 4y + 3z
• 3b - 3a - 5c + 4b
• 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
• 5xy – 2yx + 7y + 3x – 4xy + 2x
A
A
A
A
You Try #1
• Simplify the following:
1. 5x + 3y - 6x + 4y + 3z
5x, -6x
3y, 4y
3z
-x + 7y + 3z
You Try #2
• Simplify the following:
2. 3b - 3a - 5c + 4b
3b, 4b
-3a
-5c
-3a + 7b – 5c
You Try #3
• Simplify the following:
3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
4ab, -ab
-2a2b, 2a2b
5, 4
ab2
3ab + ab2 + 9
You Try #4
• Simplify the following:
4. 5xy – 2yx + 7y + 3x – 4xy + 2x
5xy, -2yx, -4xy
7y
3x, 2x
-xy + 7y + 5x
Conclusion
• A variable or algebraic expression is an
expression that consists of one or more
numbers
variables
________
and _________
along with one
arithmetic
operations
or more ________
_________.
(Note: No
equal
_______
sign)
• To evaluate an expression write the
expression
_________,
substitute a _______
for
number
simplify
each variable, and _________
the result.
Conclusion Continued…
• In an expression, __________
are
like terms
the terms that have the same
variables
________,
raised to the same
power
________
(same exponents).
• A coefficient is a number that
multiplies
________
a variable.