Transcript Simplifying Algebraic Expressions

Simplifying Algebraic Expressions
What we can and can’t do……
Vocabulary
Term: Parts of an algebraic expression separated by + or Coefficient: The numerical factor of a term; the number with the variable
Constant: A term without a variable
Like terms: Terms that have the same variable
three terms
3x + 7 + x
like terms
7 is the constant
because it has no
variable.
Terms….there are 3
4n + 2n + 9
Constant….no variable
Like terms….same variable
Like terms can be combined. 4n + 2n + 9 =
6n + 9
Simplifying Algebraic Expressions
To simplify an algebraic expression, you may have to use
properties to arrange the terms to make them easier
to work with……..you may just do what you CAN…….
3 + 3 = 2(3) = 6
x + x = 2x
Simplify the expression 4(6x)
4(6x) = (4·6)x
= 24x
Parentheses mean multiplication
Associative Property
Let’s try some…..include the steps!
1x + 1x + 1x **
(3 · x) · 11
x + x + x = 3x 7x + 8 + x
7x + x + 8 commutative
(x · 3) · 11 Commutative
x · (3 · 11) Associative
Combine like (7x + x) + 8
33x or x33 **
terms
8x + 8
Three friends will pay $x each for admission to the museum, plus
$1 each to view the mummy exhibit. A fourth friends will pay
admission but will NOT view the mummy exhibit. The expression
that models this is given. Use the distributive and commutative
properties to simplify the expression.
3(x + 1) + x
3x + 3 + x
commutative 3x + x + 3
4x + 3 combine like terms
distributive
Circle the coefficients
Expression
Number
of terms
2
none
3
8b, 2b
5x + 7
8b + 9 - 2b
4(5)x
7p + 2p + p + 18
9r + 6s + 5s + 12
Like terms?
List them
1
4
4
7
6s 5s
8b – 2b + 9 = 6b + 9
none
1p
Simplified by Combining Like Terms
5x + 7
9
none
7p 2p
Constant
20x
18
10p + 18
12
9r + 11s + 12
Writing Expressions
forMarket
Word Problems
The Farmer’s
The Farmer’s market sells fruit baskets. Each basket has 3 apples and 1 pear. Use “a” to
represent the cost of each apple and “p” to represent the cost of each pear. Write
and simplify an expression that represents the total cost of 5 baskets.
3a + p in one basket, so…..
5(3a + p) in 5 baskets
15a + 5p would represent the cost
of 5 baskets.
Application: Word Problems
Myka’s Gift Bags
Myka is making eight gift bags. In each bag she will put
5 bottles of nail polish and 2 tubes of lip gloss.
Write an expression for one bag.
(5p + 2g)
Write an expression for 8 bags.
8(5p + 2g)
Evaluate for the total of all bags.
40p + 16g
Today, six friends went to the museum. All paid admission, but only
four of them viewed the mummy exhibit.
Write an expression using parentheses. Simplify with the distributive
and commutative properties. Combine like terms.
Where did these
values come from??
combine like terms
4(x + 1) + 2x
4x + 4 + 2x
distributive
4x + 2x + 4
commutative
6x + 4
Matching Expressions to Stories
Four friends went to the museum. Two
of the friends watched the video tour. The other two did not.
The cost of admission was $ X. The video tour was an
additional $2. Find the expression.
Four friends went to a local amusement park. Three of the friends
bought ride tickets for x dollars, plus a game pass for $2. The
other friend bought just a ride ticket. Write and simplify an
expression showing the amount of total money spent.
Three people had pizza for lunch. Two more students had pizza
and salads. Let x represent the pizza, and s represent the salad.
3(x + 2) + x
3x + 2(x + s)
2(x + 2) + 2x
Challenge
Numerical: 3 + 3 + 4 = 2(3) + 4 = 6 + 4 = 10
Algebraic: x + x + y = 2x + y
This is ALL we can do!!!!!
Simplifying
(14y + x) + 22y
Commutative
= (x + 14y) + 22y
Associative
= x + (14y + 22y)
Combine like terms
Simplifying
Distribute:
4(2x + y)
= 8x + 4y
= x + 36y
Start by distributing the 4.
No like terms, so we have finished!
Factor and Simplify
Factor:
27x + 18y
9(3)x + 9(2) y
9( 3x + 2 y )
3x + 9y + 2x
3x + 2x + 9y
5x + 9y
7(3x + y)
12x + 8y
21x + 7y
4(3)x + 4(2)y
4(3x + 2y)
What did we accomplish?
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We continued working with algebraic expressions.
We identified parts of the expressions.
We simplified using properties.
We wrote expressions for word problems.
We matched problems with the expression that would
“tell the story” of the problem.