Transcript Combine Like Terms

December 7-11, 2015
Complete the
following
questions.
 1. The King has 7 more crowns than the Queen. The
queen has k crowns. Write the expression that shows
how many crowns king has.
 2. Moore has 20 songs. His friend bought him M more
songs. Write an expression that shows how many songs
Moore has now.
 3. There were Y whales in the sea and 15 more whales
came to the sea. Write an expression that shows how
many whales are in the sea.
Complete the
following
questions.
4. George earned 80 points in the subjects.
Bruno earned B fewer points than George.
Write an expression that shows how many
extra points Bruno earned.
5. Karen has h pens. Helen has 25 more
pens than Karen. Write an expression for
how many pens Helen has.
Find the value
of each power
120
132
(2/7)3
0.42
(4/9)1
0.73
Evaluate the
expression for
the given value
2(x2-9) ; x=9
w + y2 + 3w; w= 2, y=6
Generating equivalent expressions
What does the word equivalent mean?
What is an algebraic expression?
What is a numerical expression?
Get out your INB.
INB
Title:
Distributive
Property
Write these examples down in
your INB.
5(3 + x) = 15 + 5x
3(2x + 9) = 6x + 27
is 5(2 + 4x) equivalent to 10 + 8x?
Are they
equivalent
Is 3(x + 6) equivalent to 4x + 12?
Every Saturday, Matt takes his brother
Sam to the movie theater. The cost of
tickets (t) is $6.00 each and they always
split a bag of popcorn (p) that costs $3.50.
•
Warm Up
Write an expression to show how much the
brothers will spend over a 4 week period.
What is the total amount Matt and Sam
have spent by the end of the 4 weeks? Use
words, numbers, and/or pictures to show
your work. Write your answer(s) on the
paper provided.
Warm Up
EVALUATE.
2
3x + 4x – 3 when x = 2
5y + 65 when y = 5
5(p+1) when p = 2
1 + 2(3 + x) when x =8
Let’s go over the quiz!!!
Distributive
Property
4(x+3)
12(4x - 2)
3(x3 – 4)
2(3x5 + 2)
4(5x2 + 3y -7)
9(2x + x + 5y)
When you are
done with your
quiz, copy this
into your INB.
Title: Like
Terms
 LIKE TERMS: terms with the same variable(s)
raised to the same power(s)
 Example: 3x2 and 5x2 are like terms. They
have the same variable of x and they are
both squared (raised to the second power).
 You can combine like terms.
 Example: 6x – 4x = 2x
 Example: 9y2 + 6y2= 15y2
 You keep the same variable and the same
exponent. You add or subtract the
coefficient.
 6x and 7y are not like terms! They have
different variables! You cannot combine
unlike terms.
3x2 + 9y + 10y – 4
Combining
Like Terms
How many terms are in this expression?
Are any of the terms considered like
terms?
So let’s simplify this expression.
Now how many terms are there?
Combine Like
Terms
6x2 + 5x2 + 4y – 2y + 9 + 6
9x5 – 5x5 + 5z + 4 – 1
8m + 14 – 12 + 4n
5x + 3y + 6z + 2x + y + 3z
Turn in your
book to page
280
Do YOUR TURN at
the top of page 80
Warm
Up
INB
Combine Like Terms
12 + 35y + 3y – 4
22x + 9x + 3y + 90y – z
2
2
4(2x + 10) + 3x + 5
½(4x + 6) + 3
Answers to
your
homework
Page 280
15. 2x4
16. 37y
17. 13b – 10
18. 5x + 4
19. 4y + 10
20. 6a2 + 16
21. 15y2 – 6
22. 4z3 + 5z2 + z
23. 0.5x4 + 10.5
24. 4 + p
Algebra Tiles
We are going to use algebra tiles to
represent expressions and to
combine like terms.
Let’s create
these
expressions
using algebra
tiles.
3x – 5
2x + 3
4x + 5
2
x + 4x – 3
2
2x + 2x – 4
Combine Like
Terms using
Algebra Tiles
2
2x
2
x
+ + 4x – 3
2
2x + x + 3x + 5 – 2
Commutative Property
of Addition
Properties
When adding, changing
the order of the numbers
does not change the
sum.
3 + 4 = 4 + 3
Commutative Property
of Multiplication
Properties
When multiplying,
changing the order of the
numbers does not
change the product.
2 x 4 = 4 x 2
Associative Property of
Addition
Properties
When adding more than
two numbers, the grouping
of the numbers does not
change.
(3 + 4) + 5 = 3 + (4 + 5)
Associative Property of
Multiplication
Properties
When multiplying more
than two numbers, the
grouping of the numbers
does not change the
product.
(2 x 4) x 5 = 2 x (4 x 5)
Properties
Distributive Property
You tell me. What is this?
Identity Property of
Addition
Properties
Adding zero to a number
does not change its
value.
9 + 0 = 9
Identity Property of
Multiplication
Properties
Multiplying a number by
one does not change its
value
1 x 7 = 7
For each
expression, use
a property to
write an
equivalent
expression. Tell
which property
you used.
(ab)c =
______________________________
3y + 4y =
______________________________
6x7 =
______________________________
Use the
properties to
determine if
the
expressions
are equivalent.
3(x – 2) and 3x – 6
Which property did you
use to answer figure this
out?
Use the
properties to
determine if
the
expressions
are equivalent.
6x – 8 and 2(3x – 5)
Which property did you
use to answer figure this
out?
Homework: Page
280-281 #1-14 ALL
You may begin
working quietly.
Use one of the properties of operations to
write an expression that is equivalent to 4+m.
Tell which property you used.
ELT: Do
in your
INB
Use the properties of operations to determine
if the expressions are equivalent.
3 + y and ⅓(6 + y)
4(y – 3) and 4y – 12
Combine like terms.
9y2 – 6y2
5c + 4(d + 6c)
x + 10y – 4y + 4x
Use the
Distributive
Property to
evaluate.
Combine like
terms if
necessary.
4(2x + 3y + 9)
2(12x + 22x + 10y)
22x + 33y
12x + 24x
45x + 35y + 30
Number of Eggs
12
24
36
n
Number of
Cartons
1
2
3
?
An egg company puts 12 eggs into each
carton. How many cartons will the
company need for n eggs?
a.12n
b.n ÷ 12
c. n + 12
d.12 - n
Zachary had 5 piano lessons one
month and 4 lessons the next
month. He pays $15 for a lesson.
One way to find the total he paid is
15(5 + 4). Which other expression
could Zachary use?
A. 15 x 5 + 4
B. 15 x 5 x 4
C. (15 + 5) x (15 + 4)
D. (15 x 5) + (15 x 4)
Write this
problem in
you INB
Which expressions is the same
as 3(6 – 2)?
A. 3 – 6 + 3 – 2
B. 3 x 6 – 3 x 2
C. 3 + 6 – 3 x 2
D. 3 x 6 + 3 x 2
Write this
problem in
you INB
Which expression is
equivalent to 7y?
A. 3y + 4y
B. 3y + 5y
C. 7y + y
D. 7 + y
Work on page 283284 in your
textbook.
When everyone is
finished, we will go
over the answers.
Review
for your
test!
In order to review for your
test, complete pages 285287 and pages 289 – 290 in
your textbook.
NEXT THURSDAY! TEST
DAY AND INB DUE!!!