Transcript 1.5 Distributive Property

1.5 Distributive
Property
Distributive Property
• What does the word distribute mean?
Deal out, hand out/around, share,
divide up, disperse, spread
• What do you think the distributive
property means to do?
Get rid of the parenthesis, share by
multiplication
DISTRIBUTIVE PROPERTY
DEFINTION:
• If a (b + c), then a (b + c) = ab + ac
Arrow Method:
Box Method:
a ( b + c) =
a ( b + c) =
Examples:
1.
6(x  3) 
2.
2(4  x) 
3.
x(2  y) 
Practice
▫ (4y + 5z) 6
• c ( 2d + 6)
(2r + 3s – 7t) (-4)
–r (- 5 + 11s)
▫ 5 (2x + 1)
▫ (y – 3) (-2)
2 (7 – b – c)
▫ –3 ( 7x + 2)
▫ 3 (x + 7 – 9y)
5 ( -6m + 4n – 11p)
▫ 4 ( 3 – x)
▫ ( x + 6 + 3y)5
• Does the number of items in the parentheses or a
subtraction change the distributive property?
No
more arrows
• More Terms just mean ____________.
4 (x + 2 + y)
5 (6 + 3y + 4x)
4x + 8 + 4y
30 + 15y + 20x
same
addition
• Subtraction is the __________
as ______________
negative
with a ____________
number.
Subtraction Example:
• 12 – 5 = 12 + -5
Distributive Property Example:
3(12 – 5) = 3(12) + 3(-5)
36+ -15=21
Example 1
• Mr. Smith has three apples
and 2 bananas.
3 Apples + 2 Bananas
• He wants to double all the
fruit that he has.
2(3 Apples + 2 Bananas)
• That means he must double
each kind of fruit he has.
2(3 Apples) + 2(2 Bananas)
• How much fruit will Mr.
Smith have?
6 Apples & 4 Bananas (10
total pieces of fruit)
Example 2
• A freshman has 1 binder, 2
pencils, and 3 erasers on the
first day of school.
1 Binder + 2 Pencils + 3 Erasers
• On the next day of school he
needs to triple the number of
supplies.
3(1 Binder + 2 Pencils + 3
Erasers)
• That means the freshman must
triple each type of supply.
3(1 Binder) + 3(2 Pencils) + 3(3
Erasers)
• How many supplies will
freshman have?
3 Binders + 6 Pencils + 9 Erasers
(18 total supplies)
The X Games last 4 days in Los Angeles,
California. There are BMX,
Skateboarding, MOTO, and Rally Car
Events. The expected attendance on each
day for BMX is 12,000 people, for
Skateboarding 15, 000 people and for
both MOTO and Rally Car 25,000 people.
One Day= 12,000+15,000+25,000+25,000
4(12,000+15,000+25,000+25,000)= 308,000
In a typical week, the administrative
assistance spends 10 hours using email,
12 hours meeting people and 6 hours on
the phone. Set up an expression to
determine how many hours the
administrative assistant spends on these
activities after 12 weeks of work.
One week= 10e + 12m + 6p
12(10e + 12m + 6p)=120e + 144m + 72p
What is a like term?
• Any terms that contain the same variables and
the same number of each variable (look at
exponents) are called like terms.
• Numbers by themselves are like terms together
Identify the Like Terms
7x + 3 – 4yx + 2 – 8x
2x - x2 – x + 5
5x2 + 7 – 4y + 6y – x
m3 + m2 + m – 5 + 6m2
What is a coefficient?
• The number multiplied by a variable
Identify the coefficients.
7x + 3
m + 2n2
5x2 + 6y – x
What does it mean to combine like
terms?
• Add or subtract the coefficients of like terms.
Combine Like Terms
15x + 18x + 1
10n + 10n2 + 9n2 - 7
Practice
• 3 (x + 4) + 2
5(x + 3) + 7 (4 + 2x)
• 5(y + 2) + 7y
–9 ( 5r – 3) + 16
• 6(x – 2) – 8
• x (y – 2) + 2x
– 3 (z + y) – 4 (3 + z)
HOMEWORK
• Pg. 30 20-28 EVEN, 37-38, 39-41