Day 1
The _____ is the greatest common factor that two or more numbers share.
12: 1, 2, 3, 4, 6, 12
21: 1, 3, 7, 21
GCF
Use the ladder method to find the GCF of 18 and 36.
GCF = 18
Use the ladder method to find the GCF and LCM of 36 and 27.
Hint:36 is even and 27 is odd. For your prime factor, 2 will not work so try 3.
GCF = 9, LCM = 108
Use the ladder method to find the GCF and LCM
of 28 and 56.
Hint: Both 28 and 56 are even, therefore both numbers are divisible by 2.
GCF = 28, LCM = 56
What is the GCF of 24 and 32?
What is the LCM of 24 and 32?
GCF = 8, LCM = 96
The ___________ is the least common multiple that two or more numbers share.
2: 2, 4, 6, 8
3: 3, 6, 9
LCM
Use the ladder method to find the LCM of 18 and 36.
LCM = 36
Rewrite the expression using the GCF and the distributive property.
36 + 27 = ____(___ + ___)
GCF
36 + 27 = 9(4 + 3)
Rewrite the expression using the GCF and the distributive property.
28 + 56 = ____(___ + ___)
GCF
28 + 56 = 28(1 + 2)
Factor 24 + 32. Write your answer in the form
a(b + c) where a is the GCF of 24 and 32.
Hint: 24 + 32 = ____(____ + _____)
GCF
24 + 32 = 8(3 + 4)
The d_____________ property is demonstrated below.
a(b + c) = ab + ac
2(3x + 5) = 6x + 10
The Distributive Property
Rewrite the expression using the GCF and the distributive property.
18 + 36 = ____ (____ + ____)
GCF
18 + 36 = 18(1 + 2)
Bowie has 12 cans of regular soda and 15 cans of diet soda. She wants to make identical refreshment tables that will operate during the football game with no sodas left over. What is the greatest number of refreshment tables that Bowie can make?
Hint: Use GCF or LCM
GCF = 3
She can make 3 refreshment tables.
Which expression shows ways to factor 28 + 56?
a) 14(2 + 1)
b) 28(1 + 2)
c) 7(6 + 8)
d) 2(14 + 23)
Which expression shows ways to factor 28 + 56?
a) 14(2 + 1)
b) 28(1 + 2)
c) 7(6 + 8)
d) 2(14 + 23)
What is the GCF of 35 and 60?
What is the LCM of 35 and 60?
Hint: 35 and 60 are both divisible by 5.
GCF = 5, LCM = 420
2, 3, 5, 7, 11 are the first five ___________ numbers because each number has only 2 factors.
Prime
Which expression shows ways to factor 15x + 25?
Hint: Check each choice.
a) 3(5x + 8)
b) 5(3x + 5)
c) 5(2x + 5)
d) 3(6x + 8)
Which expression shows ways to factor 15 + 25?
a) 3(5x + 8)
b) 5(3x + 5)
c) 5(2x + 5)
d) 3(6x + 8)
Bowie is making gift bags using 30 candy bars and 15 lollipops. She wants each bag to be identical, with no candy bars or lollipops left over. What is the greatest number of gift bags she can make?
Hint: Use GCF or LCM
GCF = 15
She can make 15 gift bags.
Bowie is buying flowers for her garden. She wants to buy the same number of tulips and the same number of daisies. If tulips come in packs of 10 and daisies come in packs of 5, what is the least number of each type of flower Bowie will need to buy?
Hint: Use GCF or LCM
LCM = 10
She will need to buy 10 tulips and 10 daisies.
Factor 35 + 60. Write your answer in the form
a(b + c) where a is the GCF of 35 and 60.
Hint: 35 + 60 = ____(___ + ___)
GCF
35 + 60 = 5(7 + 12)
Use the ladder method to find the GCF and LCM of 18 and 24.
Hint: 18 and 24 are even numbers, therefore each number is divisible by 2.
GCF = 6
LCM = 72
Bowie and her friends made dinner reservations at two restaurants on two different days. The first restaurant sat all the friends in groups of 8, and the second sat the friends in groups of 4. What is the smallest number of people that could be in the group?
Hint: Use GCF or LCM.
LCM = 8
8 people
Select three expressions that are equivalent to 14x + 7y
Hint: Distribute. Combine like terms.
a) 12(x + 7y)
b) 7(2x + y)
c) 2(7x + 2y)
d) 7x + 7x + 3y + 4y
e) 7x + 3y + 4y +7x
Select three expressions that are equivalent to 14x + 7y
Hint: Distribute. Combine like terms.
a) 12(x + 7y)
b) 7(2x + y)
c) 2(7x + 2y)
d) 7x + 7x + 3y + 4y
e) 7x + 3y + 4y + 7x
Select three expressions that are equivalent to
10x + 6y.
Hint: Distribute. Combine like terms.
a) 10(x + 6y)
b) 2(5x + 3y)
c) 3x + 3x + 5y + 5y
d) 5x + 5x + 3y + 3y
e) 5x + 3y + 5x + 3y
Select three expressions that are equivalent to 10x + 6y.
Hint: Distribute. Combine like terms.
a) 10(x + 6y)
b) 2(5x + 3y)
c) 3x + 3x + 5y + 5y
d) 5x + 5x + 3y + 3y
e) 5x + 3y + 5x + 3y
Which expression shows ways to factor 12 + 18?
Hint: Check each choice.
a) 2(6 + 8)
b) 6(2 + 4)
c) 2(6 + 7)
d) 6(2 + 3)
Which expression shows ways to factor 12 + 18?
a) 2(6 + 8)
b) 6(2 + 4)
c) 2(6 + 7)
d) 6(2 + 3)