Distributive Property
What is the distributive property?
It allows you to decompose one factor. Then you can use smaller known facts to find products (the answer to multiplication facts).
What does the associative property state?
The order in which you group factors does not change the product
Todd bought 4 stickers. Jim bought twice as many stickers as Todd. If Todd and Jim combine their stickers, how many stickers do they have altogether?
12
Lola is making chex mix. She buys 2 bags of peanuts, 4 bags of M&Ms, and 5 bags of pretzels. Write an equation that would show the amount of bags used to create the chex mix.
2 + 4 + 5 = 11
What is another name for an equation? AND do expressions or equations have an equal sign?
Number sentence and equations
Use the distributive property to solve the following problem:
8 x 12 =
Answers vary...
(8 x 6) + (8 x 6) = 96
(8 x 5) + (8 x 7) = 96
Based on the associative property of multiplication, do these two expressions have the same product?
2 x (5 x 2)
(2 x 5) x 2
Yes
Mary picked 3 buckets of strawberries at the strawberry patch. Olivia picked 9 times as many buckets as Mary. How many buckets did Olivia fill?
27
Sam collected cans for the food drive at his school. He collected 24 cans Monday, 44 cans Tuesday, and 67 cans Friday. How many cans did he collect altogether?
135 cans
Write an expression:
Eight boxes with four books in each box
8 x 4
Use the distributive property to solve the following problem:
9 x 9
Answers vary...
(9 x 5) + (9 x 4) = 81
(9 x 6) + (9 x 3) = 81
Based on the associative property of multiplication, do these two expressions have the same product?
3 x (3 x 3)
(3 x 3) x 2
No
Grandma picks five times as many apples as pears. What is the difference in the number of apples and pears picked if she picks 6 pears.
5 x 6 = 30
30 - 6 =
24
A bus had 20 passengers. At a stop five more people got on and six got off. How many people are on the bus now?
20 + 5 - 6 = 19
19 people
Evaluate each expression if a = 3 and b = 5
13 + a - b
11
Use the distributive property to solve the following problem:
7 x 13
Answers vary:
(7 x 7) + (7 x 6) = 91
(7 x 5) + (7 x 8) = 91
Solve:
5 x (3 x 4)
60
Jenny is making a fruit salad. He bought 5 bags with 3 apples in each bag. He bought 6 bags with 3 bananas. Write an equation that represents this problem and solve.
(5 x 3) + (6 x 3) = 33
Midan has 50 books. He keeps 10 books for himself and divides the rest equally among his friends. If each friend gets 4 books, how many friends did he give books to?
(50 - 10) ÷ 10 = 4
10 friends
Evaluate each expression if a = 3 and b = 5
(a x 4) ÷ 3
4
Use the distributive property to solve the following problem:
12 x 15
Answers vary..
(12 x 7) + (12 x 8) = 180
Solve:
4 x (6 x 6) =
144
Four friends each have a pet. Each of their pets are different animals. Nicholas has a dog, Fernandez has a cat, and Julio has a lizard. What is a possible animal that Joe has?
Anything but a dog, cat, and lizard
Lila bought some toys from the store. She bought 3 toys for $4 and 6 toys for $4. How much money did she spend on toys altogether?
$36
7 people equally divide 35 cookies
35 ÷ 7