Multiplication Properties
Which Property of Multiplication is shown:
4 x 8 = 8 x 4
a) Associative Property
b) Distributive Property
c) Commuting Property
c) Commutative Property
Which Property of Multiplication is shown:
(2 x 3) x 4 = 2 x (3 x 4)
a) Associative Property
b) Distributive Property
c) Commuting Property
a) Associative Property
Egypt has 9 boxes of chocolates. Each box contains 5 chocolates. How many chocolates does she have? Explain your strategy.
Make 9 groups of 5 chocolates:
O O O O O O O O O O
O O O O O O O O O O
O O O O O O O O O O
O O O O O O O O O O
O O O O O
9 groups x 5 chocolates = 45 chocolates
OR
Skip count by 5, 9 times:
5, 10, 15, 20, 25, 30, 35, 40, 45
9 x 5 = 45 chocolates
What is the pattern for all multiples of 10?
All multiples of 10 end in 0 (zero).
Any number times 10 equals that same number moved to the next place value with a 0 (zero) added to the ones place.
Which Property of Multiplication is shown:
8 x 4 = (2 x 4) + (6 x 4)
a) Associative Property
b) Distributive Property
c) Commuting Property
b) Distributive Property
What missing factor makes the equation true?
(4 x 3) + ( ___ x 3) = 7 x 3
Which Property of Multiplication is shown above?
(4 x 3) + (3 x 3) = 7 x 3
Distributive Property
Aicha has 6 flowerpots that each hold 8 roses. Kadidia has 8 flowerpots that each hold 6 roses. Who has more roses?
What Property of Multiplication is used?
They both have 48 roses.
6 x 8 = 8 x 6
48 = 48
The Commutative Property of Multiplication is being used.
5 x 8 = 40
Identify which numbers are the factors and which are the product.
5 and 8 are the factors. Factors are the numbers you multiply.
40 is the product. A product is what you get when you multiply two or more factors.
How can you rewrite the expression so that the product remains the same?
(6 x 4) x 3
Any of the following ways:
6 x (4 x 3)
(6 x 3) x 4
6 x (3 x 4)
(4 x 6) x 3
4 x (6 x 3)
(4 x 3) x 6
4 x (3 x 6)
3 x (4 x 6)
(3 x 4) x 6
(3 x 6 ) x 4
3 x (6 x 4)
Tyrone broke up a large array into a 4 x 7 array and a 5 x 7 array. What was the large array?
9 x 7
Saxton attends a bookfair that has 3 displays on each of its 4 walls. Each display holds 2 books. How many books are on display?
(3 x 4) x 2 = 24 books
3 x (4 x 2) = 24 books
Draw it:
Wall1 Wall2 Wall 3 Wall4
O O O O O O O O Display 1
O O O O O O O O Display 2
O O O O O O O O Display 3
Draw a bar diagram to solve 63 divided by 9.
63 divided by 9 equals 7.
63 is the product.
There are 9 groups.
Each group contains 7 objects.
Amir broke his ball of slime into the following array:
O O O O O
O O O O O
O O O O O
Using the Distributive Property, what two facts could he use to write an equation for the array?
Any of the following:
(1 x 5) + (2 x 5) = 15
(3 x 1) + (3 x 4) = 15
(3 x 2) + (3 x 3) = 15
Jayla arranged her buttons in an array:
O O O O O O
O O O O O O
O O O O O O
O O O O O O
O O O O O O
If she uses doubles and the Distributive Property, what two expressions must she use to find the total number of buttons?
(5 x 3) + (5 x 3)
Leah uses 2 buckets of paint for each of her paintings. She is painting 5 pictures for each of the 4 walls in her room. How many buckets of paint will she need?
40 buckets of paint
(2 x 5) x 4 = 40
2 x (5 x 4) = 40
If you drew an array for 7 x 8, how many columns would you draw? How many rows?
7 rows, 8 columns
In a multiplication expression, the first factor represents the rows, and the second factor represents the columns.
If (2 x 4) is doubled, and then doubled again, what equation can be written to represent this?
(2 x 4) + (2 x 4) + (2 x 4) + (2 x 4) = 32
OR
2 x (2 x 4) + 2 x (2 x 4) = 32
OR
4 x (2 x 4) = 32
Markees says that a 10s fact, like 3 x 10, can be broken into two 5s facts. Is he correct? If so, write an equation to prove it.
1 x 10 = (1 x 5) + (1 x 5)
2 x 10 = (2 x 5) + (2 x 5)
3 x 10 = (3 x 5) + (3 x 5)
4 x 10 = (4 x 5) + (4 x 5)
5 x 10 = (5 x 5) + (5 x 5)
...and the pattern continues!
Movie Tickets Prices
Adults: $8
Students: $4
How much would of family of 2 adults and 4 children pay for the movies?
Adults + Students = Cost
(2 x 8) + (4 x 4) =
16 + 16 = 32
The family would spend $32.
Can an array with 3 rows and 9 columns be broken apart using doubles?
O O O O O O O O O
O O O O O O O O O
O O O O O O O O O
No because both factors, 3 and 9, are odd, meaning neither factor can be evenly broken.
3 x 9 = 27
27 is an odd number, meaning it cannot be broken into 2 even groups.
Only even products (multiples of 2) can be broken into 2 equal groups.