Word Problems
40 miles each month x 5 months = 200 miles
2 x 50 =
2 x 5 = 10, so 2 x 50 = 100
Which property of multiplication states that we can change the grouping of the factors and the product will stay the same?
The Associative Property
10, 20, 30, 40, 50, 60, 70, 80, 90, 100
Christy is making a savings plan. She wants to know how much she would save if she saved $40 every week for 6 weeks.
6 x $40 = $240
4 x 30 =
4 x 3 = 12, so 4 x 30 = 120
Which property of multiplication does this represent?
4 x 20 = (2 + 2) x 20
4 x 20 = (2 x 20) + (2 x 20)
4 x 20 = 40 + 40
4 x 20 = 80
Distributive Property
Kelsey writes the equation 6 x ? = 180. What value makes the equation true?
6 x 30 = 180
Tonya lined up 4 rows of train tracks on her bedroom floor. In each row, there are 20 trains. How many trains are there?
4 rows x 20 trains per row = 80 trains total
40 x 5 =
4 x 5 = 20, so 40 x 5 = 200
Which property does this represent?
7 x 60 = 7 x ( 6 x 10)
7 x 60 = (7 x 6) x 10
7 x 60 = 42 x 10
7 x 60 = 420
The associative property.
Kevin says that the product of 8 x 90 is 723. Without solving, how can you tell if Kevin is correct or not?
Kevin is incorrect. We can easily tell because the digit in his ones place is not a zero, so it can't be the product of a multiple of 10.
David buys 7 sheets of postage stamps at the post office. Each sheet has 20 stamps. How many stamps does David buy in all?
7 sheets x 20 stamps on each sheet = 140 stamps in all
30 x 8 =
3 x 8 = 24, so 30 x 8 = 240
Why can you say that 3 x 20 = (2 x 20) + 20?
We can represent 3 as 2 + 1. Then the distributive property lets us represent the equation as (2 x 20) + (1 x 20).
The digit in the ones place of a multiple of 10 is always ____.
Zero
There are 3 gardens on Mark's land. Last year, Mark planted 10 lilies in one of the gardens. This year, Mark planted 30 lilies on each plot. How many lilies are there this year?
3 gardens x 30 lilies on each plot = 90 lilies total
(The 10 lilies from last year is not important to this problem.)
60 x 7 =
6 x 7 = 42, so 60 x 7 = 420
Why can you say that 3 x 20 = (3 x 2) x 10?
We can represent 20 as 2 x 10. The associative property then lets us solve 3 x 2 = 6 first, then solve 6 x 10 = 60.
Explain why there are two zeros in the product of 5 x 40.
We can represent the problem as (5 x 4) x 10. 5 x 4 = 20, and then 20 x 10 = 200. One of the zeros comes from the 20, the other comes from multiplying by 10.