Multiplying 2-digit by 1-digit word problems
About this video
A bakery makes 7 trays of 36 cookies, so we find 7 x 36. The video solves it with the distributive property (7 x 30 + 7 x 6 = 210 + 42) and then with a vertical method. Both give 252, and both are the same idea written in different ways.
You'll be able to
- write a multiplication for an equal-groups word problem.
- multiply a 2-digit number by a 1-digit number using the distributive property.
- see how the vertical method uses the same partial products.
Key words
- equal groups
- Groups that each have the same number of things, like trays that each hold 36 cookies.
- distributive property
- Splitting a number into parts, multiplying each part, then adding: 7 x 36 = 7 x 30 + 7 x 6.
Transcript
- [Instructor] A bakery makes 7 trays of cookies on Friday. Each tray holds 36 cookies. How many cookies does the bakery bake on Fridays? Pause this video and try to figure that out. Okay, so we have 7 trays, 7 trays, and each of them has 36 cookies. So it's really 7 sets or 7 groups of 36.
So what we really wanna do is multiply 7 times 36. Now there's a couple of ways we could do this. One way is to think about it, "Well, that's the same thing as 7 times, and instead of 36, 36 is the same thing as 30 plus 6." And so here we can use the distributive property.
We could multiply 7 times 30 and 7 times 6 to get, and let me just do that separately. So we are going to have, I need to keep track of the colors. We're gonna have 7 times 30, and then we're gonna add that to 7 times 6. And so let me put the 30 here. 30 and then the 6.
And then what is that going to be? Well, this first part right over here, 7 times 3 is 21. So 7 times 30 is 210, and then 7 times 6 is 42. And so now we're going to want to add these two together. What's 210 plus 42? Well, 210 plus 40 is 250 plus we have that other 2, so this is going to be 252.
So that's one way that you could approach it, another way that you could think about it is you could take 36 and you could multiply it by 7, put the 7 in the one's place right below the 6. And then you could say, "Alright, first this is going to be," let me use different colors here.
"7 times 6." 7 times 6 is 42. And then you can think about, "Well, what is 7 times 30?" Well, that's 210. And then you add everything together. Same idea, 2 plus 0 is 2, 4 tens plus 1 ten is 5 tens, and then you have two hundreds, bring that down, you, we got 252 again.
And it's interesting to see it's really just different ways of writing the same thing. I really did 7 times 30, plus 7 times 6, 7 times 30, plus 7 times 6.
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