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This lesson is about multiplication. We'll just be multiplying large numbers by 1 digit
numbers. By the end of the video, you should be able to multiply a large number by a 1
digit number using a method called grid multiplication. So, let's get started. Let's say it's a nice
hot day and you and your friend decide you want to open up a lemonade stand. You buy
all the lemons and sugar you need to make lemonade, you squeeze the lemon juice, mix
in sugar and water and you end up with 38 liters of lemonade. After some experimenting,
you find that each 1 liter of lemonade will pour 6 cups for your customers. Then you and
your partner decide that for every 1 cup, you're going to sell it for 7 swedish crowns.
Then your partner turns to you and asks "If we sold all this lemonade, how much money
would we make?" Well, how could we answer this problem? You could start by figuring
out how many cups of lemonade you can sell altogether. So, let's work that out. Well,
you know that 1 liter will give you 6 cups of lemonade and you also know that we have
38 liters of lemonade. So, every liter gives us 6 sups, that means we're going to get 6
cups, 38 times. That means its a multiplication problem because we're counting the same number
over and over again. 6+6+6+6... 38 times. So our problem is 38 multiplied by 6. Now,
using grid multiplication, we need to set up a little grid and the grid will depend
on how many digits we have. We have a 2 digit number multiplied by a 1 digit number, so
our grid should be 2 rectangles by 1 rectangle. Here we put our 1 digit, the 6 and then up
on top, we are going to write the 38, but broken up into it's individual pieces. The
8 is in the units place, so that's worth 8. The 3 is in the tens place, so it's actually
worth 30. Now, we multiply each of these individual pieces to fill in the little squares. We'll
start with this one. 8 times 6 is 48 and to find this square's value, you multiply 30
and 6. You might not know that off the top of your head, but you should know that 6 times
3 is 18. 6 times 30 has to be 10 times bigger than that, so 10 times bigger than 18 is 180.
Now, we've broken the 38 up into these pieces and multiplied, now we have to put them back
together. We have 180 and we need to put that together with 48, that involves the operation
of addition. We have 180 plus 48. 0 + 8 is 8. 8 + 4 is 12 so we carry our tens digit
over and we have 2 there. Then we have 1 + 1 is 2. So, once we've added all those pieces
back together we have 228 which means our multiplication 38 times 6 is finished. The
answer is 228. But remember, that just represents the number of cups we are able to sell. So,
we have 228 cups. We still want to know how much money is involved. For every 1 cup, we
will get paid 7 swedish crowns, that means for 228 cups, we are going to get 7 swedish
crowns, 228 times. So again we've got another multiplication. This time it's 228 multiplied
by 7. Now, can you guess how this multiplication grid is going to look different from the other
one? Since 228 is a 3 digit number, we are going to need 3 columns this time in our grid.
So, we need a little bit longer grid, here. 1 column, 2 and 3 columns. So now again, we
put our 1 digit number on the left, the 7. The 228 is going to be split up into its separate
pieces along the top. So, by place value place, we have the units place: that's got an 8 so
that is worth 8. In the tens place we have a 2, so that's worth 20. And in the hundreds
place, we have another 2 so then that would be worth 200. Ok, now lets go from left to
right this time, it doesn't really matter which order we go in because we have to do
all the boxes eventually. So, 7 times 200. Well, 7 time 2 is 14 so 7 times 200 has to
be 100 time bigger than that. That gives us 1400. In this box here, we've got 20 times
7. Again 7 times 2 is 14, so 7 times 20 has to be 140 (ten times bigger than 14). And
in the final box, we have 7 times 8 and that is 56. And finally, we have these different
pieces again, they need to be put back together so we have a single answer. We need to do
this using column addition, so I'm going to use this space that I've got over here. We
have 1400 + 140 + 56. Alright, 0+0+6 is 6, 0+4+5 is 9, 4+1 is 5, and 1 + nothing is 1.
So after all that multiplying we are left with 1596 and that number represents all of
those swedish crowns that we have collected throughout the day. How about that?1596! Remember
that you probably had to spend some money on your lemons and sugar so all of that money
isn't profit, but still... well done!