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# Multiplication with arrays

CCSS.Math:

## Video transcript

so I have several groups of these ball looking things so let's think about how many balls are in each group we have 1 2 3 4 5 6 7 8 9 10 11 12 and what I want to do is think about the different ways of dividing these twelve balls into different numbers of groups so for example I could view these twelve balls as one so that's one group of three two groups of three three groups of three four groups of three so I could view 12 as being four groups of three and the way that we would write that the way that we would write that is that 12 is that 12 is equal to four groups four groups of three four groups of three or another way of reading this is that 12 is equal to 4 times 3 if I have one two three four groups and in each of those groups I have one two three objects I'm going to have a total of twelve objects but that's not the only way we can get to 12 we could also view it as three groups of four so let's look at that so we could have it as one one group of four two groups of four three groups three groups of four so now we could view 12 as being three groups of four or we could say we could say that three we get the right tool out we can say that 3 3 times 4 3 times 4 is equal to 12 so whether we're doing 4 times 3 or 3 times 4 they're both going to be equal to 12 4 groups of 3 is 12 3 groups of 4 but we don't have to stop there we could also view 12 as well we could view it as 2 groups of 6 let's look at that could be so this is one group of 6 right over here so that's one group of 6 that's another group of six so once again we could view this as two times six two times six will also get us a twelve well what about viewing it is six groups of two well we can draw that out to six groups of two so that's one group of two let me do that in a different color we have this purple color we have one group of two two groups of two three groups of two four groups of two five groups of two and six groups of two so once again this is all different ways of writing twelve something equivalent to 12 we could write six times two six six groups of two six times two is also is also equal twelve but we don't have to stop there we could also literally view twelve as one group of twelve so how would that look so one group of twelve so this whole thing is just one one group one group of twelve here so we could literally say one one times 12 one times 12 is equal to 12 we have one entire group of twelve one times 12 is equal to 12 and we could think of it the other way around we could view this as 12 groups of one twelve groups of one let me draw that so twelve groups of one this is one group of one two groups of one three four five six seven eight nine ten eleven and twelve twelve groups of one so we could also write we could also write 12 12 groups and in each one I have one well that's still going to get me to 12