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CCSS.Math:

what is 700 times 10 well let's focus first on this times 10 part of our expression because multiplying by 10 has some patterns in math that we can use to help us solve one pattern we can think of when we multiply by 10 is if we take a whole number and multiply it by 10 we'll simply add a zero to the end of our whole number so for example if we have a whole number like 9 and we multiply by 10 our solution will be a 9 with one zero at the end or 90 because 9 times 10 is the same as nine tens and nine tens is 90 so let's use that pattern first to try to solve here we have seven hundreds so seven times we have a hundred or seven hundred and we're multiplying again times ten use this pattern over here our solution will add a zero at the end so if we had seven hundred ten times we would have seven hundred with a zero on the end or seven thousand so seven hundred times 10 is equal to seven thousand but there's another pattern we could use here another pattern to think about when we multiply by ten and that is that we multiply by ten we move every digit one place value one place value left or one place value greater so let's look at that one on a place value chart here we have a place value chart to use that earlier example when we had nine ones and we multiplied it by 10 our 9 moved one place value to the left and moved up to the tens now we had nine tens and we filled in a zero here because there were no ones left there were zero ones left and so we saw that nine times 10 was equal to 90 so again it's the same as adding a zero at the end but we're looking at it another way we're looking at in terms of place value and multiplying by ten moved every digit one place value to the left so if we do that with the same question 700 700 if we move hundreds one place value to the left we'll end up with thousands so 700 times 10 is seven thousands or as we saw earlier seven thousand so either one of these is a correct answer 700 times ten is seven thousand and here's an example with division now we have dividing by ten and as you might predict dividing by ten is the opposite of multiplying by ten so our patterns are also the opposite instead of adding a zero to the end of a whole number we would drop a zero at the end we would drop a zero at the end so for an example if we had 40 divided by ten we would drop that zero and end up with four if you divide 40 into groups of ten you have four groups let's use that over here 210 or 212 10 so we have 212 tens so 212 ten times so how we got the zero there and we divide that by ten we can use this first pattern we thought of and just drop the zero on the end let's drop that zero and our answer will be 212 but we could also we could use the place value pattern we could think in terms of place value and instead of moving one place value to the left one place value larger we're going to move place-value smart smaller or to the right when place value to the right so what's one place value smaller than 212 tens if we have 212 tens divided by 10 we want to move this tens one place value to the right or smaller which is ones so our solution would be 212 ones which is equal to what we already saw simply 212 so 212 tens divided by 10 we could write the number out and drop a 0 or we could think about place value and move one place value to the right either way our answer is 212 ones