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CCSS.Math:

dividing by 10 a lot like multiplying by 10 creates a pattern with numbers so let's dig in and look at dividing by 10 look at what happens when we divide by 10 and see if we can figure out that pattern and maybe even how it relates to the pattern for multiplying by 10 let's take a very simple one to start let's say something like 30 divided by 10 one way to think about this is we're taking the number 30 and we're dividing it into groups of 10 so let's see how many groups of 10 it takes to make 30 one group of 10 is 10 so that's not enough plus a second group is 20 plus a third group is 30 so 30 can be thought of as 10 plus 10 plus 10 or 3 groups of 10 so if we divide 30 by 10 divide 30 into groups of 10 we end up with 3 groups let's try another one maybe something slightly trickier maybe let's go with a hundred 10 divided by 10 and again we're dividing we're taking 110 and dividing it into groups of 10 so let's see how many groups of 10 it takes to get to 110 110 plus another is 20 30 40 50 another 10 gets us to 60 70 80 we're getting closer 90 100 and 110 so this right here is how many groups of 10 it takes us to get to 110 so let's see how many groups is that 1 2 3 4 5 6 7 8 9 10 11 our solution is 11 if we have a hundred 10 and we divide it into groups of 10 we end up with eleven groups well let's look at these first two let's pause here and see if we see a pattern 30 divided by 10 was 3 110 divided by 10 was 11 so what happened what happened to the 30 and the 110 to get these quotients and what happened is the zero the zero on the end was taken off our solution is the same but with the zero taken off the end here again the solution is the same with a zero taken off the end and if we remember from multiplication it was the opposite if we had two times 10 instead of dividing times 10 our solution was 20 or a to our original number with a zero added to the end remembering another one something like 13 times 10 our product our solution is a 13 the original number with a zero added to the end so in multiplication when we multiply by 10 we add a zero to our whole number at the end and when we divide when we do the opposite by 10 we take off a zero from the end of our whole number so knowing that pattern let's try one more maybe one where we don't work out all the tens but just try to use the pattern to solve it if we had something like say 7,000 divided by 10 well our solution is going to be 7,000 but with the zero taken off of the end because we're dividing by 10 so instead of 7,000 we would have 700 7,000 divided into groups of 10 would be 700 groups of 10 so our solution is 700 let's take this all a step further and let's think about what dividing by 10 is doing to these numbers 232 110 in terms of their place value so here's a place value chart let's use it to look at one of the numbers we already tried something like 30 and when we divided 30 by 10 remember what happened to the three instead of being three tens our solution was three ones the three moved one place value to the right and the zero really did - it would move after a decimal which would be three point zero which is the same as three which is the reason we didn't need to write that zero the reason that we could cross it off so our number instead of being three tens when we divide it by ten became three ones let's look at a little bit trickier of one we also tried seven thousand so that will be seven thousands zero hundred zero tens and zero ones and when we divided by ten our seven in our thousands place became seven hundredths and the zero hundreds became zero tens and zero tens became zero ones and that last zero we were able to cross off and moved after the decimal so seven thousand divided by ten was seven hundred again everything moved one place value to the right so there's two ways to think about dividing by ten we could either say you drop a zero off the end or we could say that you move every digit one place value to the right let's think about it again in terms of place value with a new number let's try something like 630 if we divide 630 by ten we're going to move everything one place value to the right so the 600's will become six tens six ten three tens will become three ones and the zero ones will move after the decimal so we can say it's 630 divided by 10 is equal to sixty three or six tens and three ones so again two ways to think about dividing by ten either we can cross off a zero or we move every digit each digit one place value to the right