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Video transcript

let's solve 350 divided by 50 so one way to think about this is if we have 350 of something let's say something delicious like brownies if we had 350 brownies and we were dividing them into groups of 50 how many groups of 50 could we get well one idea is to count by 50s until we get to 350 and see how many groups there are one group of 50 would be 50 plus another group of 50 would be a hundred plus another group of 50 is 150 another one will be 200 200 plus 50 is 250 plus another 50 is 300 and plus one more 50 is 350 so when we added all these 50s these groups of 50 50 100 150 200 250 300 350 we ended up with 350 so 350 can be divided into this many groups of 50 and how many groups is this 1 2 3 4 5 6 7 so 350 divided into groups of 50 is 7 now let's look at that quotient that's solution of 7 and let's notice something if we had simply divided 35 by 5 we would have also gotten 735 divided into groups of 5 is also equal to 7 so in a way these zeroes didn't matter they didn't affect our answer we were able to cancel them out having the zero in the first number is cancelled out by having that zero in the second number and let's look at why that is let's think about why that is division is really the same as a fraction so if we wrote this as a fraction let's say 350 over 50 well this fraction bar right here is the same as the division sign up here 350 / 50 is the same as 350 over 50 and when we have a fraction like this fraction down here we can simplify it in this case because there's zeros on the end we know they're both multiples of 10 so we can divide them both by 10 we can divide our numerator and our denominator by 10 and when we divide whole numbers by 10 we have a trick we can use a pattern really which is that the whole number in this case 350 when it's divided by 10 we drop a zero from the end so 350 divided by 10 is 35 350 could be divided into ten groups of 35 and then 50 divided by 10 will be the same thing when we divide 50 by 10 we drop that zero off the end or another way to think about it is 50 divided into groups of 10 would make 5 groups and then we end up with our simplified fraction of 35 fifths or 35 divided by 5 which is the same thing here so in both of these cases we can see that 350 divided by 50 is the same as 35 divided by 5 so in both whole numbers when we're dividing whole numbers and they both end in zeros we can cancel those zeros basically we're factoring out of 10 we're taking the 10 the divided by 10 out of both of them out of both numbers so we can cancel those zeros which leaves us with smaller numbers and at least for me I find division a lot simpler when I'm working with smaller numbers let's try a few more let's try one like 420 divided by 70 so we can see we have two whole numbers both end in zero so we're gonna cancel those zeros basically we're dividing a 10 out of both numbers and end up with a simpler division problem of 42 divided by 7 42 divided by 7 equals 6 therefore 420 divided by 70 also equals 6 and here's one last one what if we had five thousand six hundred or fifty six hundred divided by 80 so the first thing I notice is I have zeros at the end of both of my whole numbers if I cancel out this one I can cancel out one on the other side I can't cancel both of them over here there were two canceling we have to cancel the same amount of zeros on both sides and now we end up with 560 divided by eight this leaves us with a new division problem that's still a little bit tricky but easier than dividing by eighty so here we can think of 560 as 56 tens because of the zero on the end and 56 tens or 560 could be re-written as 10 times 56 these are equivalent 560 and 10 times 56 because 10 times 56 is a 56 with a zero on the end and rewriting it this way makes it so now I have a division problem right here 56 divided by 8 that we can solve 56 divided by 8 is 7 and then we still have this 10 and the time sign and 10 times 7 equals 70 so our solution here when we divided 560 by 8 was 70 so that means our solution up here for 5,600 divided by 80 is also 70 because when we cancel zeroes and divide we still get the same solution but remember we have to cancel the same amount of zeros in each number here we couldn't cancel both zeros if we cancel one zero in the dividend we can cancel one zero in the divisor and another thing to remember about this trick first thing to remember is we need to cancel the same amount of zeros and the second the zeros have to be at the end of the problem so if we had a division problem something for example like 506 divided by 20 here we cannot cancel the zeros we cannot cancel the zeros because this zero is not on the end so the new problem this would give us 56 divided by two is not equivalent does not equal the top division problem so we can't cancel zeros that does not work we cannot cancel zeros unless they're at the end of the problem and we cancel the same amount in both the dividend and the divisor