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Video transcript

let's multiply four times eighty so we can look at this a few ways one way is to say four times we have the number eighty so we have the number eighty one time two times three times four times four times we have the number eighty and we could do this computation add all of these and get our solution but let's look at it another way let's try to stick with multiplication and one way we can do that is to break up this eighty we know a pattern for multiplying by ten so let's try to break up this 80 to get a ten so if we have four times and instead of 80 let's say 8 times 10 because 80 and eight times ten are equal those are equivalent so we can replace our 80 with eight times ten and then we have this times ten back here which is super helpful because there's a nice neat pattern math that we can use to help us with the times ten part so let's start to solve this 4 times 8 is 32 and then we still have 32 times 10 and then we can use our pattern for multiplying by 10 which is at any time we multiply a whole number times 10 we take that whole number in this case 32 and we add a zero to the end so 32 times 10 is 320 and there's a reason that pattern works we went into it in another video but here just real quickly 32 times 10 is 32 tens and we can do a few examples if we had say 3 times 10 that will be 3 tens or 10 plus another 10 plus another 10 which equals 30 our whole number with a zero on the end if we had something like 12 times 10 well that would be 12 tens and if we listed out 10 12 times and counted them up there would be a hundred twenty it would add up to 120 which again is our whole number with a zero on the end our twelve with a zero on the end so we can use that pattern here to see that 32 times 10 is 32 with a zero on the end let's try another one let's do something like let's say 300 this time we'll do hundreds instead of tens times six well 300 we can break up like we did with 80 in the last one and we can say that 300 is 103 times or 100 times three and then we still have our times six after that so these two expressions one 300 times six and 100 times three times six are equivalent because we've replaced our 300 with a 100 and then from here we can multiply and let's start with our one digit numbers let's multiply those first three times six is 18 and then we still have 18 times 100 or 18 hundredths so we can write that as 18 and then to show hundreds we'll put two zeros on the end or 1800 just like up here just like we saw that 300 300 is equal to three times a hundred or our three with two zeros on the end well same thing here 18 times 100 is 18 with two zeros on the end or 1800s so 300 times six equals 1800 let's try another one but this time let's go even another place value and try thousands something like seven times 7,000 so like in the previous ones we're going to break up our thousands 7,000 is the same as seven times 1000 1000 seven times and we still have our times seven in the frontier to bring down and again we can multiply our single digits first our one digit number 7 times 7 is 49 and then 49 times a thousand is going to be 49 thousand which we can write as 49 and this time maybe the pattern is becoming clear we're going to have three zeroes on the end so it will be a 49 with three zeroes or 49 thousand just like up here seven times a thousand was a seven with three zeroes 49 times a thousand is a 49 with three zeroes or 49 thousand let's look at this as a pattern if we show this as a pattern let's do something like nine times 50 and then in another one let's do nine times five hundred and one last one we can do nine times five thousand I encourage you to pause here and see if you can work these out see if you can come up with solutions for these three expressions now we can work them out together nine times 50 will be the same as 9 times 5 times 10 because we broke up our 50 into a 5 times 10 and then if we multiply across 9 times 5 is 45 and to the end we're going to add 1 0 the pattern 4 times 10 is to add 1 0 we can keep going here 9 times 500 will be 9 and then times 5 times 100 500 is five hundreds just like 50 was 5 tens multiplying across 9 times 5 still equals 45 but this time we will add two zeros to the end or 4,500 and finally nine times 5,000 will be nine times five times 1,000 because 5000 is five thousands or thousand five times working across nine times five forty five and this time we add three zeros so forty five thousand so when we multiply each of these expressions we can see the only thing that changed was the number of zeros on the end so the pattern anytime we multiply a whole number times ten we add one zero to the end of our number anytime we multiply whole number times 100 we'll have two zeros and times a thousand we'll have three zeros and once we know that pattern we can use it to help us with questions like this where initially we don't see a 10 a 100 or a thousand but we can get one we can break up or decompose these numbers to get a ten or a hundred or thousand to help us solve the problem