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Current time:0:00Total duration:5:08

Video transcript

let's multiply 40 times 70 so 40 times we have the number 70 so we could actually list that out the number 70 40 different times and add it up but that's clearly a lot of computation to do and there's got to be a faster way so another way is to stick with multiplication but see if we can break these numbers up this 40 in the 70 decompose them break them up in some way to get numbers it might be a little easier to multiply with for me multiplying by 10 is the easiest number because I know the pattern to add a zero so I'm going to break up 40 and say instead of 40 4 times 10 4 times 10 and 40 are equivalent they're the same thing so I can replace the 40 with a 4 times 10 and then for my 70 same thing I can break this up and write 7 times 10 7 times 10 so these two expressions 40 times 70 and 4 times 10 times 7 times 10 are equal they're equivalent so they'll have the same solution but for me this one down here is simpler to work out because of these times tens so I'll solve this one knowing that I'll get the same solution as I would have for this top expression so what we can do is we can reorder these numbers in a different order to again continue making this question easier for us to solve because in multiplication the order doesn't matter if we have five times two for example that will be the same as two times five they're both 10 5 2's or two fives either way it's 10 so we can change the order of the numbers without changing the answer so again we're going to change our expression a little bit but what we're not going to change is the solution so I'm going to put my one digit numbers first 4 times 7 and then I'll put the two-digit numbers the tens times 10 and the other times 10 so we have all the same factors all the same numbers in both of these expressions they've just been reordered and now I'll solve going across 4 times 7 is 28 and then we have 28 times 10 and times another 10 well the pattern 4 times 10 that we know is when we multiply a whole number like 28 times 10 we will add a zero to the end one zero for that zero and ten because 28 times 10 is twenty eight tens 28 tens or 280 and that multiplied 28 times 10 and then if we multiply by this other 10 well we have to have another zero multiplying by 10 adds a zero so if we multiply by two tens we add two zeros so 28 times 10 times 10 is 2800 which means that this original expression we had 40 times 70 also has a solution of 2800 or 2800 let's try another example where we're multiplying tens like this let's try let's do something like let's say maybe 90 times about 30 90 times 30 so the first thing I'm going to do is break up these numbers so that I have tens because again for me tens are easier to multiply the numbers like 90 and 30 so 490 I'll write 9 times 10 and for 30 all right 3 times 10 the expressions are equivalent we've just written it in another way and now I'll reorder these numbers to put the one digit numbers first so 9 times 3 and then I'll put the tens times 10 times 10 because we need to have all the same numbers even if we change the order so we have the 9 3 the first 10 and the second 10 and now finally we multiply 9 times 3 is 27 27 times 10 will be 27 tens or 27 with a zero on the end and 270 times 10 will be 270 tens or 270 with a zero on the end so going back to the original question 90 times 30 is equal to 27 hundred or 2700