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# Developing strategies for multiplying decimals

CCSS.Math:

## Video transcript

so right over here we want to compute what three times 0.25 or 3 times 25 hundredths is and so I encourage you to pause the video and see if you can figure this out all right now let's work through this together and in this video we're going to explore multiple strategies in the future we're going to show you what's called the standard strategy which you might use a lot but the Saturdays we're going to look at in this video actually very helpful for understanding what multiplying decimals actually means how it relates to multiplying fractions as often the way that people even people who have a lot of math behind them how they actually multiply decimals so here 3 times 25 hundredths so there's a couple of ways to think about it one way is to say hey this is the same thing as three times and I'm just going to write it a different way 25 hundredths hundredths so if I have 3 times 25 of something what is it going to be well what's 3 times 25 let's see 22 times 25 is 50 3 times 25 is 75 so it's going to be 75 and I'm multiplying not just 3 times 25 I'm multiplying 3 times 25 hundredths so instead of 2500 I'm going to have 75 75 hundredths so written out in words this would be 75 hundredths now how would we write that as a decimal well that is the same thing as this 75 hundreds now another way to conceptualize this to think about what this is is if we were to write 3 times we could write it as a fraction we could write 25 over 100 this is another way of writing 25 hundredths these are all equivalent so what is 3 times 25 over 100 well same idea this is going to be equal to I'm you could say this is 25 over 100 plus 25 over 100 plus 25 over 100 this is going to be 75 75 hundredths which once again is 0.75 if you wanted a more formally view it as fraction multiplication you could view it as 3 Oh 1 times 25 over a hundred and you multiply the numerators you get 75 you multiply the denominators you get hundred either way in all of these situations you're going to get 75 hundreds or another way to think about it is hey look this thing right over here this 25 over 100 this is the same thing as 1/4 so you could view this as 3 times 1/4 in fact this is a decimal that it's good to recognize that this is the same thing as 1/4 so you could view this as 3 times 1/4 or 3/4 this is 1/4 right here 1/4 could be viewed as 1/4 so this is going to be equal to 3/4 3 over 4 3/4 all of these are equivalent now if someone wanted it written out as a decimal you could if you might know that 3/4 can be expressed as 75 hundredths what's in general is a good thing to know now let's tackle slightly more complicated examples so let's say we wanted to figure out we wanted to figure out what 0.4 times 0 just a new color times 0.3 is going to be equal to pause the video and see if you can compute this and I'll give you a hint see if you can express these as fractions all right so what we have here and right white we could read this as 4/10 4/10 and we could write it as a fraction as 4 over 10 and we're going to multiply that by what we have over here this is 3/10 3/10 which we could write as a fraction as 3/10 and so you could view this as 4/10 of 3 dents or 3 times of 4 tens but we're multiplying these fractions which we've seen before in other videos and so what's going to happen well if we multiply the numerator we get 12 we multimers must by the denominators you get 100 so you get 12 hundredths so if you wanted to write that as a decimal it would be 0.1 to 12 hundredths now you might notice something interesting here and you'll see this more and more as you get as you learn the standard method well 12 is 4 times 3 is 12 but now I have 2 digits behind the decimal but notice I have one digit behind the decimal here one digit behind the decimal here for total of two digits behind the decimal so I'm giving you a little bit of a hint about where we're going but the important thing for this video is to recognize that you can extry Express each of these as fractions and then multiply the fractions to get something expressed in terms of hundreds and then express that as a decimal