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Developing strategies for multiplying decimals

Sal uses place value and equivalent fractions to multiply decimals.

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Video transcript

- [Instructor] So right over here we wanna compute what three times 0.25 or three times 25 hundredths is. And so I encourage you to pause the video and see if you can figure this out. Alright, now let's work through this together. And in this video, we're gonna 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 strategies we're gonna look at in this video are 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, three times 25 hundredths. 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 gonna write it a different way. 25 hundredths, hundredths. If I have three times 25 of something, what is it going to be? Well, what's three times 25? Let's see. Two times 25 is 50, three times 25 is 75. So it's going to be 75, and I'm multiplying, not just three times 25, I'm multiplying three times 25 hundredths. Instead of 25 hundredths, I'm gonna have 75, 75 hundredths. Written out in words, this would be 75 hundredths. How would we write that as a decimal? That is the same thing as this, 75 hundredths. Another way to conceptualize this, to think about what this is, is if we were to write three times, we could write it as a fraction. We could write 25/100. This is another way of writing 25 hundredths. These are all equivalent. What is three times 25/100? Same idea. This is going to be equal to, you could say this is 25/100 plus 25/100 plus 25/100. This is going to be 75 hundredths, which once again is 0.75. If you wanted to more formally view it as fraction multiplication, you could view it as 3/1 times 25/100, and you multiply the numerators, you get 75, you multiply the denominators, you get 100. Either way, in all of these situations, you're gonna get 75 hundredths. Or, another way to think about it, is hey look, this thing right over here, this 25/100, this is the same thing as 1/4. So you could view this as three 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 three times 1/4, or 3/4, this is a fourth right here, 1/4 could be viewed as a fourth, so this is going to be equal to 3/4, three over four, 3/4. All of these are equivalent. If someone wanted it written out as a decimal, you could, you might know that 3/4 can be expressed as 75 hundredths, which in general, is a good thing to know. Now let's tackle slightly more complicated examples. Let's say we wanted to figure out, we wanted to figure out what 0.4 times zero, let me just do this in 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. What we have here in white, we could read this as four tenths, and we could write it as a fraction, as 4/10, and we're gonna multiply that by what we have over here. This is three tenths, three tenths, which we could write as a fraction as 3/10, and so you could view this as 4/10 of 3/10 or 3/10 of 4/10, but we're multiplying these fractions, which we've seen before in other videos. What's going to happen? Well, if we multiply the numerator we get 12, or the numerators. We multiply the denominators, you get 100. So you get 12 hundredths. If you wanted to write that as a decimal, it would be 0.12, 12 hundredths. You might notice something interesting here, and you'll see this more and more as you learn the standard method. 12 is four times three is 12, but now I have two digits behind the decimal, but notice, I have one digit behind the decimal here, one digit behind the decimal here, for a total of two digits behind the decimal. 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 re-express each of these as fractions, and then multiply the fractions to get something expressed in terms of hundredths, and then express that as a decimal.