Developing strategies for multiplying 2-digit decimals

- [Instructor] Let's say I want to multiply 3.1 or 3 1/10 times times 2.4 which could also be described as 2 4/10ths so pause the video if you can do this and once again, I'll give you a hint. See if you can express these as fractions. So there's a couple ways you can express it as a fraction. You can express this as 3 1/10th times 2 4/10ths two, let's get the same color, 2 4/10ths. Now whenever you're multi these are mixed numbers right over here and mixed numbers are not the super straightforward to multiply, it's easier if they were written as what's often known as improper fractions but essentially not as mixed numbers. So three is the same thing as 30/10ths. So 30/10ths plus 1/10th, this is 31 10ths times two is the same thing as 20/10ths. So 20/10ths plus four is 24/10ths. 24 over 10. And hopefully this makes sense too that 3.1 this three right over here, this is 30/10ths or I can write, let me write 30/10ths and that this is 1/10th. So this total is going to be 31/10ths. Likewise, this two is 20/10ths plus 4/10th because it's 24/10ths. And now we can multiply. So this is going to give us our denominator's pretty straightforward. 10 times 10 is 100 and then 31 times 24, we can multiply in the traditional way that we're used to multiplying two digit numbers. 31 times 24 is going to be equal to four times one is four, four times three is 12, now we're gonna be multiplying in the tenths place. We're going to put a zero here. So two times one is two. We're really saying 20 times one is 20. But you get the idea. Two times one is two. Two times three is six. Really 600, because it's 20 times 30. But I'm just following the standard multi the method for multiplication then you add these. And you're gonna get four four seven. So when you multiply these two things together, in the numerator, you get 744 100ths. Which can also be expressed as this is the same thing as 700ths or 700 100ths I should say, plus 44/100ths and 700/100ths, that's just going to be equal to seven. So this is seven plus 44/100ths which we could write as .44 that's our seven and 44/100ths. And we would be done. And you might already be seeing a pattern. If you just took 31 and multiplied it by 24, you get 744. And notice, I have one and two digits behind the decimal point. Notice I have one and two digits behind the decimal point. And so think about whether that always works. Think about and why that might work. If you just multiply the numbers as if they didn't have decimals, so you would've gotten 744 and you say, I got two numbers behind the decimal, so my product is going to have two numbers behind the decimal, why does that work? Or does it always work? And how does it relate to what we did here which is converting these things to improper fractions and then multiplying it that way?