Video: Dividing Rational Numbers Involving Terminating Decimals

Evaluate 0.8 ÷ 0.4.

02:57

Video Transcript

Evaluate 0.8 divided by 0.4.

So what we have here are two terminating decimals, and we’re going to divide them. And we have a couple of methods to do this. So what we’re gonna do is have a look at both of them. So for method one, what we’re gonna do is we’re gonna multiply both of our decimals. And we’re gonna multiply them both by 10. And that’s because what we’re gonna do is make it so, in fact, we’re not dividing decimals at all. We’re gonna be dividing units. So if we multiply 0.8 and 0.4 by 10, what’s gonna happen is that each of the numbers is going to move one place value to the left. So what we’re gonna get is eight divided by four. And we can do this because we’ve done it to both terms. So therefore, it’s going to give us the same result. Well, this is nice and straightforward. And that’s because eight divided by four is equal to two. So therefore, we can say that 0.8 divided by 0.4 is two.

So now we’re gonna take a look at method two. And for method two, what we’re going to do is convert both of our decimals to fractions. And we can do that because they’re both terminating decimals. And we know that terminating decimals are rational numbers, so therefore can be converted to a fraction with an integer as the numerator and an integer as the denominator. Well, if we start with 0.8, what this means is eight-tenths. Well, in turn, we can simplify eight-tenths by dividing the numerator and denominator by two, which will give us four-fifths. Then we have 0.4, which is gonna be equal to four-tenths, which again we can simplify by dividing the numerator and denominator by two to give us two-fifths.

Okay, great. We now got our two fractions. So we now have four-fifths divided by two-fifths. And we’ve got a method for dividing fractions. And what we can do is use our memory aid to remind us how to do that. And that is KCF, which is keep it, change it, flip it. And this means we keep the first fraction the same, we change the sign from a divide to a multiply, and we flip the second fraction. And it’s worth noting that if we flip a fraction, this is in fact the reciprocal of that fraction. And then if we multiply two fractions, all we do is multiply the numerators and multiply the denominators. So this is gonna be equal to 20 over 10, which once again gives us an answer of two.

Now this is quite straightforward because we’re multiplying two easy fractions. However, there is a quick tip, which can be useful. If you’re ever multiplying fractions, have a look at the numerators and denominators and see if there’s a common factor. So here we can see that five is a common factor. So if we divide both the numerator and denominator by five, we’re just left with four multiplied by one over one multiplied by two, which is four over two, which again would’ve given us two.

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