Video Transcript
A farmer wants to try a new type of seed. He has bought enough seeds for a field of area one over 10 square miles. He wants to plant them in a field of width a quarter miles. What length of the field will be dedicated to this new seed type?
So, what I’ve done here is drawn a sketch of the area that’s going to be used with the new seed type. And first of all, we know that its area is one over 10 square miles, and we know its width is a quarter of a mile. And its length is what we’re looking to find out. Okay, but how are we going to do this?
Well, if we recall that the area of a rectangle is equal to the length multiplied by the width, so then therefore if we substitute in the values we know, we can say that our area, which is one-tenth, is equal to the length multiplied by our width, which is one-quarter. Well, then, if we divide both sides by a quarter, we can say that the length is gonna be equal to one-tenth divided by a quarter. So now we’ve worked out what calculation we need to complete to solve the problem. And it’s gonna be a division involving our fractions.
But how do we divide fractions? Well, in fact, what we have is a bit of a memory aid, and that is KCF. But what does KCF stand for? Well, it stands for keep it, change it, flip it. So, what that means is we keep our first fraction the same; we don’t change anything. Then, we change the divide to a multiply. And then, finally, we flip the final fraction. So, we turn it from one over four to four over one. And this is actually known as the reciprocal. So now what we have is one-tenth multiplied by four over one equals our length.
Now, if we recall how to multiply fractions, all we do is you multiply the numerators then multiply the denominators. So when we do that, we’re gonna get four over 10 is equal to the length. But are we gonna leave it like this? Well, no, we can actually cancel this fraction down. Well, two is a factor of both the numerator and dominator. So if we divide the numerator and denominator by two, we’re gonna have the length is equal to two over five miles.
