### Video Transcript

In a pride of lions, the number of male lions as a fraction of the number of female lions is two-fifths. Part a) State the number of female lions as a fraction of the number of male lions. Part b) There are eight male lions in the pride. Calculate the number of female lions in the pride.

So take a look at part a. What we’re gonna say is we’re gonna call the male lions 𝑚 and the female lions 𝑓. And we’re told that the number of male lions as a fraction of the number of female lions is two-fifths. So therefore, we can say that 𝑚, so the number of male lions, is equal to two-fifths of 𝑓, the number of female lions.

So when we deal with the word “of” when we’re dealing with fractions, it actually means multiply. So it’s two-fifths multiplied by 𝑓. So therefore, if we want to find the number of female lions as a fraction of the number of male lions, then what we need to do is first multiply by five to remove five from the denominator of our fraction on the right-hand side of the equation.

And when we do that, we get five 𝑚 and that’s because we get five multiplied by 𝑚. But we don’t need to write the multiply sign when we’re dealing with a letter. So dealing without that, it’s just five 𝑚. And then, this is equal to two 𝑓 and that’s because we had two-fifths multiplied by 𝑓 when we multiplied by five. So remove the five from the denominator. So we’ve got two multiplied by 𝑓 which is just two 𝑓.

And then, finally, we want 𝑓 on its own. So we’re gonna divide each side of the equation by two. And that’s because we got two 𝑓 and we just want one 𝑓. And whatever we do to one side of the equation, we must do to the other. And when we do that, we get five over two 𝑚 is equal to 𝑓. So we’ve solved part a. And we can, therefore, say that the number of female lions is five-halves of the number of male lions. Okay, so now, let’s move on to part b.

So for part b, we know that there are eight male lions in the pride and we want to calculate the number of female lions in the pride. And we know that the formula from part a is that 𝑓 is equal to five over two 𝑚 or five-halves of 𝑚. So then, what we’re gonna do is substitute in that 𝑚 is equal to eight because we’re told that there’re eight male lions. So we’re told that 𝑓 is equal to five over two multiplied by eight.

To help us understand how we work this out, we can think of it as eight over one, so think of it as a fraction. And then we do the same as we would with any pair of fractions when we’re multiplying. We multiply the numerators and then multiply denominators, which is gonna give us 𝑓 is equal to 40 over two. And that’s because five multiplied by eight is 40. Two multiplied by one is just two. So 40 divided by two is gonna be 20. So therefore, we can say that the number of female lions in the pride is equal to 20.

It is also worth mentioning though that there would have been another way that we could have worked out five over two multiplied by eight over one. And that would have been to divide eight by two because we see that we had two as the denominator and two goes into eight. And then, we’d have five multiplied by four which would have given us 20, so the same result.

So there we’ve checked it. And we can say definitely that the number of female lions in the pride is 20.