### Video Transcript

Robert had three boxes of triangular shapes and five boxes of rectangular shapes. Each box of triangular shapes contains a total of 10 shapes. Each box of rectangular shapes contains a total of 12 shapes. Write down the ratio for the total number of triangular shapes to the total number of rectangular shapes. Give your answer in its simplest form.

So in this question, what we’re actually looking at is two types of shapes. We’ve got triangular shapes, which I’m gonna call 𝑡, and rectangular shapes, which I’m gonna call 𝑟. Well, if we want to find out the total number of triangular shapes, which I said I’m gonna call 𝑡, then this is gonna be equal to the number of boxes multiplied by the number of shapes in a box.

Well, for the triangular shapes, this is gonna be three, because Robert had three boxes of triangle shapes, multiplied by 10. And that’s because each box of triangular shapes contains a total of 10 shapes. So therefore, the total number of triangular shapes is gonna be 30 shapes. So great, we know we’ve got 30 triangular shapes. Now, let’s have a look at the rectangular shapes.

Now, to actually work out the total number of rectangular shapes, what we’re gonna say is that it’s gonna be equal to five multiplied by 12. And that’s because Robert had five boxes of rectangular shapes. And there were 12 rectangular shapes in each of the boxes. So this is gonna give us a total of 60 rectangular shapes. So great, we’ve now worked out how many triangular shapes and how many rectangular shapes we have.

So now, in the question, it’s asking us to write down a ratio. So what I’ve done is I’ve written a ratio here. So we’ve got 𝑡 to 𝑟. So that’s the total number of triangular shapes to the total number of rectangular shapes. We’ve put it in that order because that’s the order that it appears in in the question, when it asked us to write the ratio for the total number of triangular shapes to the total number of rectangular shapes. So it always goes in the order that it’s written down.

Okay, so we can now put some values in because we’ve calculated those. So we now put in the values 30 and 60. And that’s because we calculated the total number of triangular shapes to be 30 and the total number of rectangular shapes to be 60. So therefore, we’ve now written down our ratio, 30 to 60.

So, have we finished? Is this question done? Well, no. We haven’t got all the way there. Because it says at the end: give your answer in its simplest form. And this isn’t in its simplest form. So now, we need to have a look at what we can do to simplify our answer.

Well, in order to simplify our ratio, what we want to do is actually look for the highest common factor of 30 and 60. And the highest common factor of 30 and 60 is in fact 30. So therefore, what we do is we divide each side of our ratio by 30. So we get the ratio one to two. And we get this because 30 divided by 30 is one. And 60 divided by 30 is two.

And we can actually work that back. So if we think, six divided by three would be two. So therefore, 60 divided by 30 would be two. So therefore, we can say that the ratio for the total number of triangular shapes to the total number of rectangular shapes is one to two. And it’s in its simplest form.