Ratios with tape diagrams (part:whole)

• [Instructor] We're told that Peni wrote a survey with open-ended and multiple-choice questions. The diagram shows the ratio of the question types. So what it shows us is that for every one, two, three, four, five open-ended questions, there are one, two, three, four multiple-choice questions.

And let's be clear, this is showing the ratio of open-ended questions to multiple-choice questions. It's not telling us exactly how many of each type of question we have. We just know for every five open-ended, there are four multiple-choice, or for every four multiple-choice, there are five open-ended.

The table shows some numbers of multiple-choice questions and total questions that could be on Peni's survey. Based on the ratio, complete the missing values in the table. So like always, pause this video and see if you can have a go at this on your own before we work through it together.

Alright, so some of you might not have realized that it says total questions here. It does not say multiple-choice questions and open-ended questions. So, one way to tackle this is to think about, well, what is going to be the ratio between multiple-choice questions and total questions?

So, let's think. If we were to create another bar for total questions that showed the ratio, for every five open-ended questions, you'll have four multiple-choice questions and you would have nine total questions. So it would look like this: one, two, three, four, five, six, seven, eight, and nine. I'm just adding these two together.

So, we could say that the ratio of multiple-choice to total questions is going to be four to nine. For every four multiple-choice questions, you're going to have nine total questions. So, in this first row, we have eight multiple-choice questions. So, that's two sets of four.

So, we're gonna have two sets of nine total questions. That still is the same ratio. Eight is to 18 as four is to nine. And now in the second row, they give us the actual number of total questions. Well, that is nine goes into 45 five times.

That's five sets of nine. So you're gonna have five sets of four multiple-choice questions. So five times four is 20, and we're done.