# Math Makes Sense 8 Practice And Homework Book Answer Key

So this first sentence tells us that she delivers, or she takes, 3 hours to deliver 189 newspapers. So if we were to just flip it, we would have 189 newspapers for every 3 hours, which is really the same information. We're just flipping what's in the numerator and what's in the denominator. So let's divide this numerator and this denominator by 3 to simplify things. Jayda takes 3 hours to deliver 189 newspapers on her paper route.

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Obviously, you can flip both sides of these in either of these equations to get two more equations.

If you're seeing this message, it means we're having trouble loading external resources on our website. And the best way that I can think of comparing them is look at a point where you're getting an equivalent fraction.

You could say that the ratio of 9 markers to 7 markers is going to be the same as the ratio of their costs, is going to be equal to the ratio of the cost of 9 markers to the cost of 7 markers. So one again, we're going to assume that what they're asking is how many apples-- let's call that x. So we kind of had the number of apples to cost, the number of apples to cost. Well, e isn't a good idea, because e represents another number once you get to higher mathematics. Or you could say the ratio between 5 and 15 is going to be equal to the ratio between the number of eggs for 5 people-- let me do that in that blue color-- and the number of eggs for 15 people.

And then, obviously, you could flip both of these sides. The ratio of 7 markers to 9 markers is the same thing as the ratio of the cost of 7 markers to the cost of 9 markers. So all of these would be valid proportions, valid equations that describe what's going on here. Now in this example, the unknown is the number of apples, so number of apples to cost, number of apples to cost. So we want to know how many eggs-- so this we'll call x. But you could call them y or z or any variable-- a, b, or c, anything. So you could say the ratio of people to eggs is constant. And obviously, you could flip both sides of this equation.

But maybe the easiest is to start with the ratio that they gave us, where they gave us both the numerator and the denominator, and then move from there. And we see from the denominator, we doubled the denominator. So we would double the numerator as well, and so you would get 48. These are all equivalent to 18/55, so all of these. So you have this situation where we see 27/75 is 54/150. So 54/165 is smaller than 54/150, which tells us that 18/55 is smaller than 27/75. So this is saying that 27/75 is greater than 18/55, and that is absolutely right. Which of these tables might show the distances one of Lunara's friends traveled over time? Each of them runs at a constant speed starting at time 0. If you multiply the distance by 5, we're multiplying the time by 5. So table 3 doesn't seem to make sense, either. So that's the same thing as-- let's see, that's the same ratio as, if we were to divide by 2, as 7 to 5 ratio.

So for example, if we look at this one right over here, the numerator is 12. So the denominator is also going to be half of the denominator here. And what we just did here is we wrote four equivalent ratios. The following table shows equivalent fractions to 27/75. And over here, we see that 18/55 is 54-- and this 54 jumped out at me because it's the same numerator-- over 165. If we divide both of these by 3, this is also a 7 to 5 ratio.

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