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# Ratios, rates, and proportions — Basic example

Watch Sal work through a basic Ratios, rates, and proportions problem.

## Want to join the conversation?

• Couldn't Sal just have done 7 divided by 8 and then multiply the result, 0.875, by 20? That is how I did the problem in just seconds.
• He could have, but that is an advanced method and does not always work, and take note in mind, most people here are just starting to learn this and need to learn the basic method.
• Can't we cross multiply?

7/8=X/20
140=8X
X=140/8
X=17.5

I think this is simpler, but I'm not sure if this is a valid method for all problems...
• You're right. Anytime you have two proportions set equal to each other, you can cross-multiply and it's perfectly valid. This is simpler than the method Sal chooses, but Sal's is easier to teach and explain the meaning behind, which is why I think he chose that way instead of cross-multiplying.
• Can't we cross multiply?

7/8=X/20
140=8X
X=140/8
X=17.5

I think this is simpler, but I'm not sure if this is a valid method for all problems...
• You can
Ratios rates and proportions are grouped together because they can be applied in either ways provided you know the right comparison
(1 vote)
• Hi, how do we get 2.5x ? Thanks!
• Sal is solving an equation with proportions, 7/8 = x/20. You can solve these multiple ways. The most straightforward is to treat it like an equation, and isolate x:
7/8 = x/20
20 (7/8) = x
Sal tries for a faster method. If you already know that 8 * 2.5 is 20, you can treat it like you're converting a fraction to a different denominator, by multiplying both numerator and denominator by the same value. We get 2.5 from 20/8, and if we multiply 8 by 2.5 to get 20, we have to multiply 7 by 2.5 to get x.
• Why didn't you cross multiply?
• He could've done that, but he maybe thought that this way was easier and faster.
• Can you help me with this:
Two friends travel 150km and 200km in time 6 hours and 5 hours respectively. What is the ratio of their average speed?
(1 vote)
• Speed is distance/time, so you should calculate the first speed and then the second one, and then see the ratio between them. (speed1 : speed2)

Hint: If you want to calculate for the first speed:
speed1 = distance1/time1 = 150/6 = 25. Can you do that for the second?

If you're stuck with the next steps please tell me. :)
• Cross multiplication seems like a harder way to do it for me.
• where does 3.5 come from?
• Finding 7 x 2.5.
7 x 2.5 = 7 x 2 + 7 x 0.5
7 x 2 = 14, 7 x 0.5 = 3.5

I think he said 5 and not 0.5 though.
(1 vote)
• Can u cross multiply to get your new answer and then make a one step equation
(1 vote)
• how did he divided 20 on 8 that so fast?
(1 vote)

## Video transcript

- [Instructor] Seven pounds of plums make eight rolls of fruit leather. If every batch of fruit leather requires the same amount of plums, how many pounds of plums are required to make 20 rolls of fruit leather? So, let's set up a ratio. We need seven pounds of plums for every eight rolls of fruit leather. Now, we need to think about how many pounds of plums we're gonna need. How many pounds of plums we're gonna need to make 20 rolls of fruit leather, 20 rolls of fruit leather. Well, let's see, what have we done to go from eight rolls to 20 rolls? How much larger is 20 than eight? Let's see, 20 divided by eight is 2 4/8, which is 2 1/2. So we multiplied by 2 1/2 or we have 2 1/2 times as many rolls when we go from eight to 20. So we're gonna need 2 1/2 times as many pounds to keep the ratios constant. So times 2.5, and what's seven times 2.5? Let's see, seven times two is 14. Seven times five is 3.5. 14 plus 3.5, this is going to be 17.5 pounds. Now, that's this choice right over here. And actually, even looking at the choices, you might have been able to get here even without doing this not too intensive mathematics, because you can say, "Okay, look, "the pounds are kind of close to the amount of leather, "but they're less than it." So we wouldn't want 23 pounds of plums if we make 20 rolls of fruit leather. This is more than 20. And if we're making more rolls than we're able to make with the seven pounds, we're not gonna be able to have fewer pounds there. So you could have actually ruled out all of them just based on the logic to get to 17.5, but it's always satisfying to do it the right way. But if you're under time pressure, deductive reasoning isn't always a bad thing.