Rate Conversions 6
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>>This is YourMathGal, Julie Harland. Please visit my website at yourmathgal.com, where all of my videos are organized by topic. This is Example 6 of Rate Conversions. And so we’re going to do this problem which is kind of the opposite of what we did in Example 5, where we converted from miles per gallon to kilometers per liter. So, in this problem, we’re given that a car gets 12 kilometers per liter. That’s a metric system, right? And we’re going to convert to miles per gallon which is how it’s often done in the USA when you compare your mileage. And we’re going to use the conversion that one gallon is about 3.785 liters then one mile is about 1.6 kilometers. All right. So, we start of with 12 kilometers per liter. So we could say 12 kilometers over one liter. All right. Now, I have to end up with miles per galloon. I want to end up with miles in the numerator and gallons in the denominator. If you want, you could write over here to keep in mind what you’re going to work. You want to end up with miles in the numerator and galloon in the denominator. So let’s see. This is our way of getting the leaders to cancel out and I know that 3.785 liters is the same as one galloon. So I can make this fraction, 3.75 liters over one galloon just like multiplying by one ’cause those represent the same number. But that’s the way of getting the liters to cancel out so that I will have kilometers in the numerator and galloons in the denominator. So this would be in kilometers per galloon, but I want miles per galloon. So what else that do I need to do? I need to get miles in the numerator, right? So I’m going to use this conversion because I’ve got miles and kilometers in the same equation here or approximate equation. So I want miles in the numerator so if I put one mile appear in 1.6 kilometers. We go down here and that means I could cancel out the kilometers. Okay. And now, we’ve got in the numerator, I’ve got my miles and then the denominators, I have my galloons. So, if I just deal with the numbers here, which is the 12 times the 3.785 divided by 1.6, remember that’s what you’re going to do in your calculator. If you have a calculator, you can do 12 times 3.785 and divided by 1.6. You will now have your answer in miles per galloon, right? Because miles over galloon could be written as miles per galloon. All right. So, let’s go ahead and put that in the calculator and, I didn’t say this, but round to the nearest tenth. Okay, round to your nearest tenth. [ Pause ] And I get that that’s proximately 28.4 miles per galloon. By the way, if this bothers you writing out like this, you can first keep it up to say you still know there’s miles in the denominator in galloons in the– miles in the numerator, galloons in the denominator, which is usually written like this MPG, miles per galloon. You could also see it written as 28.4 miles per galloon. This is YourMathGal, Julie Harland. Please visit my website at yourmathgal.com, where all of my videos are organized by topic.

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