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Studying for a test? Prepare with these 3 lessons on Module 2: Rational numbers.
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Divide. Simplify the answer and write as a mixed number. And we have 2 and 1/4 divided by 1 and 3/4. So the first thing we want to do since both of these are mixed numbers is to convert them both into improper fractions. So let's start with 2 and 1/4. So we're still going to have 4 in the denominator, but instead of 2 and 1/4, remember, 2 is the same thing as 8/4. So we have 8/4, and then we have another 1/4. That gives us 9/4. Or another way to come up with this 9, you take 4 times 2, which is 8, plus 1. That gives you 9. And then the 1 and 3/4, same process. You're going to have 4 in the denominator, and then the numerator is going to be 4 times 1, which is 4, plus 3, which is 7. So this is the exact same problem here. 2 and 1/4 divided by 1 and 3/4 is the same thing as 9/4 divided by 7/4. And we saw in several videos already that dividing by a fraction is the same thing as multiplying by its reciprocal. So this is equivalent to-- so these are all equivalent. This is equivalent to 9/4 times the reciprocal of this. We're changing the division operation to a multiplication, and we're taking the reciprocal of the 7/4. For the reciprocal of 7/4, you swap the numerator and denominator, or the top number and the bottom number, and you get 4/7. Now, we could just multiply these. We could just say this is 9 times 4, which would be 36, over 4 times 7, which is 28, and then try to put it in lowest terms, or we could do it right now because it would be simpler. We have a 4 in the numerator. We have a 4 in the denominator, that'll eventually be in the denominator, so let's divide our eventual numerators and our eventual denominators both by 4. So you divide this 4 by 4, you get 1. This 4 by 4, you get 1. So now when you multiply it, you get 9 times 1, which is 9, over 1 times 7, which is 7. So we have our answer, but right now, it's an improper fraction. They want us to write it as a mixed number. And to figure it out as a mixed number, we can do it in our heads now. I think we've seen this enough times. We say how many times does 7 go into 9? Well, it goes into it exactly one time, but when you take 7 into 9 one time, what do you have left over? Well, you're going to have 2 left over, right? 7 times 1 is 7, and you're going to have 2 left over. You need 2 more to get to 9. So you're going to have 2 left over, so this is 1 and 2/7. And we're done!