Determine if the following pair of fractions is equivalent. 9 4 \frac94 & 27 12 \frac{27}{12}

This problem asks us to determine if the following fractions are equivalent, and I want you to notice something here we're not given a specific method to use. We're not told strictly to use simplification or the cross product, so that means we can use either method that we want to. Now, looking at these fractions that I have, I can see we have 9/4, and then we're trying to figure out if this is equal to 27/12. Now, if I were to use the cross product method, I would end up with 9 times 12 and 4 times 27. And those seem like some pretty big numbers to be dealing with with multiplication. So, personally, I'm going to use the simplification method instead to figure this out. Now, What I can see is on the left side, we have 9/4. Now, 9 is the same thing as 3 x 3, and 4 is the same thing as 2 x 2. Notice nothing reduces or simplifies on the left side or for the left fraction. So because of this, I can say that 9/4 is as simple as we're going to get. This fraction is already fully simplified, so we just need to figure out if this side simplified is equal to 9/4. Well, let's do this. So, 27, I know is the same thing as 3 times 9. And 12, I know is the same thing as 3 times 4. Now, I could break down the 9 and the 4 as well, but I can already see something amazing that's happening here. These 3s cancel and we actually get the other fraction. So because of that, we can actually stop right about there and recognize that 9/4 is in fact equal to 9/4. So, the final solution to this problem would be, yes, these fractions are in fact equivalent.