Insert <<, >>, or == to form a true statement.−512?−3072-\frac{5}{12}?-\frac{30}{72}

−512=−3072-\frac{5}{12}=-\frac{30}{72}

Insert < < , > > , or = = to form a true statement. − 5 12 ? − 30 72 -\frac{5}{12}?-\frac{30}{72}

This problem asks us to insert the correct symbol between the fractions below to form a true statement. Notice I am given -5/12 and -30/72. And I need to figure out if one of these fractions is bigger or smaller, or if they're both equal. And right off the bat, it's really hard to tell. So, here's what we need to do. When we're trying to compare fractions, it's best to get a common denominator first, cause then we can just compare the numerators. Now, to get a common denominator, I'm looking for my LCD, my least common denominator. Now, I can go ahead and use prime factorization, or I can list out multiples. Now, I'm actually going to use the strategy of listing out multiples here because here's what I'm noticing. I have one denominator as 72. But another one of my denominators is 12. And I know for 12, we have 1224, 36, 48, then we have 60, and 72. So, eventually, we end up getting 72 as a multiple of 12, meaning that 72 is our least common denominator. So, what I need to do is rewrite these as fractions with the common denominator of our LCD 72. So, how did I go about doing that? Well, I can recognize these will each have the same denominator and they'll each be negative, but remember, we're writing equivalent fractions, and to get equivalent fractions, we need to multiply the numerator and denominator by the same constant. Now, for -30 over 72, Already have the desired denominator of 72, so I don't need to change anything about this numerator. However, with my first fraction -5/12, I do need to change this because 6 times 12, that gives me 72. And 6 times 5 gives me 30. So we get -30 over 72 as the equivalent fraction to our first fraction that we had -5/12. But notice what happens here. We got the exact same fraction, -30 over. 72 in both cases. So notice these fractions are actually equal. One is not greater than the other. So going to our original fractions, we can say both of these fractions are equal, giving us the solution to our problem. Hope you found this video helpful.