Insert < < , > > , or = = to form a true statement. 5 18 ? 7 10 \frac{5}{18}?\frac{7}{10}

This problem is asking us to insert the correct symbol to form a true statement. Notice we have the inequality symbols as well as the equal sign, and we need to figure this out based on the fractions we're given below. So, this is a case where we're comparing two fractions. Now, it's difficult for me to tell which fraction is equal, less than, or greater than simply by looking at the fractions right off the bat. So, what we need to do is get a common denominator that should always be our first step. Now, to find a common denominator between these fractions, I need to find the LCD. The least common denominator can be found a couple of different ways. We could list out multiples, or we could use prime factorization, which is what I'm going to use for this example. So, we have our denominator of 18, and we have our denominator of 10. Now, breaking these down into prime factors, I know that 18 is the same thing as 2 times 9, and 9 is the same thing as 3 times 3. We have all prime numbers. Now, 10 is the same thing as 2 times 5, and we have all prime numbers here as well. So, what we're going to end up getting is this 2, which is a unique prime factor. We're going to get these 2 3s, which are unique prime factors. And I don't need to include this 2 because it's not a unique prime factor. We already had a 2 up here, but I do see we have this 5, which is a unique prime factor. So, we end up getting is 2 x 3 x 3 x 5, which all comes up to 90. So, 90 is the LCD. So now that I've found my LCD of 90, I need to think about how I can get equivalent fractions, each with a denominator of 90. Well, remember, when getting equivalent fractions, you need to multiply the numerator and denominator by the same constant. I can recognize that 5 times 18 would give me 90, but if I multiply 5 in the denominator, I also need to multiply 5 in the numerator, and 5 times 5 is 25. Now, 9 times 10, that would give me 90, but I also need to multiply 9 in the numerator. So we get 9 times 7, which comes up to 63. So notice that we have 25/90 and 63/90, and looking at these two fractions, I can clearly see 63 is a larger number than 25. So what that means is that the alligator is going to want to eat the bigger number, meaning our inequality symbol is going to look like this, giving us our inequality symbol and the solution to this problem.

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Insert <<, >>, or == to form a true statement.518?710\(\frac{5}{18}\)?\(\frac{7}{10}\)

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