Learn about Ordering Fractions Now, let’s learn about ordering fractions in an order. So we’re supposed to order fractions 3/7, 3/4, and 1/4, from the least to the greatest. So, let’s write these down; 3/7, 3/4 and 1/4. We need to figure out which one is the lowest and in value and which one is the highest in value. As we can see, we have different denominators. So they are unlike fractions. So the first thing I’ve got to do is convert them to like fractions. So if I want to convert them to like fractions, what do I do? I’ve got to calculate the lowest common multiple of seven, four, and four. So seven, four, and four are all the prime factorization of seven is seven, four is two times two, and four is two times two. So the LCM becomes 7x2x2=28. So the LCM is 28. Now that I have that, we need to rewrite these three fractions so that the denominator is 28. So 3/7 will become, multiplied both sides by 4, will become 12/28. The goal is to get the denominator to 28, right. 3/4 will become, I’ll have to multiply it by 7 on both sides to get 21/28. And the last one, 1/4 will become, multiply it by 7 again, 7/28. So the three fractions are 12/28, 21/28, and 7/28. So it becomes relatively easy to compare them. This is the least in value because the numerator is all what I’m looking at. This is the greatest in value and this is the middle. So the correct order is 3, 1, and 2. So the correct order will be, if I look at the rational one, 1/4, 3/7, and 3/4. So the final answer is 1/4, 3/7, and 3/4. 1/4 is less than 3/7 which is less than 3/4. 1/4 is less than 3/7, and less than 3/4. So quickly recapping what we’ve learned, if we’re given three fractions and we have to order them, we compute their LCM, make them all like fractions, and then compare the numerators. We get the values, 1/4 is less than 3/7 is less than 3/4.