Benchmark Fractions

Here is one way to do it. First, let's look at the fraction four sevenths. Notice that in four sevenths, the whole consists of 7 equal parts. And we have four of those parts. Now, compare this fraction with one half. Is it larger than one half? Yes. Four sevenths is larger than one half. You can see that visually by looking at the shaded area in the circle representing the fraction four 7th, and you can see it represents more than half of the circle. Another way to check that is by multiplying both the numerator and the denominator of the fraction one half by four. To get four eighths. Which is the same as one half. As you remember, one half and four eighths represent the same portion of the whole. And, as we learned earlier, since the fraction four sevenths and four eighths have the same numerator, the greater fraction is the one with the smaller denominator. So for sevenths, is greater than four eighths. And because one half is equivalent to four eighths. For sevenths, is also greater than one half. 

Now, what about the fraction 7 sixteenths? Let us try to do the same thing. The fraction 7 sixteenths represents 7 parts out of the same hole, but that consists of 16 parts this time. So, is it larger than one half? Again, one way to find out is by looking at the shaded area representing the fraction 7 16th. As you can see, it is less than one half. Another way to see this is to remember that one half is equal to 8 sixteenths. Which we get by multiplying both the numerator and the denominator by 8. And since both 7 sixteenths and 8 sixteenths have the same denominator, the greater fraction is the one with the larger numerator. So 8 sixteenths is greater than 7 sixteenths. Since the fraction one half is equivalent to 8 sixteenths, one half is also greater than 7 sixteenths. Now that we know how our two fractions are compared to one half, we can say how they are compared to each other. You know how this works with whole numbers. 

For example, if you have the numbers one, two, and three, you know that three is not just bigger than two. It is also bigger than one. And one is not just less than two, it is also less than three. We can order our fractions the same way we order whole numbers. So we found out that fourth 7th is greater than one half. You can write four sevenths, followed by one half. And what about 7 sixteenths? We found out that one half is greater than 7 sixteenths. It seems that 7 16th is the smallest fraction here. So you can put 7 16th. After one half in the set. This is our final order. We start with four sevenths, then one half, then 7 16th. So now it is easy to see which fraction is greater. 7 16th, or four sevenths. 

Just look at the order. Four sevenths is the greater fraction. Fractions that are common and easy to deal with, such as one half, one fourth, or one third are called benchmark fractions. And here, when we compared our original fractions, we use the benchmark fraction one half, which is very familiar. Then we compared the two fractions to this benchmark. And this helped us figure out which one was the greater fraction. So benchmark fractions work as reference points that provide a way to evaluate and compare other fractions. In this lesson, you learned how to compare fractions with different numerators and denominators using the benchmark fraction one half.