Comparing Fractions with Like Denominators
Comparing fractions with like denominators is fairly simple. If the fractions you are comparing have the same unit, or denominator, then you simply have to look at the numerator to compare which fraction is more than or less than. Compare the fractions "three-fifths" and "two-fifths". You would need to first check if they are using the same unit. Yes! Both fractions are using "one-fifths". You then will look to how many "one-fifths" you have in each fraction given. In the first fraction there are three copies of "one-fifth" and in the second fraction there are two copies of "one-fifth". Since three is more than two, "three-fifths" is more than "two-fifths". We can illustrate this by using both the area model and the number ray model. With the area model it is probably best to use separate wholes to illustrate each fraction. These models can be side by side (figure 16) or you could also place them one above the other (figure 17).
In the number ray model (figure 18), you are looking for a specific distance from the origin. For the first fraction you are looking for three copies of "one-fifth". Beginning at the origin, you would "travel three "one-fifths" moving in the positive direction. Label the point where you "land". For the second fraction you are looking for two copies of "one-fifth". Again, beginning at the origin you would "travel" two "one-fifths" in the positive direction. Label where you "land". On the number ray you can see that "three-fifths" is further in distance from the origin. Therefore, "three-fifths" is more than "two-fifths". With additional practice comparing fractions with like denominators, students should come to the conclusion that when the denominators are the same, the numerator will tell you which fraction is larger.
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