1. Equivalent Fractions: Comparing Fractions with Different Denominators

2. Equivalent Fractions: Comparing Fractions with Different Denominators
Sets

3. GOAL: You will learn how to compare fractions with different denominators.

4. GOAL: You will learn how to compare fractions with different denominators.
HOW: You will look at the visual fraction models of sets.

5. 1 2
You know that fractions can be shown as part of a whole, part of a set, or on a number line as a value between zero and one.
You know that the top number in a fraction is called a numerator and stands for the part of the whole. (draw 1)
You also know that the number down below the line is the denominator and that represents all the parts that make up the whole. (draw 4)
You know how to compare fractions when they share common denominators, or the denominators are the same. You can also compare fractions that do not have common denominators. Sometimes you can compare these fractions to benchmark fractions like ¼, 1/3, ½, or ¾. In this lesson you are going to learn how to compare fractions with different denominators by using visual fraction models.

6.  I’m going to explain this idea by showing you visual fraction models that show fractions as part of a set.
We are going to compare 2/3 to 1/6.
While these fractions have different denominators, the whole sets are equivalent. Each fraction is a part of the whole set.

7. We’re going to start with the fraction 2/3
We’re going to start with the fraction 2/3. We can split this whole set into three equal groups (circle 4 faces to make three groups in blue)–we’re doing this because 3 is the denominator. The numerator, 2, tells us that 2 of the 3 groups are shaded in. (shade in 8 faces w/ blue)

8. Here is the same whole set -- but now the fraction is 1/6, so our set is divided into 6 parts – our denominator. (circle groups of 2 ni red) Since our numerator is 1, one of those groups will be shaded in. (shade in 2 faces in pink)
When we compare the fractions as visual fraction models next to each other, we can see that since more of the set is shaded for 2/3 that fraction is greater than 1/6 and closer to one complete whole set. (2/3 > 1/6)
Let’s see how this works in a problem.

9. Which fraction is smaller? or ?
Let’s take a look at these fractions as visual fraction models. Remember, each fraction represents part of a set.

10. Which fraction is smaller? or ?
This whole set is divided into 8 sections – we know this because our denominator is 8. Since one is the numerator, one of the eight equal groups is shaded in.

11. Which fraction is smaller? or ?
This visual model displays 1/4. The whole set is split into four parts and one section out of the four sections is shaded.
Even though the numerators are the SAME, you can see the fractions represent different amounts because the denominators are different. You can see that 1/8 less than 1/4 (write <) because less of the value is shaded in. Remember, when the denominator is larger, the set will be divided into more sections, but those equal groups or parts will be smaller.

12. In this lesson, you learned how to compare fractions of sets by looking at visual fraction models.