1. Learn to use pictures and number lines to compare and order fractions.

2. Vocabulary
like fractions
unlike fractions
common denominator

3. fractions. For example, and are unlike fractions.
When you are comparing fractions, first check their denominators. When fractions have the same denominator, they are called like fractions. For
example, and are like fractions. When two fractions have different denominators, they are called unlike
fractions. For example, and are unlike fractions. 6 7
___ 4 7
___ 7 10
___ 1 2
___

4. Additional Example 1A: Comparing Fractions
Compare. Write <, >, or =. 6 7 __ 4 __ 7 6 7 __ __ 7 4
>
From the model, > . 6 7 __ 4

5. Additional Example 1B: Comparing Fractions
Compare. Write <, >, or =. 1 9 __ __ 5 9 1 9 __ __ 9 5
<
From the model, < . 1 9 __ 5

6. Compare. Write <, >, or =.
Check It Out: Example 1A
Compare. Write <, >, or =. 4 6 __ __ 5 6 4 6 __ __ 6 5
<
From the model, < . 4 6 __ 5

7. Compare. Write <, >, or =.
Check It Out: Example 1B
Compare. Write <, >, or =. 3 9 __ __ 2 9 3 9 __ __ 9 2
>
From the model, > . 3 9 __ 2

8. To compare unlike fractions without models, first rename the fractions so they have the same denominator. This is called finding a common denominator. This method can be used to compare mixed numbers as well.

9. Additional Example 2: Cooking Application3 __ 3 4 __
Ray has cup of nuts. He needs cup to
make cookies. Does he have enough nuts for the recipe? 3 4 __
Compare and . 2
Find a common denominator by multiplying the denominators.
3 • 4 = 12

10. Additional Example 2 Continued
Find equivalent fractions with 12 as the denominator. 2 3 __ 12 __ 3 4 __ 12 __ = = 2 3
______
• 4 __ 12 8 3 4
______
• 3 __ 12 9 = =
• 4
• 3 2 3 __ __ 12 8 3 4 __ __ 12 9 = =

11. Additional Example 2 Continued
Compare the like fractions. __ 12 8 __ 12 9 2 3 __ 3 4 __
< , so < 2 3 __ 3 4 __
Since cup is less than cup, he does not
have enough.

12. Trevor has cup of soil. He needs cup to
Check It Out: Example 2 1 3 __
Trevor has cup of soil. He needs cup to
fill a small planter. Does he have enough soil to fill the planter? 1 4 __ 1 4 __
Compare and . 3
Find a common denominator by multiplying the denominators.
3 • 4 = 12

13. Check It Out: Example 2 Continued
Find equivalent fractions with 12 as the denominator. 1 3 __ 12 __ 1 4 __ 12 __ = = 1 3
______
• 4 __ 12 4 1 4
______
• 3 __ 12 3 = =
• 4
• 3 1 3 __ __ 12 4 1 4 __ __ 12 3 = =

14. Check It Out: Example 2 Continued
Compare the like fractions. __ 12 4 __ 12 3 1 3 __ 1 4 __
> , so > 1 3 __
Since cup is more than cup, he does have
enough. 1 4 __

15. Order , , and from least to greatest.
Additional Example 3: Ordering Fractions
Order , , and from least to greatest. 4 5 __ 2 3 __ 1 3 __ 4 5
_______
• 3 12 15 __ 2 3
_______
• 5 10 15 __ 1 3
_______
• 5 5 15 __
Rename with like denominators. = = =
• 3
• 5
• 5 5 15 10 15 12 15 1 1 3 2 3 4 5 1 3 __ 2
The fractions in order from least to greatest are , , . 4 5

16. Numbers increase in value as you move from left to right on a number line.
Remember!

17. Order , , and from least to greatest.
Check It Out: Example 3
Order , , and from least to greatest. 4 7 __ 3 4 __ 1 4 __ 4 7
_______
• 4 16 28 __ 3 4
_______
• 7 21 28 __ 1 4
_______
• 7 7 28 __
Rename with like denominators. = = =
• 4
• 7
• 7 21 28 7 28 16 28 1 1 4 4 7 3 4 1 4 __ 7
The fractions in order from least to greatest
are , , . 3