Comparing and Ordering Fractions

Comparing Fractions:

When comparing fractions, it's important to find a common denominator so that the fractions can be compared easily. Here's a step-by-step guide to comparing fractions:

1. Find a common denominator for the fractions.
2. Convert both fractions to have the same denominator.
3. Compare the numerators of the fractions. The fraction with the greater numerator is the larger fraction.

Ordering Fractions:

When ordering fractions from least to greatest or greatest to least, the same steps for comparing fractions can be used. Here's a step-by-step guide to ordering fractions:

1. Find a common denominator for the fractions.
2. Convert all fractions to have the same denominator.
3. Once the fractions have the same denominator, compare the numerators and order the fractions accordingly.

Study Guide:

Here are some tips and examples to help you understand and practice comparing and ordering fractions:

Tips for Comparing and Ordering Fractions:

• Always find a common denominator when comparing or ordering fractions.
• Remember to compare the numerators of the fractions after converting them to have the same denominator.
• Practice converting fractions to have the same denominator to make the comparison easier.

Examples:

Let's work through some examples to illustrate how to compare and order fractions:

Example 1: Comparing Fractions

Compare the fractions 3/4 and 2/5.

1. Find a common denominator: The common denominator for 4 and 5 is 20.
2. Convert the fractions:
   • 3/4 becomes 15/20.
   • 2/5 becomes 8/20.
3. Compare the numerators: 15 is greater than 8, so 3/4 is greater than 2/5.

Example 2: Ordering Fractions

Order the fractions 5/6, 2/3, and 3/4 from least to greatest.

1. Find a common denominator: The common denominator for 6, 3, and 4 is 12.
2. Convert the fractions:
   • 5/6 becomes 10/12.
   • 2/3 becomes 8/12.
   • 3/4 becomes 9/12.
3. Order the fractions: 8/12 < 9/12 < 10/12, so the fractions in order from least to greatest are 2/3, 3/4, 5/6.

By following these steps and practicing with different examples, you'll become more confident in comparing and ordering fractions.