Comparing and Ordering Fractions

Key Concepts

In Grade 3, we learn how to compare and order fractions. This involves understanding the size of fractions relative to each other and arranging them in ascending or descending order.

Understanding Fractions

A fraction represents a part of a whole. It consists of two numbers: the numerator (top number) and the denominator (bottom number). The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we have.

Comparing Fractions

To compare fractions, we need to ensure they have the same denominator. If the denominators are the same, we compare the numerators. The fraction with the larger numerator is the larger fraction.

Example 1: Same Denominator

Compare 3/8 and 5/8.

Since the denominators are the same (8), we compare the numerators (3 and 5). Since 5 is greater than 3, 5/8 is greater than 3/8.

Example 2: Different Denominators

Compare 1/4 and 2/5.

First, we need to find a common denominator. The least common multiple of 4 and 5 is 20. Convert each fraction:

1/4 = 5/20 (multiply numerator and denominator by 5)

2/5 = 8/20 (multiply numerator and denominator by 4)

Now compare 5/20 and 8/20. Since 8 is greater than 5, 8/20 (which is 2/5) is greater than 5/20 (which is 1/4).

Ordering Fractions

To order fractions, we follow the same steps as comparing fractions. First, ensure all fractions have the same denominator, then arrange the numerators in ascending or descending order.

Example: Ordering Fractions

Order the fractions 1/3, 2/5, and 3/4 from smallest to largest.

First, find a common denominator. The least common multiple of 3, 5, and 4 is 60. Convert each fraction:

1/3 = 20/60 (multiply numerator and denominator by 20)

2/5 = 24/60 (multiply numerator and denominator by 12)

3/4 = 45/60 (multiply numerator and denominator by 15)

Now order the numerators: 20, 24, 45. So, the fractions from smallest to largest are 1/3, 2/5, and 3/4.

Analogies

Think of fractions as pieces of a pie. If you have two pies cut into 8 pieces each, the pie with 5 pieces eaten (5/8) is more eaten than the pie with 3 pieces eaten (3/8).

Similarly, if you have three pies cut into different pieces (3, 5, and 4), you need to cut them into the same number of pieces (60) to compare how much is eaten.

Practical Tips

When comparing and ordering fractions, always start by finding a common denominator. This makes it easier to compare the sizes of the fractions. Drawing pictures or using fraction strips can also help visualize the fractions.