To compare the fractions 1/2 and 1/3, we can convert them to a common denominator. The smallest common denominator for 2 and 3 is 6.
1/2 = 3/6
1/3 = 2/6
Therefore, 3/6 is greater than 2/6.
In other words, 1/2 is greater than 1/3.
This can be visualized by dividing a unit into equal parts. If we divide the unit into two equal parts, each part represents 1/2. If we divide the unit into three equal parts, each part represents 1/3. Clearly, the parts representing 1/2 are larger than the parts representing 1/3.
Alternatively, we can use the concept of ordering fractions. Fractions can be ordered from least to greatest using the following rule:
If a/b and c/d are two fractions, then a/b < c/d if and only if ad < bc.
In this case, a = 1, b = 2, c = 1, and d = 3.
ad = 1 * 3 = 3
bc = 2 * 1 = 2
Since 3 > 2, we can conclude that 1/2 < 1/3.