Comparing Fractions: Which is the Largest in the Pair?

Understanding how to compare fractions is a fundamental skill in mathematics. This article focuses on the comparison of fractions among the given pairs, including 3/32 and 1/2, as well as 1/3 and 1/4. We'll explore different methods to determine which fractions are larger and how to convert fractions to decimals for an easy comparison.

Pair 1: 3/32 vs. 1/2

Let's consider the first pair, 3/32 and 1/2. We can use two methods to compare these fractions: by finding a common denominator or by converting them to decimals.

Method 1: Common Denominator

1/2 can be written as 16/32 because both the numerator and denominator can be multiplied by 16. 3/32 remains the same.

Comparing 3/32 and 16/32, it is clear that 16/32 is larger than 3/32. Hence, 1/2 is larger than 3/32.

Method 2: Decimal Conversion

3/32 0.09375 1/2 0.5

By comparing the decimals, 0.5 is larger than 0.09375. Therefore, 1/2 is larger than 3/32.

Pair 2: 1/3 vs. 1/4

Now let's look at the second pair, 1/3 and 1/4. Again, we can use two methods to compare these fractions.

Method 1: Common Denominator

1/3 can be written as 4/12 by multiplying both the numerator and denominator by 4. 1/4 can be written as 3/12 by multiplying both the numerator and denominator by 3.

Comparing 4/12 and 3/12, it is clear that 4/12 is larger than 3/12. Therefore, 1/3 is larger than 1/4.

Method 2: Decimal Conversion

1/3 0.33333... (repeating) 1/4 0.25

By comparing the decimals, 0.333... is larger than 0.25. Therefore, 1/3 is larger than 1/4.

Conclusion

From the above analysis, we can conclude the following:

1/2 is larger than 3/32 in the first pair. 1/3 is larger than 1/4 in the second pair.

By using common denominators and decimal conversions, we can effectively compare fractions and determine which one is larger. This skill is particularly useful in various mathematical contexts, such as solving equations, understanding probability, and analyzing real-world data.