Which of the following fractions 7/12, 9/16, 13/20 or 32/80 is the largest in value?

Introduction / Context:
This question tests your ability to compare the sizes of fractions that have different denominators. Comparing fractions is a basic aptitude skill used in percentage comparisons, ratio problems and data interpretation.

Given Data / Assumptions:

• Fractions to compare: 7/12, 9/16, 13/20 and 32/80.
• We must determine which of these fractions has the greatest numerical value.
• All fractions are positive and proper or equal to a proper fraction.

Concept / Approach:
There are two main ways to compare fractions: convert each fraction to a decimal, or convert them to equivalent fractions with a common denominator. Either method is valid. Here, using decimals provides a quick and clear comparison.

Step-by-Step Solution:

Verification / Alternative check:
We can also use a common denominator. A convenient common denominator for 12, 16, 20 and 80 is 240 or 480. Converting, we get approximate equivalents where 13/20 becomes the largest numerator, confirming our decimal comparison.

Why Other Options Are Wrong:
7/12 is about 0.5833 and smaller than 0.65. 9/16 is 0.5625 and smaller still. 32/80 equals 0.4, which is clearly smaller than all the others. Therefore none of these can be the largest fraction.

Common Pitfalls:
Candidates often rely on comparing denominators only, thinking that a smaller denominator automatically means a larger fraction. This is only true when numerators are equal. Another mistake is forgetting to simplify 32/80 to 2/5, which can hide how small it really is.

Final Answer:
The largest fraction among the given options is 13/20.