Verified Answer :

  • Convert each fraction to its decimal equivalent: \(\frac{6}{10} = 0.6\), \(\frac{2}{3} \approx 0.6667\), \(\frac{5}{8} = 0.625\), and \(\frac{7}{12} \approx 0.5833\).
  • Compare the decimal results: \(0.6667 > 0.625 > 0.6 > 0.5833\).
  • Identify the largest value, which corresponds to the fraction \(\frac{2}{3}\).
  • Final answer: \(\boxed{\frac{2}{3}}\).

Explanation

  1. Problem Analysis

We are given four fractions and need to determine which one has the greatest value:

A\(\frac{6}{10}\)
B\(\frac{2}{3}\)
C\(\frac{5}{8}\)
D\(\frac{7}{12}\)

To compare these fractions effectively, we can convert each of them into a decimal representation or find a common denominator. Converting to decimals provides a clear way to rank their values.

  1. Decimal Comparison

Let's convert each fraction to its decimal equivalent:

  • For A, \(\frac{6}{10} = 0.6\).
  • For B, \(\frac{2}{3} = 2 \div 3 \approx 0.6667\).
  • For C, \(\frac{5}{8} = 5 \div 8 = 0.625\).
  • For D, \(\frac{7}{12} = 7 \div 12 \approx 0.5833\).

Comparing these decimal values:
\(0.6667 > 0.625 > 0.6 > 0.5833\).

Thus, \(\frac{2}{3}\) is the greatest value.

  1. Conclusion and Final Answer

We have evaluated all four options:

  • Option A: \(0.6\)
  • Option B: \(\approx 0.6667\)
  • Option C: \(0.625\)
  • Option D: \(\approx 0.5833\)

Comparing them side by side, we see clearly that \(0.6667\) is the largest. Therefore, the fraction \(\frac{2}{3}\) is the greatest. The final answer is \(\boxed{\frac{2}{3}}\).

Examples

Imagine you are sharing a pizza with friends and need to decide who gets the largest slice. If one person receives \(\frac{6}{10}\) of a pizza, another receives \(\frac{2}{3}\), the third gets \(\frac{5}{8}\), and the last gets \(\frac{7}{12}\), you can use this method of decimal conversion to quickly identify that the person who received \(\frac{2}{3}\) of the pizza has the largest share. This is a practical way to handle comparisons of portions or quantities in everyday life.

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