Answered

Turn each fraction into a decimal and determine which number has the greatest value.


A$\frac{5}{8}$
B$\frac{1}{3}$
C$\frac{4}{5}$
D$\frac{1}{2}$

Verified Answer :

  • Divide the numerator of each fraction by its denominator to find the decimal equivalent: \(\frac{5}{8} = 0.625\), \(\frac{1}{3} \approx 0.333\), \(\frac{4}{5} = 0.8\), and \(\frac{1}{2} = 0.5\).
  • Compare the decimal results: \(0.333 < 0.5 < 0.625 < 0.8\).
  • Identify the greatest value, which corresponds to \(\frac{4}{5}\).
  • Final answer: \(\boxed{\frac{4}{5}}\).

Explanation

  1. Problem Analysis and Strategy

To determine which of the fractions \(\frac{5}{8}\), \(\frac{1}{3}\), \(\frac{4}{5}\), and \(\frac{1}{2}\) has the greatest value, we convert each fraction into its decimal representation by dividing the numerator by the denominator.

  1. Decimal Conversion

We perform the divisions for each fraction:

  • For \(\frac{5}{8}\): \(5 \div 8 = 0.625\)
  • For \(\frac{1}{3}\): \(1 \div 3 = 0.333...\)
  • For \(\frac{4}{5}\): \(4 \div 5 = 0.8\)
  • For \(\frac{1}{2}\): \(1 \div 2 = 0.5\)
  1. Comparison and Final Conclusion

Comparing the calculated decimal values:

  • \(0.8 > 0.625 > 0.5 > 0.333...\)

Since \(0.8\) is the largest decimal value, the fraction corresponding to \(0.8\) is the greatest. Comparing the results, \(\frac{4}{5}\) is the greatest fraction.

Examples

Comparing fractions is a foundational skill in real life. For example, if you are shopping and see different items on sale, you might need to determine which discount is the largest. If one store offers 4/5 off and another offers 5/8 off, converting them to decimals helps you instantly realize that 0.8 (or 80%) is a bigger discount than 0.625 (or 62.5%), allowing you to choose the best deal.

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