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Question

Difficulty: MediumFractions, Decimals, and Percentages

Four real estate agents reported the proportion of their home listings that sold above asking price last month as follows: Agent W reported 3150\frac{31}{50}, Agent X reported 58\frac{5}{8}, Agent Y reported 63%63\%, and Agent Z reported 0.640.64. Place the four agents in order from the smallest proportion of listings sold above asking price to the largest proportion.

  1. 1Agent W: 3150\frac{31}{50}
  2. 2Agent X: 58\frac{5}{8}
  3. 3Agent Y: 63%63\%
  4. 4Agent Z: 0.640.64

Answer

The correct order from smallest to largest proportion is Agent W (31/50 = 0.62), Agent X (5/8 = 0.625), Agent Y (63% = 0.63), and Agent Z (0.64).
To place the values in ascending order, convert all values to decimals: Agent W = 31/50 = 0.620, Agent X = 5/8 = 0.625, Agent Y = 63% = 0.630, and Agent Z = 0.640. Arranging these from least to greatest gives 0.620 < 0.625 < 0.630 < 0.640, corresponding to the sequence Agent W, Agent X, Agent Y, and Agent Z.

Step-by-Step Solution

1
Convert each fraction, percentage, and decimal to a common decimal representation to facilitate comparison.
All four numbers will be expressed as decimals rounded/extended to three decimal places.
Converting all values to decimals makes comparing their magnitudes straightforward.
2
Convert Agent W's value: 3150\frac{31}{50}.
3150=62100=0.620\frac{31}{50} = \frac{62}{100} = 0.620
Multiply numerator and denominator by 2 to convert to hundreds.
3
Convert Agent X's value: 58\frac{5}{8}.
58=5÷8=0.625\frac{5}{8} = 5 \div 8 = 0.625
Perform long division of 5 by 8.
4
Convert Agent Y's value: 63%63\%.
63%=63100=0.63063\% = \frac{63}{100} = 0.630
Divide percentage value by 100 to obtain decimal format.
5
Note Agent Z's value, which is already a decimal.
0.64=0.6400.64 = 0.640
Align decimal places with the other converted values.
6
Order the decimal values from smallest to largest.
0.620<0.625<0.630<0.6400.620 < 0.625 < 0.630 < 0.640, which corresponds to Agent W, Agent X, Agent Y, and Agent Z.
Comparing digits from left to right establishes the proper sequence.

Key Concept

Comparing and ordering real numbers by converting fractions, decimals, and percentages into a unified numerical format.
Estimated Time:1m 15s
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Topics

Fractions, Decimals, and Percentages

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