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Difficulty: MediumFractions, Decimals, and Percentages

A nutritionist analyzed the proportion of daily recommended fiber provided by four different snack bars. The proportions were recorded as follows: Fruit Bar (58%58\%), Oat Bar (712\frac{7}{12}), Nut Bar (0.5850.585), and Seed Bar (35\frac{3}{5}). Arrange the four snack bars in order from the LEAST proportion of daily recommended fiber to the GREATEST proportion of daily recommended fiber.

  1. 1Fruit Bar (58%58\% of daily recommended fiber)
  2. 2Oat Bar (712\frac{7}{12} of daily recommended fiber)
  3. 3Nut Bar (0.5850.585 of daily recommended fiber)
  4. 4Seed Bar (35\frac{3}{5} of daily recommended fiber)

Answer

Fruit Bar (58%58\%), Oat Bar (712\frac{7}{12}), Nut Bar (0.5850.585), Seed Bar (35\frac{3}{5})
To order the values from least to greatest, convert each representation into a standard decimal form: Fruit Bar = 58%=0.58058\% = 0.580, Oat Bar = 712≈0.5833\frac{7}{12} \approx 0.5833, Nut Bar = 0.58500.5850, and Seed Bar = 35=0.6000\frac{3}{5} = 0.6000. Arranging these decimals in increasing order yields 0.5800<0.5833<0.5850<0.60000.5800 < 0.5833 < 0.5850 < 0.6000, which corresponds to Fruit Bar, Oat Bar, Nut Bar, and Seed Bar.

Step-by-Step Solution

1
Convert each numerical value into a common format (decimal representation) to allow direct comparison.
Fruit Bar: 58%=58100=0.58058\% = \frac{58}{100} = 0.580; Oat Bar: 712=7÷12≈0.5833\frac{7}{12} = 7 \div 12 \approx 0.5833; Nut Bar: 0.5850.585; Seed Bar: 35=610=0.600\frac{3}{5} = \frac{6}{10} = 0.600.
Converting all numbers to decimals makes it straightforward to compare place values from left to right.
2
Compare the resulting decimal values up to the thousandths place: 0.58000.5800, 0.58330.5833, 0.58500.5850, and 0.60000.6000.
In order from smallest to largest decimal value: 0.5800<0.5833<0.5850<0.60000.5800 < 0.5833 < 0.5850 < 0.6000.
Comparing the hundredths and thousandths digits shows that 0.5800.580 is smallest, followed by 0.58330.5833, then 0.5850.585, and finally 0.6000.600.
3
Map the ordered decimals back to their original snack bar representations.
Fruit Bar (58%58\%) < Oat Bar (712\frac{7}{12}) < Nut Bar (0.5850.585) < Seed Bar (35\frac{3}{5}).
This establishes the exact required sequence from least to greatest fiber proportion.

Key Concept

Converting and Comparing Mixed Numerical Representations (Fractions, Decimals, and Percentages)
Estimated Time:1m 15s
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Topics

Fractions, Decimals, and Percentages

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