Examkin

Soru

Zorluk: ZorConverting Between Fractions, Decimals, and Percents

A military medical unit is inventorying a shipment of emergency first-aid kits. Upon inspection, they determine that 1125\frac{11}{25} of the kits have missing components, and an additional 2.5%2.5\% of the kits have expired medications. If the remaining kits are fully stocked and ready for deployment, what fractional portion of the total shipment is ready for deployment?

  1. 107200\frac{107}{200}Cevap
  2. B
    93200\frac{93}{200}
  3. C
    31100\frac{31}{100}
  4. D
    5365\frac{53}{65}

Cevap

The correct fractional portion of the total shipment that is ready for deployment is 107200\frac{107}{200}.
To find the portion of kits ready for deployment, all given values must first be converted into a common format, such as percentages. The fraction of kits with missing components is 1125\frac{11}{25}. To convert this to a percentage, multiply the numerator and denominator by 44 to get 44100\frac{44}{100}, which is 44%44\%. Adding this to the 2.5%2.5\% of expired kits gives a total defective portion of 46.5%46.5\%. Since the entire shipment represents 100%100\%, the portion ready for deployment is 100%−46.5%=53.5%100\% - 46.5\% = 53.5\%. Finally, this percentage must be converted back into a fraction. 53.5%53.5\% is equivalent to 53.5100\frac{53.5}{100}, which can be written as 5351000\frac{535}{1000}. Dividing both the numerator and denominator by 55 simplifies this fraction to its lowest terms, 107200\frac{107}{200}.

Adım Adım Çözüm

1
Convert the fraction of kits with missing components into a percentage.
1125=44100=44%\frac{11}{25} = \frac{44}{100} = 44\%
Converting all values to percentages makes it easier to add the different defective portions together.
2
Calculate the total percentage of defective kits in the shipment.
44%+2.5%=46.5%44\% + 2.5\% = 46.5\%
Adding the missing component percentage and the expired medication percentage gives the total portion that cannot be deployed.
3
Determine the percentage of kits that are ready for deployment.
100%−46.5%=53.5%100\% - 46.5\% = 53.5\%
The entire shipment is 100%100\%. Subtracting the defective portion reveals the remaining ready portion.
4
Convert the final percentage back into a fully simplified fraction.
53.5%=53.5100=5351000=10720053.5\% = \frac{53.5}{100} = \frac{535}{1000} = \frac{107}{200}
The question specifically asks for the answer as a fractional portion.

Anahtar Kavram

Converting between fractions, decimals, and percentages to solve multi-step problems involving parts of a whole.
Tahmini Süre:1m 30s
Bu soruyu puanla

Konular

Converting Between Fractions, Decimals, and Percents

Bu konudan daha fazla soru