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Zorluk: OrtaDividing in a Ratio

A signal corps detachment has a continuous spool of tactical fiber optic cable that is 240240 meters long. A technician must cut the entire spool into three separate sections to establish command, perimeter, and relay links in a ratio of 2:3:52:3:5 respectively. What is the length of the shortest section in centimeters?

  1. A
    4848
  2. 4,8004,800Cevap
  3. C
    6,0006,000
  4. D
    7,2007,200

Cevap

4,8004,800
The correct answer is found by first converting 240240 meters to 24,00024,000 centimeters. Then, the ratio 2:3:52:3:5 is summed to find 1010 total parts. The shortest section corresponds to 22 parts. Taking 22 out of 1010 parts of 24,00024,000 centimeters gives 210×24,000=4,800\frac{2}{10} \times 24,000 = 4,800 centimeters.

Adım Adım Çözüm

1
Convert the total length of the cable from meters to centimeters.
240 meters×100 cm/meter=24,000 cm240 \text{ meters} \times 100 \text{ cm/meter} = 24,000 \text{ cm}
The total length is given in meters, but the final question asks for the answer in centimeters.
2
Determine the total number of parts in the ratio.
2+3+5=10 total parts2 + 3 + 5 = 10 \text{ total parts}
To find the size of a single part, the ratio must be converted into a fraction of the whole.
3
Calculate the length of the shortest section.
24,000 cm×210=4,800 cm24,000 \text{ cm} \times \frac{2}{10} = 4,800 \text{ cm}
The shortest section corresponds to the smallest number in the ratio (22). Multiplying the total length by this fraction gives the length of that section.

Anahtar Kavram

To divide a quantity in a given ratio, first sum the parts of the ratio to find the total number of parts, then multiply the total quantity by the fraction representing the desired share. Always ensure units match the final question.

Alternatif Yöntem

You could also calculate the length of a single part first: 240240 meters divided by 1010 total parts is 2424 meters per part. The shortest section is 22 parts, making it 24×2=4824 \times 2 = 48 meters. Finally, convert 4848 meters to centimeters by multiplying by 100100, which gives 4,8004,800 centimeters.
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Dividing in a Ratio

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