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A CB radio antenna measures 56 ⅙ cm when it is fully extended but only 31 ⅔ cm when it is retracted. How long is the extension?

User Spire
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1 Answer

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Final answer:

To find the extension length of the antenna, subtract the retracted length from the extended length. After doing the fraction subtraction, it is found that the antenna extends by 24 1/2 cm or 24.5 cm.

Step-by-step explanation:

The question asks us to calculate how long the extension of a CB radio antenna is, when it is known that the fully extended length is 56 1/6 cm and the retracted length is 31 2/3 cm.

To find the length of the antenna extension, we subtract the retracted length from the fully extended length.

Steps to calculate the antenna extension:

  1. Convert the mixed fractions to improper fractions for easier calculation. 56 1/6 cm becomes (6×56+1)/6 = 337/6 cm and 31 2/3 cm becomes (3×31+2)/3 = 95/3 cm.
  2. Subtract the retracted length from the fully extended length: (337/6) cm - (95/3) cm.
  3. Find a common denominator and subtract the fractions: (337/6 - 190/6) cm = 147/6 cm.
  4. Convert the improper fraction back to a mixed number: 147/6 cm = 24 1/2 cm.

Therefore, the length of the antenna's extension is 24 1/2 cm or 24.5 cm.

User Andrei Solero
by
8.3k points

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