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:
- 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.
- Subtract the retracted length from the fully extended length: (337/6) cm - (95/3) cm.
- Find a common denominator and subtract the fractions: (337/6 - 190/6) cm = 147/6 cm.
- 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.