What is 4.65 converted to a fraction? The answer should be given in simplest form.(1 point)

Responses

41320
4 Start Fraction 13 over 20 End Fraction

465
4 Start Fraction 6 over 5 End Fraction

465100
4 Start Fraction 65 over 100 End Fraction

465
Start Fraction 4 over 65 End Fraction

1 answer

To convert 4.65 to a fraction in simplest form, you can follow these steps:

  1. Separate the whole number and decimal:
    4.65 can be written as \( 4 + 0.65 \).

  2. Convert the decimal to a fraction:
    \( 0.65 \) is the same as \( \frac{65}{100} \).

  3. Reduce the fraction \( \frac{65}{100} \):
    The greatest common divisor (GCD) of 65 and 100 is 5.
    Dividing both the numerator and denominator by 5 gives:
    \[ \frac{65 \div 5}{100 \div 5} = \frac{13}{20} \]

  4. Combine with the whole number:
    So, \( 4.65 = 4 + \frac{13}{20} = \frac{4 \times 20 + 13}{20} = \frac{80 + 13}{20} = \frac{93}{20} \).

Therefore, the simplest form of 4.65 as a fraction is: \[ \frac{93}{20} \]

So, among the provided choices, the equivalent form for 4.65 is: \[ 4 \frac{13}{20} \]

The correct answer is 4 Start Fraction 13 over 20 End Fraction.