Question

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

Answer 1

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**.