To determine which of the given options represents 9.2 as a mixed number in its simplest form, let's analyze and simplify 9.2 step-by-step:
1. Convert 9.2 to a Fraction:
- 9.2 can be expressed as 9.2/1.
- To eliminate the decimal, multiply both the numerator and denominator by 10, resulting in 92/10.
2. Simplify the Fraction:
- The fraction 92/10 can be simplified. The greatest common divisor (GCD) of 92 and 10 is 2.
- Dividing both the numerator and the denominator by 2, we get (92 ÷ 2) / (10 ÷ 2) = 46 / 5.
3. Convert to a Mixed Number:
- The fraction 46/5 can be expressed as a mixed number.
- Divide 46 by 5. The quotient is 9 and the remainder is 1.
- So, 46/5 is equivalent to 9 whole and 1/5.
Thus, 9.2 as a mixed number in simplest form is [tex]\(9 \frac{1}{5}\)[/tex].
Now we compare this with the given options:
A. [tex]$9 / 2$[/tex] - This fraction is not equivalent to 9.2.
B. [tex]$91 / 5$[/tex] - Simplifies to 18 [tex]\(\frac{1}{5}\)[/tex] which is not correct.
C. [tex]$29 / 10$[/tex] - This is not equivalent to 9.2.
D. [tex]$2 / 9$[/tex] - This fraction is clearly incorrect.
Since none of these options match [tex]\(9 \frac{1}{5}\)[/tex] correctly, the answer is:
None of the options are correct.
