To simplify [tex]\(\frac{9}{10} \div 2\)[/tex], follow these steps:
1. Understand the divisor operation:
Dividing by a number is the same as multiplying by its reciprocal. So, dividing by [tex]\(2\)[/tex] is equivalent to multiplying by [tex]\(\frac{1}{2}\)[/tex].
2. Rewrite the expression using multiplication:
[tex]\[
\frac{9}{10} \div 2 = \frac{9}{10} \times \frac{1}{2}
\][/tex]
3. Multiply the fractions:
To multiply two fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{9}{10} \times \frac{1}{2} = \frac{9 \times 1}{10 \times 2} = \frac{9}{20}
\][/tex]
4. Determine the simplified fraction:
The result of the division is [tex]\(\frac{9}{20}\)[/tex]. Converting this to a decimal, we get [tex]\(0.45\)[/tex].
Given the options:
A. [tex]\(5 \frac{5}{6}\)[/tex]
B. [tex]\(\frac{1}{4}\)[/tex]
C. [tex]\(2 \frac{9}{10}\)[/tex]
D. [tex]\(\frac{9}{20}\)[/tex]
The correct answer is:
[tex]\[
\boxed{\frac{9}{20}}
\][/tex]
