Sure, let's address each question step-by-step.
### Question 1: How many groups of [tex]\(\frac{9}{2}\)[/tex] are in 1?
1. We start by understanding what it means to find how many groups of [tex]\(\frac{9}{2}\)[/tex] fit into 1. This can be expressed as division: [tex]\(1 \div \frac{9}{2}\)[/tex].
2. When we divide by a fraction [tex]\(\frac{a}{b}\)[/tex], it is equivalent to multiplying by its reciprocal [tex]\(\frac{b}{a}\)[/tex]. Hence,
[tex]\[
1 \div \frac{9}{2} = 1 \times \frac{2}{9} = \frac{2}{9}
\][/tex]
3. Converting [tex]\(\frac{2}{9}\)[/tex] to a decimal, we get approximately [tex]\(0.2222222222222222\)[/tex].
Therefore, the number of groups of [tex]\(\frac{9}{2}\)[/tex] in 1 is [tex]\(\boxed{0.2222222222222222}\)[/tex] groups.
### Question 2: Evaluate [tex]\(4 \div \frac{9}{2}\)[/tex]
1. To evaluate the division of 4 by [tex]\(\frac{9}{2}\)[/tex], we again multiply by the reciprocal of [tex]\(\frac{9}{2}\)[/tex]:
[tex]\[
4 \div \frac{9}{2} = 4 \times \frac{2}{9}
\][/tex]
2. Simplify the multiplication:
[tex]\[
4 \times \frac{2}{9} = \frac{4 \times 2}{9} = \frac{8}{9}
\][/tex]
3. Converting [tex]\(\frac{8}{9}\)[/tex] to a decimal, we get approximately [tex]\(0.8888888888888888\)[/tex].
So, [tex]\(4 \div \frac{9}{2} = \boxed{0.8888888888888888}\)[/tex].
By following these steps, we have found the solutions to both questions.
