Let's work through this homework sheet. I'll solve each part step by step for clarity.

1. Solve each equation (fractions):

a. $\frac{9}{10} = \frac{n}{100}$
To solve for $n$, cross-multiply: $9 \times 100 = 10 \times n \implies 900 = 10n \implies n = \frac{900}{10} = 90$ So, $\frac{9}{10} = \frac{90}{100}$.

b. $\frac{5}{2} = \frac{n}{100}$
Cross-multiply: $5 \times 100 = 2 \times n \implies 500 = 2n \implies n = \frac{500}{2} = 250$ So, $\frac{5}{2} = \frac{250}{100}$.

c. $\frac{3}{15} = \frac{5}{n}$
Cross-multiply: $3 \times n = 15 \times 5 \implies 3n = 75 \implies n = \frac{75}{3} = 25$ So, $\frac{3}{15} = \frac{5}{25}$.

d. $\frac{9}{12} = \frac{n}{100}$
Cross-multiply: $9 \times 100 = 12 \times n \implies 900 = 12n \implies n = \frac{900}{12} = 75$ So, $\frac{9}{12} = \frac{75}{100}$.

2. Divide using long division:

a. $13 \div 2 = 6$ remainder $1$ or $6.5$

b. $27 \div 5 = 5$ remainder $2$ or $5.4$

c. $30 \div 5 = 6$

d. $6.84 \div 6 = 1.14$

3. Lin bought 3 hats for $22.50.

a. What is the price per hat?
Divide the total cost by the number of hats: $\frac{22.50}{3} = 7.50$ So, each hat costs $7.50.

b. At this rate, how many hats could she buy with $60.00?
Divide $60.00 by the price per hat: $\frac{60}{7.50} = 8$ So, she could buy 8 hats.

4. Length and inches:

a. How many inches is 4 feet?
Since 1 foot = 12 inches, multiply: $4 \times 12 = 48 \text{ inches}$

b. How many feet is 36 inches?
Divide by the number of inches in a foot: $\frac{36}{12} = 3 \text{ feet}$

c. Celeste is 5 feet 2 inches. How many inches is she?
Convert 5 feet to inches and add the extra 2 inches: $5 \times 12 + 2 = 60 + 2 = 62 \text{ inches}$

d. What is your height in inches?
You'll have to fill this one based on your height!

Would you like further explanation on any of the steps? Here are some additional questions related to this homework:

1. If Lin bought 5 hats for $37.50, what would be the price per hat?
2. How many hats could Lin buy for $45.00 at the same price per hat?
3. If a person is 6 feet 3 inches tall, how many inches is that?
4. If a car drives 5280 feet, how many miles has it traveled? (1 mile = 5280 feet)
5. What is the remainder when 29 is divided by 4?

Tip: When converting units, always make sure to apply the same conversion ratio (like 1 foot = 12 inches) correctly across all parts of the problem!