Question

1. the height of a dvd storage case is $2\frac{4}{5}$ inches tall. if each slot to hold a dvd is $\frac{1}{5}$ inches high, how many discs can it hold?
2. an automobile plant produces 8 cars per day. if the plant is open 5 days in a week, how many cars can it produce in 3 weeks?
3. on saturday, monica walked $3\frac{1}{2}$ miles and $1\frac{2}{5}$ hours. what was her walking pace in miles per hour? write your answer in simplest form.
4. the side pieces of a butterfly house are $8\frac{1}{4}$ inches long. how many side pieces can be cut from a board measuring $49\frac{1}{2}$ inches long?

Explanation:

Problem 3

Step1: Convert mixed number to improper fraction

The height of the DVD storage case is \( 2\frac{4}{5} \) inches. Convert it to an improper fraction: \( 2\frac{4}{5}=\frac{2\times5 + 4}{5}=\frac{14}{5} \) inches.

Step2: Divide total height by slot height

Each slot height is \( \frac{1}{5} \) inches. To find the number of discs, divide the total height by the slot height: \( \frac{14}{5}\div\frac{1}{5}=\frac{14}{5}\times5 = 14 \).

Step1: Calculate cars per week

The plant produces 8 cars per day and is open 5 days a week. So cars per week: \( 8\times5 = 40 \) cars.

Step2: Calculate cars in 3 weeks

Multiply cars per week by 3: \( 40\times3 = 120 \) cars.

Step1: Recall pace formula (miles/hour)

Pace is distance divided by time. Distance is \( 3\frac{1}{2}=\frac{7}{2} \) miles, time is \( 1\frac{2}{5}=\frac{7}{5} \) hours.

Step2: Divide distance by time

\( \frac{7}{2}\div\frac{7}{5}=\frac{7}{2}\times\frac{5}{7}=\frac{5}{2}=2\frac{1}{2} \) miles per hour.

Answer:

14

Problem 4