Question

directions: for each problem, write either a multiplication or a division expression that can be used to solve the problem. then solve. show all steps.

1. if a puppet requires \\(\frac{3}{4}\\) yard of material, how many puppets can be made from 9 yards of material?
2. robin has read \\(\frac{3}{4}\\) of a book. mark said he had read \\(\frac{1}{2}\\) as much as robin. what fraction of the book has mark read?
3. a radio station spends \\(\frac{1}{40}\\) of each 24 hours on public service announcements. how many hours are spent on public service announcements each day?
4. randy has two 28-pound blocks of ice for his snow cone stand. if each snow cone requires \\(\frac{2}{3}\\) pound of ice, how many snow cones can randy make?

Explanation:

Problem 5:

Step1: Identify operation

To find the number of puppets, divide total material by material per puppet: \( 9 \div \frac{3}{4} \).

Step2: Divide by fraction

Dividing by a fraction is multiplying by its reciprocal: \( 9 \times \frac{4}{3} \).

Step3: Simplify

\( 9 \times \frac{4}{3} = 3 \times 4 = 12 \).

Step1: Identify operation

To find Mark's reading, multiply Robin's fraction by \( \frac{1}{2} \): \( \frac{3}{4} \times \frac{1}{2} \).

Step2: Multiply fractions

Multiply numerators and denominators: \( \frac{3 \times 1}{4 \times 2} = \frac{3}{8} \).

Step1: Identify operation

To find hours on announcements, multiply total hours by \( \frac{1}{40} \): \( 24 \times \frac{1}{40} \).

Step2: Simplify

\( 24 \times \frac{1}{40} = \frac{24}{40} = \frac{3}{5} = 0.6 \) hours.

Answer:

12 puppets

Problem 6: