Question

name date period
unit 4 lesson 9 cumulative practice problems

1. a group of friends is sharing $2\frac{1}{2}$ pounds of berries.

• if each friend received $\frac{5}{4}$ of a pound of berries, how many friends are sharing the berries?
• if 5 friends are sharing the berries, how many pounds of berries does each friend receive?

1. $\frac{2}{5}$ kilogram of soil fills $\frac{1}{3}$ of a container. can 1 kilogram of soil fit in the container? explain or show your reasoning.

1. 3 tickets to the museum cost $12.75. at this rate, what is the cost of:

• 1 ticket?
• 5 tickets?

Explanation:

Problem 1a: Step1: Convert mixed number to improper fraction

$2\frac{1}{2} = \frac{5}{2}$

Problem 1a: Step2: Divide total berries by per-friend amount

$\frac{5}{2} \div \frac{5}{4} = \frac{5}{2} \times \frac{4}{5} = 2$

Problem 1b: Step1: Convert mixed number to improper fraction

$2\frac{1}{2} = \frac{5}{2}$

Problem 1b: Step2: Divide total berries by number of friends

$\frac{5}{2} \div 5 = \frac{5}{2} \times \frac{1}{5} = \frac{1}{2}$

Problem 2: Step1: Find container total capacity

$\frac{2}{5} \div \frac{1}{3} = \frac{2}{5} \times 3 = \frac{6}{5}$

Problem 2: Step2: Compare capacity to 1 kilogram

$\frac{6}{5} = 1.2$, which is greater than 1

Problem 3a: Step1: Divide total cost by number of tickets

$\$12.75 \div 3 = \$4.25$

Problem 3b: Step1: Multiply single ticket cost by 5

$\$4.25 \times 5 = \$21.25$

Answer:

1.

• Number of friends: 2
• Berries per friend: $\frac{1}{2}$ pounds

1. Yes, 1 kilogram of soil can fit. The container's total capacity is $\frac{6}{5}$ (or 1.2) kilograms, which is larger than 1 kilogram.

3.

• Cost of 1 ticket: $\$4.25$
• Cost of 5 tickets: $\$21.25$