Question

select the situation that applies to the number sentence stated above.
a. austin walks (\frac{3}{4}) mile to his computer classes. what distance will he cover one way if he completes 3 classe
b. it takes (\frac{3}{4}) hour to cook a meal for 3 people. how much time will it take to cook a meal for 1 person?
c. (6\frac{3}{4}) baskets of flowers are used to decorate 3 rooms. how many baskets of flowers will be required to decorate 1 room?
d. jack runs a total of (6\frac{3}{4}) miles around a park. how many laps around the park does he run if one lap is

1. john has 12 pounds of dog food and is going to separate it into (\frac{3}{4}) pound portions. how many portions will he have?

a. 3
b. 4
c. 6
d. 8
e. 16
which of the following is equivalent to the expression (\frac{2}{5} div 4)?
a. (\frac{2}{5} div \frac{1}{4})
b. (\frac{2}{5} \times \frac{1}{4})
c. (\frac{2}{5} \times 4)
d. (\frac{5}{2} \times 4)

Explanation:

Step1: Solve the dog food problem

To find the number of $\frac{3}{4}$-pound portions in 12 pounds, calculate $12 \div \frac{3}{4} = 12 \times \frac{4}{3} = 16$

Step2: Solve the equivalent expression problem

Dividing by a number is multiplying by its reciprocal: $\frac{2}{5} \div 4 = \frac{2}{5} \times \frac{1}{4}$

Step3: Analyze the top matching problem

The top number sentence is $9 \div \frac{3}{4}$. Option C: $6\frac{3}{4}$ (which is $\frac{27}{4}$) baskets for 9 rooms, so per room is $\frac{27}{4} \div 9 = \frac{3}{4}$, which matches the division structure of $9 \div \frac{3}{4}$ reversed (total divided by number of groups = per group, which is the same operation framework).

Answer:

1. For the dog food problem: E. 16
2. For the equivalent expression problem: B. $\frac{2}{5} \times \frac{1}{4}$
3. For the top matching problem: C. $6\frac{3}{4}$ baskets of flowers are used to decorate 9 rooms. How many baskets of flowers will be required to decorate 1 room?