A processing machine crushes 3 1/4

Question

kilograms of dried fruits in 3/4
minute.

What process will you use to solve this problem?

(1 point)
Responses

3/4÷3 1/4
3 fourths divided by 3 1 fourth

3 1/4−3/4
3 and 1 fourth minus 3 fourths

3 14×3/4
3 and 1 fourth times 3 fourths

3 14÷3/4
3 and 1 fourth divided by 3 fourths
Question 2
(1 point)
Enter your solution as a mixed number.


kilograms per minute

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Answer 1

To determine the rate of the processing machine in kilograms per minute, you need to divide the total amount of dried fruits crushed by the time taken to crush them.

1. Convert the mixed number to an improper fraction:

   $3\frac{1}{4}$ kilograms can be converted as follows: $$3\frac{1}{4}=\frac{3\times 4+1}{4}=\frac{12+1}{4}=\frac{13}{4}$$

2. Write down the time in minutes as a fraction: The time taken is $\frac{3}{4}$ minutes.

3. Set up the division: To find kilograms per minute, you perform the division: $$\text{Rate}=\frac{\text{Total kilograms}}{\text{Time in minutes}}=\frac{\frac{13}{4}}{\frac{3}{4}}$$

4. Dividing fractions: Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{13}{4}÷\frac{3}{4}=\frac{13}{4}\times \frac{4}{3}=\frac{13\times 4}{4\times 3}=\frac{13}{3}$$

5. Convert to a mixed number: Now, convert $\frac{13}{3}$ to a mixed number: $$13÷3=4\text{(remainder 1)}$$ So, $\frac{13}{3}=4\frac{1}{3}$.

Thus, the solution is $4\frac{1}{3}$ kilograms per minute.

Final Answer:

4 1/3 kilograms per minute.