Question

john has 12 pounds of dog food and is going to separate it into \\(\frac{3}{4}\\) pound portions. how many portions of dog food will he have?
a) 3
b) 4
c) 8
d) 9
e) 16

Explanation:

Step1: Identify the operation

To find the number of portions, we divide the total amount of dog food by the size of each portion. So we use the formula \( \text{Number of portions} = \frac{\text{Total amount}}{\text{Portion size}} \). Here, total amount is 12 pounds and portion size is \( \frac{3}{4} \) pound.

Step2: Perform the division

Dividing 12 by \( \frac{3}{4} \) is the same as multiplying 12 by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \). So \( 12\times\frac{4}{3} \).
First, simplify 12 and 3: 12 divided by 3 is 4. Then multiply 4 by 4, which gives 16.

Answer:

E. 16