Question

When fresh fish is dried, it becomes $\dfrac{1}{3}$ of its weight. How much fish Gracy will get if she dries: 300 kg fresh fish = __________ kg dried fish, 900 kg fresh fish = __________ kg dried fish.

Answer 1

Hint: First, we must understand that the weight is reduced to $\dfrac{1}{3}$ of its initial value, after the fish is dried. Hence, we need to divide the given weights of fresh fish, that is, 300 kg and 900 kg, to set the value of weight of dried fish for both cases.

Complete step by step answer:
We are given that when a fresh fish is dried, it loses $\dfrac{2}{3}$ of its weight and the final weight is $\dfrac{1}{3}$ of the weight of fresh fish.
So, if the weight of fresh fish is $x$ kg, then the weight of dried fish will be equal to $\dfrac{x}{3}$ kg.
Hence, using this information we can say that, if the weight of fresh fish is 300 kg, then the weight of dried fish will be equal to $\dfrac{300}{3}$ kg.
We can easily tell that 3 is a factor of 300, and so we can perfectly divide 300 by 3. We will see that on division, the quotient will be equal to 100.
Thus, we can say that, if the weight of fresh fish is 300 kg, then the weight of dried fish will be equal to 100 kg.
Again, using the same technique, we can say that if the weight of fresh fish is 900 kg, then the weight of dried fish will be equal to $\dfrac{900}{3}$ kg.
We can easily tell that 3 is a factor of 900, and so we can perfectly divide 900 by 3. We will see that on division, the quotient will be equal to 300.
Thus, we can say that, if the weight of fresh fish is 900 kg, then the weight of dried fish will be equal to 300 kg.
Hence, 300 kg of fresh fish = 100 kg of dried fish, and 900 kg of fresh fish = 300 kg of dried fish.

Note: We must understand that a multiplication by the fraction $\dfrac{1}{3}$, is exactly the same as division by 3. Also, we must note that the answer for the above question can also be in decimals or fraction, if the data is changed.