Nita , Craig , and chris catch a total of 300 fish on their trip if Chris catches 45% of the fish and Craig catches 25 fish what fraction of the 300 fish does Nita catch ?

Options

A. `(23)/(30)`
B. `(41)/(60)`
C. `(1)/(2)`
D. `(7)/(15)`

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Calculate the number of fish Chris caught.
Chris catches 45% of the total fish. The total number of fish caught is 300.

\[ \text{Fish caught by Chris} = 45\% \text{ of } 300 = \frac{45}{100} \times 300 \]

Calculating this:

\[ \text{Fish caught by Chris} = \frac{45 \times 300}{100} = \frac{13500}{100} = 135 \]

### Step 2: Determine the number of fish Craig caught.
According to the problem, Craig catches 25 fish.

\[ \text{Fish caught by Craig} = 25 \]

### Step 3: Calculate the total number of fish caught by Chris and Craig.
Now, we add the number of fish caught by Chris and Craig:

\[ \text{Total fish caught by Chris and Craig} = \text{Fish caught by Chris} + \text{Fish caught by Craig} = 135 + 25 = 160 \]

### Step 4: Calculate the number of fish caught by Nita.
To find out how many fish Nita caught, we subtract the total fish caught by Chris and Craig from the total number of fish:

\[ \text{Fish caught by Nita} = \text{Total fish} - \text{Total fish caught by Chris and Craig} = 300 - 160 = 140 \]

### Step 5: Find the fraction of fish caught by Nita.
Now, we need to find the fraction of the total fish that Nita caught:

\[ \text{Fraction of fish caught by Nita} = \frac{\text{Fish caught by Nita}}{\text{Total fish}} = \frac{140}{300} \]

### Step 6: Simplify the fraction.
To simplify the fraction \(\frac{140}{300}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 20:

\[ \frac{140 \div 20}{300 \div 20} = \frac{7}{15} \]

### Final Answer:
Thus, the fraction of the 300 fish that Nita caught is \(\frac{7}{15}\).

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