What fraction is `3 L` `150 mL` of `7 L` `350 mL`?

Options

A. `(9)/(7)`
B. `(3)/(7)`
C. `(8)/(7)`
D. `(3)/(2)`

Answer

To find the fraction of `3 L 150 mL` of `7 L 350 mL`, we can follow these steps:

### Step 1: Convert liters to milliliters
We know that `1 liter = 1000 milliliters`. Therefore, we need to convert both `3 L 150 mL` and `7 L 350 mL` into milliliters.

- For `3 L 150 mL`:
\[ 3 L = 3 \times 1000 = 3000 \text{ mL} \]
Adding the `150 mL`:
\[ 3000 \text{ mL} + 150 \text{ mL} = 3150 \text{ mL} \]

- For `7 L 350 mL`:
\[ 7 L = 7 \times 1000 = 7000 \text{ mL} \]
Adding the `350 mL`:
\[ 7000 \text{ mL} + 350 \text{ mL} = 7350 \text{ mL} \]

### Step 2: Write the fraction
Now we can write the fraction of `3 L 150 mL` of `7 L 350 mL` as:
\[ \frac{3150 \text{ mL}}{7350 \text{ mL}} \]

### Step 3: Simplify the fraction
To simplify the fraction, we can divide both the numerator and the denominator by `3150`:
\[ \frac{3150 \div 3150}{7350 \div 3150} = \frac{1}{\frac{7350}{3150}} \]

Calculating `7350 ÷ 3150` gives us `2.3333`, which is not an integer. So, we can further simplify the fraction by finding the greatest common divisor (GCD).

The GCD of `3150` and `7350` is `3150`. Therefore:
\[ \frac{3150}{7350} = \frac{1}{2.3333} \text{ (not simplified)} \]

Instead, we can divide both numbers by `1050`:
\[ \frac{3150 \div 1050}{7350 \div 1050} = \frac{3}{7} \]

### Final Answer
Thus, the fraction of `3 L 150 mL` of `7 L 350 mL` is:
\[ \frac{3}{7} \]

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