`2 of 3//4div3/4+1/4`

Options

A. (3/2)
B. (9/4)
C. (1/4)
D. none of these

Answer

To solve the expression \( 2 \text{ of } \frac{3}{4} \div \frac{3}{4} + \frac{1}{4} \), we will follow the order of operations. Let's break it down step by step.

### Step 1: Understand the expression
The term "2 of" means multiplication. Therefore, we can rewrite the expression as:
\[ 2 \times \frac{3}{4} \div \frac{3}{4} + \frac{1}{4} \]

### Step 2: Perform the multiplication
Now, we will calculate \( 2 \times \frac{3}{4} \):
\[ 2 \times \frac{3}{4} = \frac{2 \times 3}{4} = \frac{6}{4} = \frac{3}{2} \]

### Step 3: Substitute back into the expression
Now, we substitute this result back into the expression:
\[ \frac{3}{2} \div \frac{3}{4} + \frac{1}{4} \]

### Step 4: Perform the division
To divide by a fraction, we multiply by its reciprocal. Thus:
\[ \frac{3}{2} \div \frac{3}{4} = \frac{3}{2} \times \frac{4}{3} \]
Now, we can simplify:
\[ = \frac{3 \times 4}{2 \times 3} = \frac{12}{6} = 2 \]

### Step 5: Add the remaining term
Now we add \( \frac{1}{4} \) to the result:
\[ 2 + \frac{1}{4} \]
To add these, we convert 2 into a fraction with a denominator of 4:
\[ 2 = \frac{8}{4} \]
Now we can add:
\[ \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \]

### Final Answer
Thus, the final answer is:
\[ \frac{9}{4} \]

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