In each question, what will come in place of question mark?
`4 ¼ + 2 ¼ div ¾ xx 4 2 /3 = ?`

Options

A. 9
B. 7
C. `1 2/7`
D. None of these

Answer

To solve the expression \( 4 \frac{1}{4} + 2 \frac{1}{4} \div \frac{3}{4} \times 4 \frac{2}{3} = ? \), we will follow the order of operations (BODMAS/BIDMAS).

### Step 1: Convert mixed numbers to improper fractions
- Convert \( 4 \frac{1}{4} \) to an improper fraction:
\[ 4 \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \]
- Convert \( 2 \frac{1}{4} \) to an improper fraction:
\[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
- Convert \( 4 \frac{2}{3} \) to an improper fraction:
\[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]

### Step 2: Substitute the improper fractions back into the expression
Now, the expression becomes:
\[ \frac{17}{4} + \frac{9}{4} \div \frac{3}{4} \times \frac{14}{3} \]

### Step 3: Perform the division
- Dividing \( \frac{9}{4} \) by \( \frac{3}{4} \):
\[ \frac{9}{4} \div \frac{3}{4} = \frac{9}{4} \times \frac{4}{3} = \frac{9 \times 4}{4 \times 3} = \frac{9}{3} = 3 \]

### Step 4: Substitute back into the expression
Now the expression is:
\[ \frac{17}{4} + 3 \times \frac{14}{3} \]

### Step 5: Perform the multiplication
- Multiply \( 3 \) by \( \frac{14}{3} \):
\[ 3 \times \frac{14}{3} = \frac{3 \times 14}{3} = 14 \]

### Step 6: Substitute back into the expression
Now the expression is:
\[ \frac{17}{4} + 14 \]

### Step 7: Convert 14 to a fraction with a common denominator
Convert \( 14 \) to a fraction with a denominator of 4:
\[ 14 = \frac{14 \times 4}{4} = \frac{56}{4} \]

### Step 8: Add the fractions
Now we can add:
\[ \frac{17}{4} + \frac{56}{4} = \frac{17 + 56}{4} = \frac{73}{4} \]

### Final Answer
Thus, the value that comes in place of the question mark is:
\[ \frac{73}{4} \]

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