Simplify : a. `((4)/(7) div (36)/(49)) - (1)/(2)`

Answer

To simplify the expression \(\frac{4}{7} \div \frac{36}{49} - \frac{1}{2}\), we will follow these steps:

### Step 1: Rewrite the Division as Multiplication
The division of fractions can be rewritten as multiplication by the reciprocal. Therefore, we can rewrite the expression as:
\[ \frac{4}{7} \div \frac{36}{49} = \frac{4}{7} \times \frac{49}{36} \]

### Step 2: Multiply the Fractions
Now, we can multiply the fractions:
\[ \frac{4 \times 49}{7 \times 36} \]

### Step 3: Simplify the Multiplication
Next, we can simplify the multiplication:
- \(49 = 7 \times 7\)
- \(36 = 9 \times 4\)

So, the expression becomes:
\[ \frac{4 \times (7 \times 7)}{7 \times (9 \times 4)} \]

### Step 4: Cancel Common Factors
Now, we can cancel the common factors in the numerator and denominator:
- The \(4\) in the numerator and denominator cancels out.
- The \(7\) in the numerator and denominator cancels out.

This leaves us with:
\[ \frac{7}{9} \]

### Step 5: Subtract \(\frac{1}{2}\)
Now we need to subtract \(\frac{1}{2}\) from \(\frac{7}{9}\):
\[ \frac{7}{9} - \frac{1}{2} \]

### Step 6: Find the LCM
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of \(9\) and \(2\) is \(18\).

### Step 7: Rewrite the Fractions with the Common Denominator
Now, we rewrite both fractions with the common denominator of \(18\):
\[ \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} \]
\[ \frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18} \]

### Step 8: Perform the Subtraction
Now we can perform the subtraction:
\[ \frac{14}{18} - \frac{9}{18} = \frac{14 - 9}{18} = \frac{5}{18} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{5}{18} \]