Simplify : b. `(5)/(9) div ((3)/(10) xx (5)/(12))`

Answer

Let's simplify the expression step by step:

### Step 1: Write the expression
We start with the expression:
\[ \frac{5}{9} \div \left( \frac{3}{10} \times \frac{5}{12} \right) \]

### Step 2: Simplify the bracket
First, we need to simplify the term inside the bracket:
\[ \frac{3}{10} \times \frac{5}{12} \]
To multiply fractions, we multiply the numerators and the denominators:
\[ = \frac{3 \times 5}{10 \times 12} = \frac{15}{120} \]

### Step 3: Reduce the fraction
Now, we can simplify \(\frac{15}{120}\):
\[ \frac{15 \div 15}{120 \div 15} = \frac{1}{8} \]

### Step 4: Rewrite the division as multiplication
Now we rewrite the original expression:
\[ \frac{5}{9} \div \frac{1}{8} \]
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ = \frac{5}{9} \times \frac{8}{1} \]

### Step 5: Multiply the fractions
Now we multiply the fractions:
\[ = \frac{5 \times 8}{9 \times 1} = \frac{40}{9} \]

### Step 6: Convert to mixed fraction (if needed)
To convert \(\frac{40}{9}\) into a mixed fraction, we divide 40 by 9:
- 9 goes into 40 four times (since \(9 \times 4 = 36\)).
- The remainder is \(40 - 36 = 4\).

Thus, we can write:
\[ \frac{40}{9} = 4 \frac{4}{9} \]

### Final Answer
The simplified form of the expression is:
\[ \frac{40}{9} \text{ or } 4 \frac{4}{9} \]

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