Solve the following expression :
`9 3/5 - 5 3/9`

Answer

To solve the expression \( 9 \frac{3}{5} - 5 \frac{3}{9} \), follow these steps:

### Step 1: Convert mixed numbers to improper fractions
First, we convert the mixed numbers into improper fractions.

For \( 9 \frac{3}{5} \):
\[ 9 \frac{3}{5} = 9 + \frac{3}{5} = \frac{9 \times 5 + 3}{5} = \frac{45 + 3}{5} = \frac{48}{5} \]

For \( 5 \frac{3}{9} \):
\[ 5 \frac{3}{9} = 5 + \frac{3}{9} = \frac{5 \times 9 + 3}{9} = \frac{45 + 3}{9} = \frac{48}{9} \]

### Step 2: Find the least common multiple (LCM) of the denominators
The denominators are 5 and 9. The LCM of 5 and 9 is 45.

### Step 3: Convert the fractions to have a common denominator
Now, we convert both fractions to have the common denominator of 45.

For \( \frac{48}{5} \):
\[ \frac{48}{5} = \frac{48 \times 9}{5 \times 9} = \frac{432}{45} \]

For \( \frac{48}{9} \):
\[ \frac{48}{9} = \frac{48 \times 5}{9 \times 5} = \frac{240}{45} \]

### Step 4: Subtract the two fractions
Now we can subtract the two fractions:
\[ \frac{432}{45} - \frac{240}{45} = \frac{432 - 240}{45} = \frac{192}{45} \]

### Step 5: Simplify the fraction
Now we simplify \( \frac{192}{45} \). We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3.

\[ \frac{192 \div 3}{45 \div 3} = \frac{64}{15} \]

### Step 6: Convert to a mixed number
Finally, we convert \( \frac{64}{15} \) to a mixed number:
\[ 64 \div 15 = 4 \quad \text{(whole number)} \]
The remainder is \( 64 - (15 \times 4) = 64 - 60 = 4 \).

Thus, we have:
\[ \frac{64}{15} = 4 \frac{4}{15} \]

### Final Answer
The final answer is:
\[ 4 \frac{4}{15} \]

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