Evaluate the difference:
`5(2)/(7)-4(1)/(9)`

Answer

To evaluate the difference \( 5\frac{2}{7} - 4\frac{1}{9} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 5\frac{2}{7} \):
\[ 5\frac{2}{7} = \frac{(5 \times 7) + 2}{7} = \frac{35 + 2}{7} = \frac{37}{7} \]

For \( 4\frac{1}{9} \):
\[ 4\frac{1}{9} = \frac{(4 \times 9) + 1}{9} = \frac{36 + 1}{9} = \frac{37}{9} \]

So, we rewrite the expression:
\[ 5\frac{2}{7} - 4\frac{1}{9} = \frac{37}{7} - \frac{37}{9} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the least common multiple (LCM) of the denominators 7 and 9.

The LCM of 7 and 9 is 63.

### Step 3: Convert Fractions to Have a Common Denominator
Now we convert both fractions to have the common denominator of 63.

For \( \frac{37}{7} \):
\[ \frac{37}{7} = \frac{37 \times 9}{7 \times 9} = \frac{333}{63} \]

For \( \frac{37}{9} \):
\[ \frac{37}{9} = \frac{37 \times 7}{9 \times 7} = \frac{259}{63} \]

### Step 4: Subtract the Fractions
Now we can subtract the two fractions:
\[ \frac{333}{63} - \frac{259}{63} = \frac{333 - 259}{63} = \frac{74}{63} \]

### Step 5: Final Answer
Thus, the final answer is:
\[ \frac{74}{63} \]

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