Simplify the following :
`5-4""3/8+17/18`

Answer

To simplify the expression \( 5 - 4 \frac{3}{8} + \frac{17}{18} \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 4 \frac{3}{8} \) can be converted to an improper fraction.

\[ 4 \frac{3}{8} = \frac{(4 \times 8) + 3}{8} = \frac{32 + 3}{8} = \frac{35}{8} \]

### Step 2: Rewrite the expression
Now we can rewrite the original expression using the improper fraction:

\[ 5 - \frac{35}{8} + \frac{17}{18} \]

### Step 3: Convert whole number to a fraction
Next, we convert \( 5 \) to a fraction with a denominator of \( 1 \):

\[ 5 = \frac{5}{1} \]

### Step 4: Find the Least Common Multiple (LCM)
We need to find the LCM of the denominators \( 1, 8, \) and \( 18 \) to combine the fractions. The LCM of \( 1, 8, \) and \( 18 \) is \( 72 \).

### Step 5: Convert each fraction to have the same denominator
Now we convert each fraction to have a denominator of \( 72 \):

1. For \( \frac{5}{1} \):
\[ \frac{5}{1} = \frac{5 \times 72}{1 \times 72} = \frac{360}{72} \]

2. For \( \frac{35}{8} \):
\[ \frac{35}{8} = \frac{35 \times 9}{8 \times 9} = \frac{315}{72} \]

3. For \( \frac{17}{18} \):
\[ \frac{17}{18} = \frac{17 \times 4}{18 \times 4} = \frac{68}{72} \]

### Step 6: Rewrite the expression with the new fractions
Now we can rewrite the expression:

\[ \frac{360}{72} - \frac{315}{72} + \frac{68}{72} \]

### Step 7: Combine the fractions
Now we can combine the fractions:

\[ \frac{360 - 315 + 68}{72} = \frac{113}{72} \]

### Final Answer
Thus, the simplified form of the expression \( 5 - 4 \frac{3}{8} + \frac{17}{18} \) is:

\[ \frac{113}{72} \]

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