Simpilfy:
`5(3)/(4)- 4 (5)/(12)+3(1)/(6)`

Answer

To simplify the expression \( 5 \frac{3}{4} - 4 \frac{5}{12} + 3 \frac{1}{6} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert each mixed number into an improper fraction.

1. For \( 5 \frac{3}{4} \):
\[ 5 \frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} \]

2. For \( 4 \frac{5}{12} \):
\[ 4 \frac{5}{12} = \frac{4 \times 12 + 5}{12} = \frac{48 + 5}{12} = \frac{53}{12} \]

3. For \( 3 \frac{1}{6} \):
\[ 3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6} \]

Now, we rewrite the expression:
\[ \frac{23}{4} - \frac{53}{12} + \frac{19}{6} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \( 4, 12, \) and \( 6 \).

- The multiples of \( 4 \) are \( 4, 8, 12, 16, 20, \ldots \)
- The multiples of \( 12 \) are \( 12, 24, 36, \ldots \)
- The multiples of \( 6 \) are \( 6, 12, 18, 24, \ldots \)

The LCM of \( 4, 12, \) and \( 6 \) is \( 12 \).

### Step 3: Convert Each Fraction to Have the Same Denominator
Now we convert each fraction to have the denominator of \( 12 \).

1. For \( \frac{23}{4} \):
\[ \frac{23}{4} = \frac{23 \times 3}{4 \times 3} = \frac{69}{12} \]

2. For \( \frac{53}{12} \), it already has the denominator of \( 12 \):
\[ \frac{53}{12} = \frac{53}{12} \]

3. For \( \frac{19}{6} \):
\[ \frac{19}{6} = \frac{19 \times 2}{6 \times 2} = \frac{38}{12} \]

Now, the expression is:
\[ \frac{69}{12} - \frac{53}{12} + \frac{38}{12} \]

### Step 4: Combine the Fractions
Now we can combine the fractions:
\[ \frac{69 - 53 + 38}{12} = \frac{69 - 53 + 38}{12} = \frac{54}{12} \]

### Step 5: Simplify the Result
Now we simplify \( \frac{54}{12} \):
\[ \frac{54 \div 6}{12 \div 6} = \frac{9}{2} \]

### Final Answer
The simplified result is:
\[ \frac{9}{2} \text{ or } 4 \frac{1}{2} \]

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