Simplify :
`12(1)/(2)-5.375+8.125-2.9+10-3(4)/(5)+11.08`

Options

A. `26.93`
B. `32.43`
C. `29.63`
D. `36.59`

Answer

To simplify the expression \( 12 \frac{1}{2} - 5.375 + 8.125 - 2.9 + 10 - 3 \frac{4}{5} + 11.08 \), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Convert \( 12 \frac{1}{2} \) and \( 3 \frac{4}{5} \) into improper fractions:
- \( 12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2} \)
- \( 3 \frac{4}{5} = 3 + \frac{4}{5} = \frac{15}{5} + \frac{4}{5} = \frac{19}{5} \)

### Step 2: Rewrite the Expression
Now rewrite the expression using the improper fractions:
\[ \frac{25}{2} - 5.375 + 8.125 - 2.9 + 10 - \frac{19}{5} + 11.08 \]

### Step 3: Convert Decimals to Fractions
Convert the decimal numbers to fractions:
- \( 5.375 = \frac{5375}{1000} = \frac{43}{8} \)
- \( 8.125 = \frac{8125}{1000} = \frac{65}{8} \)
- \( 2.9 = \frac{29}{10} \)
- \( 10 = \frac{10}{1} \)
- \( 11.08 = \frac{1108}{100} = \frac{277}{25} \)

### Step 4: Rewrite the Expression with Fractions
Now we have:
\[ \frac{25}{2} - \frac{43}{8} + \frac{65}{8} - \frac{29}{10} + \frac{10}{1} - \frac{19}{5} + \frac{277}{25} \]

### Step 5: Find a Common Denominator
The least common multiple (LCM) of the denominators \( 2, 8, 10, 1, 5, 25 \) is \( 200 \).

### Step 6: Convert Each Fraction
Convert each fraction to have a denominator of \( 200 \):
- \( \frac{25}{2} = \frac{2500}{200} \)
- \( \frac{43}{8} = \frac{1075}{200} \)
- \( \frac{65}{8} = \frac{1625}{200} \)
- \( \frac{29}{10} = \frac{580}{200} \)
- \( \frac{10}{1} = \frac{2000}{200} \)
- \( \frac{19}{5} = \frac{760}{200} \)
- \( \frac{277}{25} = \frac{2216}{200} \)

### Step 7: Combine the Fractions
Now combine all the fractions:
\[ \frac{2500 - 1075 + 1625 - 580 + 2000 - 760 + 2216}{200} \]

### Step 8: Calculate the Numerator
Calculate the numerator:
\[ 2500 - 1075 + 1625 - 580 + 2000 - 760 + 2216 = 2500 - 1075 = 1425 \]
\[ 1425 + 1625 = 3050 \]
\[ 3050 - 580 = 2470 \]
\[ 2470 + 2000 = 4470 \]
\[ 4470 - 760 = 3710 \]
\[ 3710 + 2216 = 5926 \]

### Step 9: Write the Final Result
So we have:
\[ \frac{5926}{200} \]

### Step 10: Simplify the Fraction
Now simplify \( \frac{5926}{200} \):
\[ 5926 \div 2 = 2963 \quad \text{and} \quad 200 \div 2 = 100 \]
Thus, the simplified result is:
\[ \frac{2963}{100} = 29.63 \]

### Final Answer
The simplified expression is \( 29.63 \).

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