Simplification of 2.75 -1.25 +4.75 – 3.80 in fractional form is:

Options

A. `2 (9)/(20)`
B. `2 9/(10)`
C. `1 (9)/(10)`
D. `5 (9)/(20)`

Answer

To simplify the expression \(2.75 - 1.25 + 4.75 - 3.80\) and convert it into fractional form, we will follow these steps:

### Step 1: Convert the decimals to fractions
Each decimal can be expressed as a fraction.

- \(2.75 = \frac{275}{100}\)
- \(1.25 = \frac{125}{100}\)
- \(4.75 = \frac{475}{100}\)
- \(3.80 = \frac{380}{100}\)

### Step 2: Rewrite the expression with fractions
Now, we can rewrite the expression using these fractions:

\[ \frac{275}{100} - \frac{125}{100} + \frac{475}{100} - \frac{380}{100} \]

### Step 3: Combine the fractions
Since all fractions have the same denominator, we can combine them:

\[ \frac{275 - 125 + 475 - 380}{100} \]

### Step 4: Perform the arithmetic in the numerator
Now, let's simplify the numerator step by step:

1. Calculate \(275 - 125\):
\[ 275 - 125 = 150 \]

2. Calculate \(475 - 380\):
\[ 475 - 380 = 95 \]

3. Now combine these results:
\[ 150 + 95 = 245 \]

So, the numerator becomes \(245\).

### Step 5: Write the combined fraction
Now we have:

\[ \frac{245}{100} \]

### Step 6: Simplify the fraction
Next, we simplify \(\frac{245}{100}\). The greatest common divisor (GCD) of 245 and 100 is 5.

Dividing both the numerator and the denominator by 5:

\[ \frac{245 \div 5}{100 \div 5} = \frac{49}{20} \]

### Step 7: Convert to mixed number (if needed)
To express \(\frac{49}{20}\) as a mixed number, we divide 49 by 20:

- \(20\) goes into \(49\) \(2\) times (since \(20 \times 2 = 40\)).
- The remainder is \(49 - 40 = 9\).

Thus, we can write:

\[ \frac{49}{20} = 2 \frac{9}{20} \]

### Final Answer
The simplification of \(2.75 - 1.25 + 4.75 - 3.80\) in fractional form is:

\[ \frac{49}{20} \quad \text{or} \quad 2 \frac{9}{20} \]

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