To change a decimal numeral to a fraction, express the decimal as a fraction with denominator 10,100 , 1000 and then reduce it to its lowest term.
The sum of 67.25,5.5,9.86 in fraction form is

Options

A. `( 8261)/(100)`
B. `( 413)/( 5)`
C. 207
D. `( 820)/( 100)`

Answer

To solve the problem of finding the sum of 67.25, 5.5, and 9.86 in fraction form, we will follow these steps:

### Step 1: Convert each decimal to a fraction

1. **Convert 67.25 to a fraction:**
- The decimal 67.25 has two decimal places, so we can express it as:
\[ 67.25 = \frac{6725}{100} \]

2. **Convert 5.5 to a fraction:**
- The decimal 5.5 has one decimal place, so we can express it as:
\[ 5.5 = \frac{55}{10} \]

3. **Convert 9.86 to a fraction:**
- The decimal 9.86 has two decimal places, so we can express it as:
\[ 9.86 = \frac{986}{100} \]

### Step 2: Find a common denominator

The least common multiple (LCM) of the denominators 100 and 10 is 100. We will convert all fractions to have a denominator of 100.

- For \( \frac{55}{10} \):
\[ \frac{55}{10} = \frac{55 \times 10}{10 \times 10} = \frac{550}{100} \]

### Step 3: Add the fractions

Now we can add the fractions together:
\[ \frac{6725}{100} + \frac{550}{100} + \frac{986}{100} \]

Combine the numerators:
\[ \frac{6725 + 550 + 986}{100} = \frac{7261}{100} \]

### Step 4: Reduce to lowest terms

The fraction \( \frac{7261}{100} \) is already in its simplest form since 7261 and 100 have no common factors other than 1.

### Final Answer

Thus, the sum of 67.25, 5.5, and 9.86 in fraction form is:
\[ \frac{7261}{100} \]

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