In `2/3 , 3/5 , 5/8` the difference between the the largest and the smallest fraction is

Options

A. `1/15`
B. `1/24`
C. `1/40`
D. None of these

Answer

To find the difference between the largest and smallest fractions among \( \frac{2}{3}, \frac{3}{5}, \frac{5}{8} \), we will follow these steps:

### Step 1: Identify the fractions
The fractions given are:
1. \( \frac{2}{3} \)
2. \( \frac{3}{5} \)
3. \( \frac{5}{8} \)

### Step 2: Convert each fraction to decimal form
To compare the fractions easily, we can convert them to decimal values:

- For \( \frac{2}{3} \):
\[ \frac{2}{3} \approx 0.6667 \]

- For \( \frac{3}{5} \):
\[ \frac{3}{5} = 0.6 \]

- For \( \frac{5}{8} \):
\[ \frac{5}{8} = 0.625 \]

### Step 3: Determine the largest and smallest fractions
From the decimal values:
- \( \frac{2}{3} \approx 0.6667 \) (largest)
- \( \frac{3}{5} = 0.6 \) (smallest)

Thus, the largest fraction is \( \frac{2}{3} \) and the smallest fraction is \( \frac{3}{5} \).

### Step 4: Calculate the difference between the largest and smallest fractions
Now we will find the difference:
\[ \text{Difference} = \text{Largest} - \text{Smallest} = \frac{2}{3} - \frac{3}{5} \]

### Step 5: Find a common denominator
The least common multiple (LCM) of 3 and 5 is 15. We will convert both fractions to have this common denominator:
- For \( \frac{2}{3} \):
\[ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} \]

- For \( \frac{3}{5} \):
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

### Step 6: Subtract the fractions
Now we can subtract:
\[ \frac{10}{15} - \frac{9}{15} = \frac{10 - 9}{15} = \frac{1}{15} \]

### Final Answer
The difference between the largest and smallest fraction is:
\[ \frac{1}{15} \]

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