Work out the following :
`3""2/7-1""4/7`

Answer

To solve the problem \( 3 \frac{2}{7} - 1 \frac{4}{7} \), we will follow these steps:

### Step 1: Convert the mixed fractions to improper fractions.
A mixed fraction consists of a whole number and a proper fraction. To convert a mixed fraction to an improper fraction, we use the formula:

\[ \text{Improper Fraction} = ( \text{Whole Number} \times \text{Denominator} ) + \text{Numerator} \div \text{Denominator} \]

For \( 3 \frac{2}{7} \):
- Whole number = 3
- Numerator = 2
- Denominator = 7

\[ 3 \frac{2}{7} = \frac{(3 \times 7) + 2}{7} = \frac{21 + 2}{7} = \frac{23}{7} \]

For \( 1 \frac{4}{7} \):
- Whole number = 1
- Numerator = 4
- Denominator = 7

\[ 1 \frac{4}{7} = \frac{(1 \times 7) + 4}{7} = \frac{7 + 4}{7} = \frac{11}{7} \]

### Step 2: Subtract the improper fractions.
Now we have:

\[ \frac{23}{7} - \frac{11}{7} \]

Since both fractions have the same denominator, we can subtract the numerators:

\[ \frac{23 - 11}{7} = \frac{12}{7} \]

### Step 3: Convert the result back to a mixed fraction.
To convert \( \frac{12}{7} \) back to a mixed fraction, we divide the numerator by the denominator:

- \( 12 \div 7 = 1 \) (whole number)
- Remainder = \( 12 - (7 \times 1) = 5 \)

Thus, we can write:

\[ \frac{12}{7} = 1 \frac{5}{7} \]

### Final Answer:
The result of \( 3 \frac{2}{7} - 1 \frac{4}{7} \) is \( 1 \frac{5}{7} \).

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