Simplify the following expressions :
`3/7 div 2/7 xx 21/8`

Answer

To simplify the expression \( \frac{3}{7} \div \frac{2}{7} \times \frac{21}{8} \), we can follow these steps:

### Step 1: Rewrite the Division as Multiplication
When dividing by a fraction, we can multiply by its reciprocal. Thus, we rewrite the expression:

\[ \frac{3}{7} \div \frac{2}{7} = \frac{3}{7} \times \frac{7}{2} \]

So the expression becomes:

\[ \frac{3}{7} \times \frac{7}{2} \times \frac{21}{8} \]

### Step 2: Simplify the Expression
Now we can multiply the fractions together. We can multiply the numerators and the denominators:

\[ \frac{3 \times 7 \times 21}{7 \times 2 \times 8} \]

### Step 3: Cancel Common Factors
Notice that we have a \( 7 \) in the numerator and denominator, which can be canceled:

\[ \frac{3 \times \cancel{7} \times 21}{\cancel{7} \times 2 \times 8} = \frac{3 \times 21}{2 \times 8} \]

### Step 4: Calculate the Numerator and Denominator
Now we can calculate the products:

Numerator: \( 3 \times 21 = 63 \)

Denominator: \( 2 \times 8 = 16 \)

So we have:

\[ \frac{63}{16} \]

### Step 5: Convert to Mixed Number (if needed)
To convert \( \frac{63}{16} \) to a mixed number, we divide 63 by 16:

\[ 63 \div 16 = 3 \quad \text{(whole number)} \]
\[ 63 - (16 \times 3) = 63 - 48 = 15 \quad \text{(remainder)} \]

Thus, we can express it as:

\[ 3 \frac{15}{16} \]

### Final Answer
The simplified form of the expression \( \frac{3}{7} \div \frac{2}{7} \times \frac{21}{8} \) is:

\[ 3 \frac{15}{16} \]

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