Simplify the following :
`3""2/11 times 5""9/14`

Answer

To simplify the expression \(3 \frac{2}{11} \times 5 \frac{9}{14}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers \(3 \frac{2}{11}\) and \(5 \frac{9}{14}\) into improper fractions.

For \(3 \frac{2}{11}\):
\[ 3 \frac{2}{11} = \frac{(3 \times 11) + 2}{11} = \frac{33 + 2}{11} = \frac{35}{11} \]

For \(5 \frac{9}{14}\):
\[ 5 \frac{9}{14} = \frac{(5 \times 14) + 9}{14} = \frac{70 + 9}{14} = \frac{79}{14} \]

### Step 2: Multiply the Improper Fractions
Now we will multiply the two improper fractions:
\[ \frac{35}{11} \times \frac{79}{14} \]

### Step 3: Simplify Before Multiplying
Before multiplying, we can simplify the fractions. Notice that \(35\) and \(14\) have a common factor of \(7\):
\[ 35 \div 7 = 5 \quad \text{and} \quad 14 \div 7 = 2 \]
So we can rewrite our multiplication as:
\[ \frac{5}{11} \times \frac{79}{2} \]

### Step 4: Multiply the Numerators and Denominators
Now we multiply the numerators together and the denominators together:
\[ \frac{5 \times 79}{11 \times 2} = \frac{395}{22} \]

### Step 5: Convert Improper Fraction to Mixed Number
Next, we convert the improper fraction \(\frac{395}{22}\) back to a mixed number. We divide \(395\) by \(22\):
\[ 395 \div 22 = 17 \quad \text{(whole number part)} \]
Calculating the remainder:
\[ 395 - (22 \times 17) = 395 - 374 = 21 \]
So, we can express this as:
\[ \frac{395}{22} = 17 \frac{21}{22} \]

### Final Answer
Thus, the simplified form of \(3 \frac{2}{11} \times 5 \frac{9}{14}\) is:
\[ 17 \frac{21}{22} \]

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