Simplify the following :
`4/5 times 2/3 times 2""2/11`

Answer

To simplify the expression \( \frac{4}{5} \times \frac{2}{3} \times 2 \frac{2}{11} \), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \( 2 \frac{2}{11} \) can be converted to an improper fraction.

To convert:
- Multiply the whole number (2) by the denominator (11): \( 2 \times 11 = 22 \)
- Add the numerator (2) to this product: \( 22 + 2 = 24 \)

Thus, \( 2 \frac{2}{11} = \frac{24}{11} \).

### Step 2: Rewrite the expression
Now, we can rewrite the original expression with the improper fraction:
\[ \frac{4}{5} \times \frac{2}{3} \times \frac{24}{11} \]

### Step 3: Multiply the fractions
We can multiply the fractions directly:
\[ \frac{4 \times 2 \times 24}{5 \times 3 \times 11} \]

### Step 4: Calculate the numerator and denominator
Calculating the numerator:
\[ 4 \times 2 = 8 \]
\[ 8 \times 24 = 192 \]

Calculating the denominator:
\[ 5 \times 3 = 15 \]
\[ 15 \times 11 = 165 \]

So, we have:
\[ \frac{192}{165} \]

### Step 5: Simplify the fraction
Now we need to simplify \( \frac{192}{165} \). We can find the greatest common divisor (GCD) of 192 and 165.

The GCD of 192 and 165 is 3. Now we divide both the numerator and the denominator by 3:
\[ \frac{192 \div 3}{165 \div 3} = \frac{64}{55} \]

### Step 6: Convert back to a mixed number (if necessary)
Since \( \frac{64}{55} \) is an improper fraction, we can convert it back to a mixed number:
- Divide 64 by 55, which gives 1 with a remainder of 9.

Thus, \( \frac{64}{55} = 1 \frac{9}{55} \).

### Final Answer:
The simplified form of \( \frac{4}{5} \times \frac{2}{3} \times 2 \frac{2}{11} \) is:
\[ 1 \frac{9}{55} \]

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