`2/3 xx 6/8 xx2/3xx3/4 = ?`

Options

A. 0.25
B. 0.5
C. 1.45
D. 11.8

Answer

To solve the expression \( \frac{2}{3} \times \frac{6}{8} \times \frac{2}{3} \times \frac{3}{4} \), we will follow these steps:

### Step 1: Write the expression clearly
The given expression is:
\[ \frac{2}{3} \times \frac{6}{8} \times \frac{2}{3} \times \frac{3}{4} \]

### Step 2: Multiply the fractions
When multiplying fractions, we can multiply the numerators together and the denominators together:
\[ = \frac{2 \times 6 \times 2 \times 3}{3 \times 8 \times 3 \times 4} \]

### Step 3: Calculate the numerator and denominator
Calculating the numerator:
\[ 2 \times 6 = 12 \\ 12 \times 2 = 24 \\ 24 \times 3 = 72 \]
So, the numerator is \( 72 \).

Calculating the denominator:
\[ 3 \times 8 = 24 \\ 24 \times 3 = 72 \\ 72 \times 4 = 288 \]
So, the denominator is \( 288 \).

### Step 4: Write the fraction
Now we have:
\[ \frac{72}{288} \]

### Step 5: Simplify the fraction
To simplify \( \frac{72}{288} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is \( 72 \):
\[ \frac{72 \div 72}{288 \div 72} = \frac{1}{4} \]

### Step 6: Convert to decimal
To convert \( \frac{1}{4} \) to decimal:
\[ \frac{1}{4} = 0.25 \]

### Final Answer
Thus, the final answer is:
\[ 0.25 \]

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