Suppose `a=2/3b, b=2/3c,` and `c=2/3d` what would be the value of b as a fraction of d?

Options

A. `2/3`
B. `4/3`
C. `4/9`
D. `8/27`

Answer

To find the value of \( b \) as a fraction of \( d \), we will use the relationships given in the problem step by step.

### Step 1: Write down the relationships
We have the following equations:
1. \( a = \frac{2}{3}b \)
2. \( b = \frac{2}{3}c \)
3. \( c = \frac{2}{3}d \)

### Step 2: Express \( c \) in terms of \( d \)
From the third equation, we can express \( c \) in terms of \( d \):
\[ c = \frac{2}{3}d \]

### Step 3: Substitute \( c \) into the equation for \( b \)
Now, we substitute \( c \) into the second equation:
\[ b = \frac{2}{3}c = \frac{2}{3} \left( \frac{2}{3}d \right) \]

### Step 4: Simplify the expression for \( b \)
Now we simplify the expression:
\[ b = \frac{2}{3} \times \frac{2}{3}d = \frac{4}{9}d \]

### Conclusion
Thus, the value of \( b \) as a fraction of \( d \) is:
\[ b = \frac{4}{9}d \]