1/7:30=2,5d:4

To solve the equation \( \frac{1}{7:30} = \frac{2.5d}{4} \), we first interpret the ratio \( 7:30 \).

1. Convert the ratio \( 7:30 \) into a fraction. This gives us:

\[ 7:30 = \frac{7}{30} \]

2. Next, we rewrite the left side of the equation:

\[ \frac{1}{\frac{7}{30}} = \frac{30}{7} \]

So now we have:

\[ \frac{30}{7} = \frac{2.5d}{4} \]

3. To eliminate the fraction on the right side, multiply both sides by 4:

\[ 4 \times \frac{30}{7} = 2.5d \]

This simplifies to:

\[ \frac{120}{7} = 2.5d \]

4. Now, isolate \( d \) by dividing both sides by \( 2.5 \):

\[ d = \frac{120/7}{2.5} \]

5. To simplify \( \frac{120/7}{2.5} \), note that \( 2.5 = \frac{25}{10} = \frac{5}{2} \):

\[ d = \frac{120}{7} \cdot \frac{2}{5} = \frac{240}{35} = \frac{48}{7} \]

Therefore, the solution for \( d \) is:

\[ d = \frac{48}{7} \approx 6.857 \]

If you have any further questions or need clarification, feel free to ask!