Fill in the missing number in the equivalent ratio :
`(15)/(18) = (…)/(6) = (10)/(…) = (…)/(30).`

Answer

To solve the problem of finding the missing numbers in the equivalent ratio `(15)/(18) = (…)/(6) = (10)/(…) = (…)/(30)`, we will denote the missing numbers as follows:

- Let the first missing number be \( x \) (so we have \( (15)/(18) = (x)/(6) \)).
- Let the second missing number be \( y \) (so we have \( (10)/(y) \)).
- Let the third missing number be \( z \) (so we have \( (z)/(30) \)).

Now, we will find the values of \( x \), \( y \), and \( z \).

### Step 1: Find \( x \)
We start with the first part of the ratio:
\[ \frac{15}{18} = \frac{x}{6} \]
To find \( x \), we can cross-multiply:
\[ 15 \cdot 6 = 18 \cdot x \]
This simplifies to:
\[ 90 = 18x \]
Now, divide both sides by 18:
\[ x = \frac{90}{18} = 5 \]

### Step 2: Find \( y \)
Next, we look at the second part of the ratio:
\[ \frac{10}{y} = \frac{15}{18} \]
Again, we cross-multiply:
\[ 10 \cdot 18 = 15 \cdot y \]
This simplifies to:
\[ 180 = 15y \]
Now, divide both sides by 15:
\[ y = \frac{180}{15} = 12 \]

### Step 3: Find \( z \)
Finally, we consider the last part of the ratio:
\[ \frac{z}{30} = \frac{15}{18} \]
Cross-multiplying gives us:
\[ z \cdot 18 = 15 \cdot 30 \]
This simplifies to:
\[ 18z = 450 \]
Now, divide both sides by 18:
\[ z = \frac{450}{18} = 25 \]

### Final Answers
The missing numbers are:
- \( x = 5 \)
- \( y = 12 \)
- \( z = 25 \)

Thus, the complete equivalent ratio is:
\[ \frac{15}{18} = \frac{5}{6} = \frac{10}{12} = \frac{25}{30} \]