Fill in the missing number in the equivalent ratio :
`(24)/(21) = (…)/(3) = (6)/(…)`

Answer

To solve the problem of finding the missing numbers in the equivalent ratio \( \frac{24}{21} = \frac{?}{3} = \frac{6}{?} \), we can follow these steps:

### Step 1: Set up the ratios
We know that the ratios are equivalent, so we can set up the equations based on the given ratios:
1. \( \frac{24}{21} = \frac{x}{3} \) (where \( x \) is the missing number)
2. \( \frac{24}{21} = \frac{6}{y} \) (where \( y \) is the other missing number)

### Step 2: Solve for \( x \)
From the first equation \( \frac{24}{21} = \frac{x}{3} \), we can cross-multiply to find \( x \):
\[ 24 \cdot 3 = 21 \cdot x \]
\[ 72 = 21x \]
Now, divide both sides by 21 to isolate \( x \):
\[ x = \frac{72}{21} \]
We can simplify \( \frac{72}{21} \) by dividing both the numerator and the denominator by 3:
\[ x = \frac{72 \div 3}{21 \div 3} = \frac{24}{7} \]

### Step 3: Solve for \( y \)
Now, we will solve for \( y \) using the second equation \( \frac{24}{21} = \frac{6}{y} \):
\[ 24y = 21 \cdot 6 \]
Calculating the right side:
\[ 24y = 126 \]
Now, divide both sides by 24 to isolate \( y \):
\[ y = \frac{126}{24} \]
We can simplify \( \frac{126}{24} \) by dividing both the numerator and the denominator by 6:
\[ y = \frac{126 \div 6}{24 \div 6} = \frac{21}{4} \]

### Final Answers
Thus, the missing numbers in the equivalent ratio are:
- \( x = \frac{24}{7} \)
- \( y = \frac{21}{4} \)

### Summary
The complete equivalent ratio is:
\[ \frac{24}{21} = \frac{24/7}{3} = \frac{6}{21/4} \]