Chech whether rate two ratios `9: 15` and `18: 24` form a proportion or not.

Answer

To determine whether the ratios \(9:15\) and \(18:24\) form a proportion, we need to check if the two ratios are equivalent. Here's how to do it step by step:

### Step 1: Write down the ratios
We have the two ratios:
- Ratio 1: \(9:15\)
- Ratio 2: \(18:24\)

### Step 2: Simplify the first ratio \(9:15\)
To simplify \(9:15\), we need to find the greatest common divisor (GCD) of 9 and 15. The GCD is 3.

Now, divide both terms by the GCD:
\[ \frac{9}{3} : \frac{15}{3} = 3:5 \]

### Step 3: Simplify the second ratio \(18:24\)
Next, we simplify \(18:24\). The GCD of 18 and 24 is 6.

Now, divide both terms by the GCD:
\[ \frac{18}{6} : \frac{24}{6} = 3:4 \]

### Step 4: Compare the simplified ratios
Now we compare the simplified ratios:
- Simplified Ratio 1: \(3:5\)
- Simplified Ratio 2: \(3:4\)

Since \(3:5\) is not equal to \(3:4\), the two ratios are not equivalent.

### Conclusion
Therefore, the ratios \(9:15\) and \(18:24\) do not form a proportion.

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