Are the ratios `70:98 and 140:196` in proportion ?

Answer

To determine if the ratios \(70:98\) and \(140:196\) are in proportion, we need to check if the two ratios are equal. We can do this by cross-multiplying and comparing the products.

### Step-by-Step Solution:

1. **Write the Ratios**:
We have two ratios:
\[ \frac{70}{98} \quad \text{and} \quad \frac{140}{196} \]

2. **Cross-Multiply**:
To check if these ratios are equal, we cross-multiply:
\[ 70 \times 196 \quad \text{and} \quad 98 \times 140 \]

3. **Calculate the Products**:
- For \(70 \times 196\):
\[ 70 \times 196 = 13720 \]
- For \(98 \times 140\):
\[ 98 \times 140 = 13720 \]

4. **Compare the Products**:
Since both products are equal:
\[ 13720 = 13720 \]
This means that:
\[ \frac{70}{98} = \frac{140}{196} \]

5. **Conclusion**:
Since the two ratios are equal, we conclude that the ratios \(70:98\) and \(140:196\) are in proportion.

### Final Answer:
Yes, the ratios \(70:98\) and \(140:196\) are in proportion.

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