Question
how can you show that two ratio are proportional?
Also, There are 3 ways to show that ratios are proportional. Can you explain at least one way? Explain
Also, There are 3 ways to show that ratios are proportional. Can you explain at least one way? Explain
Answers
GPT-4o mini
To show that two ratios are proportional, you can check if the cross products of the ratios are equal. If you have two ratios \(a:b\) and \(c:d\), they are proportional if:
\[
\frac{a}{b} = \frac{c}{d} \quad \text{if and only if} \quad a \cdot d = b \cdot c
\]
This means that if you cross-multiply the ratios, the products should be equal.
### Example:
Consider the ratios \(2:3\) and \(4:6\).
1. **Set up the equation**:
- Here, \(a = 2\), \(b = 3\), \(c = 4\), and \(d = 6\).
2. **Cross multiply**:
- Calculate \(a \cdot d\) and \(b \cdot c\):
\[
2 \cdot 6 = 12
\]
\[
3 \cdot 4 = 12
\]
3. **Check if they are equal**:
- Since \(12 = 12\), the ratios \(2:3\) and \(4:6\) are proportional.
### Summary of Method:
Cross-multiplication is a straightforward way to demonstrate that two ratios are proportional by equating the cross products. If they match, the two ratios are indeed proportional.
\[
\frac{a}{b} = \frac{c}{d} \quad \text{if and only if} \quad a \cdot d = b \cdot c
\]
This means that if you cross-multiply the ratios, the products should be equal.
### Example:
Consider the ratios \(2:3\) and \(4:6\).
1. **Set up the equation**:
- Here, \(a = 2\), \(b = 3\), \(c = 4\), and \(d = 6\).
2. **Cross multiply**:
- Calculate \(a \cdot d\) and \(b \cdot c\):
\[
2 \cdot 6 = 12
\]
\[
3 \cdot 4 = 12
\]
3. **Check if they are equal**:
- Since \(12 = 12\), the ratios \(2:3\) and \(4:6\) are proportional.
### Summary of Method:
Cross-multiplication is a straightforward way to demonstrate that two ratios are proportional by equating the cross products. If they match, the two ratios are indeed proportional.