Question

Use the given tables to compare the ratios 7:9 and 4:6 .79141821272836354546812121816242030(1 point)$$Skip to navigation

Answer 1

To compare the ratios \( 7:9 \) and \( 4:6 \), we can convert each ratio to a decimal.

1. **For the ratio \( 7:9 \)**:
- Divide \( 7 \) by \( 9 \):
\[
7 \div 9 \approx 0.7777\ldots \text{ (repeating)}
\]

2. **For the ratio \( 4:6 \)**:
- First, simplify the ratio \( 4:6 \) by dividing both numbers by their greatest common divisor (which is \( 2 \)):
\[
\frac{4}{6} = \frac{2}{3}
\]
- Now divide \( 2 \) by \( 3 \):
\[
2 \div 3 \approx 0.6666\ldots \text{ (repeating)}
\]

Now we can compare the two decimal values:
- \( 7:9 \approx 0.7777\ldots \)
- \( 4:6 \approx 0.6666\ldots \)

Since \( 0.7777\ldots \) is greater than \( 0.6666\ldots \), we can conclude that:

\[
7:9 > 4:6
\]

In summary, the ratio \( 7:9 \) is greater than the ratio \( 4:6 \).