Question

Use the given tables to compare the ratios 7:9 and 4:6.
7,9
14,18
21,27
28,36
35,45

Answer 1

To compare the ratios 7:9 and 4:6, we can simplify them and express them as decimals for easier comparison.

1. **Simplifying the Ratios:**
- The ratio \( \frac{7}{9} \) is already in its simplest form.
- The ratio \( \frac{4}{6} \) can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
\[
\frac{4}{6} = \frac{2}{3}
\]

2. **Finding Decimal Values:**
- The decimal value for \( \frac{7}{9} \):
\[
7 \div 9 \approx 0.7777\ldots
\]
- The decimal value for \( \frac{2}{3} \):
\[
2 \div 3 \approx 0.6666\ldots
\]

3. **Comparing the Values:**
- \( 0.7777\ldots > 0.6666\ldots \)

Thus, we can conclude that the ratio \( 7:9 \) is greater than the ratio \( 4:6 \).

To double-check using the provided tables:
- The pairs in the first table represent multiples of 7 and 9.
- The pairs in the second table (corresponding to the ratio \( 4:6 \)) represent multiples of 4 and 6.

When we compare their values from the tables directly, notice that:
- For each pair corresponding to the ratios:
- \( 7 \) to \( 9 \): \( 14 \) to \( 18 \), \( 21 \) to \( 27 \), etc.
- \( 4 \) to \( 6 \): \( 8 \) to \( 12 \), \( 12 \) to \( 18 \), etc. (derived from the ratio)

In every case, the value pairs for \( \frac{7}{9} \) (or \( 7, 9, \ldots \)) will yield greater results than those for \( \frac{4}{6} \) when stated in similar fractions or ratios.

Therefore, the conclusion remains that the ratio \( 7:9 \) is greater than the ratio \( 4:6 \).

Answer 2

Can you give me a simple answer?

Answer 3

Yes, here’s the simple answer:

The ratio \(7:9\) is greater than the ratio \(4:6\).

Answer 4

Which way does the mouth go?

Answer 5

The mouth typically goes **upward** when forming a smile and **downward** when forming a frown. If you are referring to a specific context or drawing, please provide more details!