Question

Compare the ratios 4:5 and 8:10 using the following tables. Finish the tables by filling in the missing values a and b

Answer 1

To compare the ratios 4:5 and 8:10 using a table format, we can express both ratios in fractional form and then determine the missing values a and b to complete the comparison.

The ratio \( 4:5 \) can be expressed as the fraction:
\[
\frac{4}{5}
\]
The ratio \( 8:10 \) can be expressed as the fraction:
\[
\frac{8}{10}
\]

We can simplify the ratio \( 8:10 \):
\[
\frac{8}{10} = \frac{4}{5}
\]
This shows that the two ratios \( 4:5 \) and \( 8:10 \) are equivalent.

Now, we can create tables to reflect the ratios and identify the missing values a and b.

### Table for 4:5

| Part | Value |
|------|-------|
| a | 4 |
| b | 5 |

### Table for 8:10

| Part | Value |
|------|-------|
| a | 8 |
| b | 10 |

Based on this information, we can fill in the missing values:

- In the table for the ratio \( 4:5 \), \( a = 4 \) and \( b = 5 \).
- In the table for the ratio \( 8:10 \), \( a = 8 \) and \( b = 10 \).

Since both ratios are equivalent, we conclude they have the same value, confirming their proportional relationship.

So the completed tables will look like this:

### Table for 4:5

| Part | Value |
|------|-------|
| a | 4 |
| b | 5 |

### Table for 8:10

| Part | Value |
|------|-------|
| a | 8 |
| b | 10 |

In summary, \( 4:5 \) and \( 8:10 \) are equivalent ratios, and the completed tables provide their corresponding values.