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.