Compare the ratios in Table 1 and Table 2.

Question

Table 1     
3
5
6
10
9
15
12
20

Table 2
7
10
14
20
21
30
28
40

Which statements about the ratios are true? Check all that apply.
The ratio 3:5 is less than the ratio 7:10.
The ratio 3:5 is greater than the ratio 7:10.
The ratio 14:20 is less than the ratio 9:15.
The ratio 14:20 is greater than the ratio 9:15.
The ratios in Table 1 are less than the ratios in Table 2.
The ratios in Table 1 are greater than the ratios in Table 2.

GPT-4o mini · Answer

To compare the ratios from both tables, we will calculate the simplified form of each ratio and then compare them.

Table 1 Ratios (Numerator:Value)

3:5 = 0.6
6:10 = 0.6
9:15 = 0.6
12:20 = 0.6

Table 2 Ratios (Numerator:Value)

7:10 = 0.7
14:20 = 0.7
21:30 = 0.7
28:40 = 0.7

Analysis

Comparing the ratios 3:5 and 7:10:
- 3:5 = 0.6
- 7:10 = 0.7
- Therefore, 3:5 < 7:10
- Statement: The ratio 3:5 is less than the ratio 7:10. (True)
Comparing the ratios 14:20 and 9:15:
- 14:20 = 0.7
- 9:15 = 0.6
- Therefore, 14:20 > 9:15
- Statement: The ratio 14:20 is greater than the ratio 9:15. (True)
Comparing overall ratios in Table 1 and Table 2:
- All ratios in Table 1 (0.6) are less than all ratios in Table 2 (0.7).
- Statement: The ratios in Table 1 are less than the ratios in Table 2. (True)
Statments about the ratios being greater:
- Since all ratios in Table 1 (0.6) are indeed less than those in Table 2 (0.7),
- Statement: The ratios in Table 1 are greater than the ratios in Table 2. (False)

Final Statements

Thus, the true statements are:

The statement that "The ratio 3:5 is less than the ratio 7:10." is true.
The statement that "The ratio 14:20 is greater than the ratio 9:15." is true.
The statement that "The ratios in Table 1 are less than the ratios in Table 2." is true.

Summary of True Statements:

The ratio 3:5 is less than the ratio 7:10. (True)
The ratio 14:20 is greater than the ratio 9:15. (True)
The ratios in Table 1 are less than the ratios in Table 2. (True)