Which of the following tables could you use to compare the ratios 2:5 and 3:4 ?
2 5
4 10
3 4
6 8
2 5
6 15
10 25
2 5
3 10
4 15
5 20
6 25
3 4
4 8
5 12
6 16
7 20
3 4
6 8
9 12
12 16
15 20
The correct table to compare the ratios 2:5 and 3:4 would be:
3 4
4 8
5 12
6 16
7 20
To compare the ratios 2:5 and 3:4, we need to find a table that shows equivalent ratios for both sets. Let's go through the options and see which one allows us to calculate equivalent ratios for both.
1. 2 5
4 10
This table does not show equivalent ratios for 3:4.
2. 2 5
6 15
10 25
This table does not show equivalent ratios for 3:4.
3. 2 5
3 10
4 15
5 20
6 25
This table has equivalent ratios for both 2:5 and 3:4. The pairs (2,5) and (4,15) represent the ratios 2:5 and 3:4, respectively.
4. 3 4
4 8
5 12
6 16
7 20
This table only shows equivalent ratios for 3:4, not 2:5.
5. 3 4
6 8
9 12
12 16
15 20
This table does not show equivalent ratios for 2:5.
Therefore, the correct answer is option 3:
2 5
3 10
4 15
5 20
6 25
To compare the ratios 2:5 and 3:4, we need to find a common unit that can be used to express both ratios. One way to do this is to find the least common multiple (LCM) of the denominators in both ratios.
The denominators in the ratios 2:5 and 3:4 are 5 and 4, respectively. The LCM of 5 and 4 is 20.
Now, we will express both ratios using this common unit (20).
Ratio 2:5 = (2/5) * 20 = 8:20
Ratio 3:4 = (3/4) * 20 = 15:20
Now, we can compare the ratios:
- Option 1: 2 5 <- Incorrect, this ratio does not match with the common unit of 20.
- Option 2: 6 15 <- Incorrect, this ratio does not match with the common unit of 20.
- Option 3: 2 5 3 10
8 20 15 20
This table matches the common unit of 20 and represents the ratios 2:5 and 3:4 when expressed in terms of this common unit. Therefore, this is the correct table to compare the given ratios.
- Option 4: 3 4 <- Incorrect, this ratio does not match with the common unit of 20.
- Option 5: 6 8 <- Incorrect, this ratio does not match with the common unit of 20.
Therefore, the correct table to compare the ratios 2:5 and 3:4 is:
2 5
3 10