Compare the ratios 2:5 and 3:7 using the following tables. Finish the tables by filling in the missing values A and B. Which ratio is greater? 2 5 4 10 6 15 8 20 10 25 12 30 A 35 3 7 6 14 9 21 12 28 15 B 18 42 21 49(2 points) Missing Value A = . Missing Value B = . The ratio is greater.
To compare the ratios 2:5 and 3:7, we can fill in the missing values in the tables.
Table for 2:5 ratio:
2 5 --> 4 10 --> 6 15 --> 8 20 --> 10 25 --> 12 30 --> A 35
Table for 3:7 ratio:
3 7 --> 6 14 --> 9 21 --> 12 28 --> 15 B --> 18 42 --> 21 49
Now, we can determine the missing values A and B by continuing the pattern in each table.
For the table of 2:5 ratio, we can deduce that if you multiply the first number by 2, you get the second number. Applying this pattern to the last known values (12 and 30), we can find that A would be 35 (12 multiplied by 2 equals 24, and 30 multiplied by 2 equals 60, so the missing value is 35).
For the table of 3:7 ratio, we can observe that if you multiply the first number by 2, you get the second number, then multiply the second number by 3, you get the third number. Applying this pattern to the last known values (15 and 42), we can deduce that B would be 49 (15 multiplied by 2 equals 30, and 42 multiplied by 3 equals 126, so the missing value is 49).
Therefore, Missing Value A = 35 and Missing Value B = 49.
To determine which ratio is greater, we can compare the last values in each table. The last value in the table for 2:5 ratio is 35, and the last value in the table for 3:7 ratio is 49. Since 49 is greater than 35, the ratio 3:7 is greater than the ratio 2:5.
To compare the ratios 2:5 and 3:7, let's fill in the missing values in the tables:
Table for ratio 2:5:
2 5
4 10
6 15
8 20
10 25
12 30
A 35
Table for ratio 3:7:
3 7
6 14
9 21
12 28
15 B
18 42
21 49
To find the missing values, we can use the relationship between the first and second numbers in each ratio. In the first table, the second number is always 2.5 times the first number (e.g., 5 = 2 * 2.5, 10 = 4 * 2.5). Applying the same pattern, we can find the missing value A by multiplying 12 by 2.5, which gives us A = 12 * 2.5 = 30.
In the second table, the second number is always approximately 2.33 times the first number (e.g., 7 ≈ 3 * 2.33, 14 ≈ 6 * 2.33). Applying the same pattern, we can estimate the missing value B by multiplying 15 by 2.33, which gives us B ≈ 15 * 2.33 = 34.95 ≈ 35.
So, Missing Value A = 30, Missing Value B = 35.
To determine which ratio is greater, we compare the second numbers in each ratio. The second number in the ratio 2:5 is 5, and the second number in the ratio 3:7 is 7. Since 7 is greater than 5, we can conclude that the ratio 3:7 is greater than the ratio 2:5.
To compare the ratios 2:5 and 3:7, we can create equivalent ratios by finding the missing values A and B in the provided tables.
For the first ratio 2:5, we can see that the pattern is multiplying the first number (2) by a constant to get the second number (5). In this case, the constant is 2. So, to find the missing values A and B, we need to multiply the previous second number (5) by 2.
By applying the constant (2) to the second number (5), we can calculate the missing values in the first table:
A = 5 * 2 = 10
B = 15 * 2 = 30
Completing the first table, we have:
2 5
4 10
6 15
8 20
10 25
12 30
For the second ratio 3:7, we can follow the same pattern. The constant here is 3. By multiplying the previous second number (7) by 3, we can find the missing values in the second table:
A = 7 * 3 = 21
B = 14 * 3 = 42
Completing the second table, we have:
3 7
6 14
9 21
12 28
15 42
Now we can compare the ratios based on the calculated values in the tables. We can see that when both ratios are written in fraction form, 2/5 and 3/7, the numerator and denominator of the second ratio are larger than the first ratio. Therefore, the ratio 3:7 is greater than the ratio 2:5.
In summary, the missing values in the tables are A = 10 and B = 30. The ratio 3:7 is greater than the ratio 2:5.