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.
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To compare the ratios 2:5 and 3:7, we can simplify them by dividing both numbers in each ratio by their greatest common factor.
For the ratio 2:5, the greatest common factor is 1. So the simplified ratio is 2/1 : 5/1 = 2:5.
For the ratio 3:7, the greatest common factor is 1. So the simplified ratio is 3/1 : 7/1 = 3:7.
Now, let's fill in the missing values in the tables:
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
To find the missing values, we can multiply the second number in each row of the first table by 7/5 to match the ratio 2:5.
A = 35 * (7/5) = 49
So, Missing Value A = 49.
To find the missing values, we can multiply the second number in each row of the second table by 5/7 to match the ratio 3:7.
B = 15 * (5/7) = 10.71 (rounded to two decimal places)
So, Missing Value B = 10.71.
Since the ratio 2:5 is less than the ratio 3:7, we can conclude that the ratio 3:7 is greater.
It’s wrong
To compare the ratios 2:5 and 3:7 using the tables, we need to fill in the missing values A and B.
Looking at the second column of the first table, we can see that the pattern is multiplying each number by 5. So, A would be 35.
Next, we can use the same pattern to fill in the second column of the second table. Multiplying each number by 7, we find that B would be 42.
Now let's compare the ratios:
2:5 = 2/5 = 0.4
3:7 = 3/7 ≈ 0.429
Since 0.429 is greater than 0.4, 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 complete the tables by finding the missing values A and B. We can do this by observing the pattern in the given ratios.
Looking at the first ratio 2:5, we can see that when the first number increases by 2 (from 2 to 4), the second number increases by 5 (from 5 to 10). This pattern continues for the rest of the values as well. Therefore, we can fill in the missing values in the table for the first ratio:
2 5
4 10
6 15
8 20
10 25
12 30
A 35
To find the missing value A, we can continue the pattern by increasing the first number by 2 (from 12 to 14), and therefore, the second number should increase by 5 (from 30 to 35). So, the missing value A = 14:35.
Now, let's complete the table for the second ratio:
3 7
6 14
9 21
12 28
15 B
Similar to the first ratio, we can notice that when the first number increases by 3 (from 3 to 6), the second number increases by 7 (from 7 to 14). This pattern continues for the rest of the values. Therefore, we can fill in the missing value in the table for the second ratio:
3 7
6 14
9 21
12 28
15 B
To find the missing value B, we can follow the pattern by increasing the first number by 3 (from 12 to 15), and therefore, the second number should increase by 7 (from 28 to B). So, the missing value B = 15:35.
Now we can compare the two ratios:
Ratio 1: 2:5 = A:35
Ratio 2: 3:7 = 15:B
By comparing the values of A and B, we can see that A (35) is greater than B (35). Therefore, the ratio 2:5 is greater than the ratio 3:7.