Use the given tables to compare the ratios 7:9 and 4:6 .
7 9
14 18
21 27
28 36
35 45
4 6
8 12
12 18
16 24
20 30(1 point)
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To compare the ratios 7:9 and 4:6, we can compare the values in the tables.
For example, in the first table, when the ratio is 7:9, the corresponding values are:
- 7 corresponds to 9
- 14 corresponds to 18
- 21 corresponds to 27
- 28 corresponds to 36
- 35 corresponds to 45
In the second table, when the ratio is 4:6, the corresponding values are:
- 4 corresponds to 6
- 8 corresponds to 12
- 12 corresponds to 18
- 16 corresponds to 24
- 20 corresponds to 30
We can see that the values in the second table are half the values in the first table. Therefore, the ratios 7:9 and 4:6 are equivalent.
To compare the ratios 7:9 and 4:6, we can simplify both ratios by dividing each term by their greatest common divisor.
For the ratio 7:9:
- Divide both terms by 1
- The simplified ratio is 7:9
For the ratio 4:6:
- Divide both terms by 2
- The simplified ratio is 2:3
Now we can compare the simplified ratios:
- 7:9 is greater than 2:3
To compare the ratios 7:9 and 4:6 using the given tables, we need to determine if the two ratios are equivalent or if one ratio is greater than the other.
The given tables show two sets of numbers that represent the ratios 7:9 and 4:6. The first column in the tables represents the numerator of the ratio, and the second column represents the denominator.
To determine if the ratios are equivalent, we can check if the corresponding values in both tables are proportional. If the ratios are equivalent, every value in the first table should be directly proportional to the corresponding value in the second table.
For the first ratio 7:9, we can check if the values in the first and second columns of the first table are directly proportional to the values in the first and second columns of the second table.
Starting with the first set of values, 7 and 9, we can see that they are directly proportional since 7*2 = 14 and 9*2 = 18. Continuing with the second set of values, 14 and 18, we can see that they are also directly proportional since 14*2 = 28 and 18*2 = 36. We can continue this process for the remaining sets of values to verify if the ratios are equivalent.
Similarly, for the second ratio 4:6, we can check if the values in the first and second columns of the first table are directly proportional to the values in the first and second columns of the second table.
Starting with the first set of values, 4 and 6, we can see that they are directly proportional since 4*2 = 8 and 6*2 = 12. Continuing with the second set of values, 8 and 12, we can see that they are also directly proportional since 8*2 = 16 and 12*2 = 24. We can continue this process for the remaining sets of values to verify if the ratios are equivalent.
By comparing the two ratios, we can see that for each set of values, the first ratio (7:9) is larger than the second ratio (4:6), indicating that 7:9 is greater than 4:6.