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 simplify both ratios by dividing each number by their greatest common factor.
First, let's look at the ratio 7:9. The greatest common factor of 7 and 9 is 1 (since they are both prime numbers), so we can't simplify it any further.
Next, let's look at the ratio 4:6. The greatest common factor of 4 and 6 is 2, so we can divide both numbers by 2. This gives us the simplified ratio of 2:3.
Therefore, the ratio 7:9 is not equal to the ratio 4:6.
To compare the ratios 7:9 and 4:6, we can find the equivalent ratios by multiplying or dividing the numerator and denominator by the same value.
For the ratio 7:9:
- Multiplying the numerator and denominator by 2 gives us 14:18.
- Multiplying by 3 gives us 21:27.
- Multiplying by 4 gives us 28:36.
- Multiplying by 5 gives us 35:45.
For the ratio 4:6:
- Multiplying the numerator and denominator by 2 gives us 8:12.
- Multiplying by 3 gives us 12:18.
- Multiplying by 4 gives us 16:24.
- Multiplying by 5 gives us 20:30.
Comparing the equivalent ratios:
- For the ratio 7:9, the equivalent ratios are 14:18, 21:27, 28:36, and 35:45.
- For the ratio 4:6, the equivalent ratios are 8:12, 12:18, 16:24, and 20:30.
We can see that all the equivalent ratios for 7:9 are larger than the equivalent ratios for 4:6. Therefore, 7:9 is a larger ratio than 4:6.
To compare the ratios 7:9 and 4:6, we need to check if they are equivalent. To do this, we can simplify both ratios to their simplest form.
For the ratio 7:9, we can divide both the numbers by their greatest common divisor, which is 1. This gives us the simplified ratio of 7:9.
For the ratio 4:6, we can also divide both numbers by their greatest common divisor, which is 2. This gives us the simplified ratio of 2:3.
Now we can compare the simplified ratios.
The simplified ratio for 7:9 is 7:9
The simplified ratio for 4:6 is 2:3
Since the simplified ratios 7:9 and 2:3 are not the same, we can conclude that the original ratios 7:9 and 4:6 are not equivalent.