Use the given tables to compare the ratios 16:18 and 5:6. Which ratio is greater?
8 9
16 18
24 27
32 36
5 6
10 12
15 18
20 24(1 point)
Responses
More rows need to be added to the tables to be able to compare the ratios.
More rows need to be added to the tables to be able to compare the ratios.
16:18 is greater.
ratio of 16 to 18 is greater.
5:6 is greater.
ratio of 5 to 6 is greater.
The two ratios are equal.
The two ratios are equal.
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The ratio 16:18 simplifies to 8:9, and the ratio 5:6 cannot be simplified further.
Comparing these simplified ratios, we can see that 8:9 is smaller than 5:6.
Therefore, the ratio 5:6 is greater.
To compare the given ratios 16:18 and 5:6, we can simplify them to their simplest form:
16:18 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 2:
16 ÷ 2 = 8
18 ÷ 2 = 9
So, 16:18 simplifies to 8:9.
Similarly, 5:6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 1:
5 ÷ 1 = 5
6 ÷ 1 = 6
So, 5:6 simplifies to 5:6.
Now we can compare the simplified ratios: 8:9 and 5:6.
To determine which ratio is greater, we can compare the corresponding terms of the ratios. In this case, we compare the first term (8) of the first ratio to the first term (5) of the second ratio.
8 is greater than 5.
Therefore, the ratio 16:18 is greater than the ratio 5:6.
To compare the ratios 16:18 and 5:6, we need to check if they are equivalent or if one is greater than the other.
First, let's simplify the ratios by dividing both sides by their greatest common divisor (GCD):
For the ratio 16:18, we can divide both sides by 2: 16 ÷ 2 = 8 and 18 ÷ 2 = 9. So the simplified ratio is 8:9.
For the ratio 5:6, we can divide both sides by 1: 5 ÷ 1 = 5 and 6 ÷ 1 = 6. So the simplified ratio is 5:6.
Now, to compare the two ratios, we need to determine which is greater.
One way to do this is to find a common denominator for the two ratios. In this case, the common denominator is 9, since it is the least common multiple of the denominators 9 and 6.
Now we can compare the numerators:
For the ratio 8:9, when multiplied by 1 (9 ÷ 9), the numerator becomes 8.
For the ratio 5:6, when multiplied by 1.5 (9 ÷ 6), the numerator becomes 7.5.
Since 8 is greater than 7.5, we can conclude that the ratio 16:18 is greater than the ratio 5:6.
Therefore, the ratio 16:18 is greater.