Compare Ratios Practice
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Question
Use the given tables to compare the ratios 5:9 and 3:6 .
5 9
10 18
15 27
20 36
25 45
3 6
6 12
9 18
12 24
15 30(1 point)
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The ratios 5:9 and 3:6 can be compared by simplifying them.
For the ratio 5:9, we divide both terms by their greatest common divisor, which is 1. So the simplified form of 5:9 is 5:9.
For the ratio 3:6, we divide both terms by their greatest common divisor, which is 3. So the simplified form of 3:6 is 1:2.
Comparing the simplified ratios, we can see that 5:9 is equivalent to 1:2.
To compare the ratios 5:9 and 3:6, we can simplify each ratio to its lowest terms.
For the ratio 5:9, the common factor between 5 and 9 is 1. So, the simplified ratio is 5:9.
For the ratio 3:6, the common factor between 3 and 6 is 3. So, the simplified ratio is 1:2.
Now we can compare the simplified ratios 5:9 and 1:2.
Since the numerators (5 and 1) are different, we can conclude that 5:9 is greater than 1:2.
To compare the ratios 5:9 and 3:6, we can look at the equivalent fractions for each ratio.
For the first ratio 5:9, we can write it as:
5/9
And for the second ratio 3:6, we can write it as:
3/6
To compare these fractions, we can simplify them by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 5 and 9 is 1, so we don't need to simplify 5/9 any further.
The GCD of 3 and 6 is 3. Dividing both the numerator and denominator of 3/6 by 3, we get:
3/3 ÷ 6/3 = 1/2
Now we have simplified fractions for both ratios:
5/9 and 1/2
To compare them, we can check if they are equal by cross-multiplying.
Cross-multiplying means multiplying the numerator of one fraction with the denominator of the other fraction.
For the fractions 5/9 and 1/2, we have:
5 * 2 = 10
9 * 1 = 9
Since 10 is not equal to 9, the two ratios are not equal.
Therefore, the ratio 5:9 is greater than the ratio 3:6.