Question
Use the given tables to compare the ratios 3:8 and 4:12. Which ratio is greater?
3 8
6 16
9 24
12 32
4 12
8 24
12 36
16 48(1 point)
Of the ratios 3:8 and 4:12, the ratio
is greater.
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To compare the ratios 3:8 and 4:12, we can simplify them by finding the greatest common divisor (GCD) of the terms in each ratio.
For the ratio 3:8, the GCD of 3 and 8 is 1. So, we can simplify the ratio to 3/1:8/1, which is equivalent to the fraction 3/8.
For the ratio 4:12, the GCD of 4 and 12 is 4. So, we can simplify the ratio to 4/4:12/4, which is equivalent to the fraction 1/3.
Now, we can compare the simplified fractions 3/8 and 1/3. To do this, we can find a common denominator and compare the numerators.
The common denominator of 8 and 3 is 24. Converting the fractions to have a denominator of 24, we get:
3/8 = (3/8) * (3/3) = 9/24
1/3 = (1/3) * (8/8) = 8/24
Comparing the numerators, we can see that 9 is greater than 8. Therefore, the ratio 3:8 is greater than the ratio 4:12.
To compare the ratios 3:8 and 4:12, we need to simplify them to their simplest form.
To simplify the ratio 3:8, we divide both numbers by their greatest common factor, which is 1.
3 ÷ 1 = 3
8 ÷ 1 = 8
So, the simplified ratio of 3:8 is 3:8.
To simplify the ratio 4:12, we divide both numbers by their greatest common factor, which is 4.
4 ÷ 4 = 1
12 ÷ 4 = 3
So, the simplified ratio of 4:12 is 1:3.
Now, we can compare the simplified ratios: 3:8 and 1:3.
To compare two ratios, we need to compare their corresponding terms.
In the first ratio, 3 is the first term, and in the second ratio, 1 is the first term.
Since 3 is greater than 1, we can conclude that the ratio 3:8 is greater than the ratio 1:3.
To compare the ratios 3:8 and 4:12, we can simplify both ratios by finding the greatest common factor (GCF) of the terms in each ratio.
For the ratio 3:8, the GCF of 3 and 8 is 1 because there is no number that evenly divides both 3 and 8 other than 1.
For the ratio 4:12, the GCF of 4 and 12 is 4 because 4 is the largest number that divides both 4 and 12 evenly.
After simplifying the ratios, we get:
3:8 simplifies to 3/1:8/1 = 3:8
4:12 simplifies to 4/4:12/4 = 1:3
Comparing the simplified ratios, we can see that the ratio 3:8 is greater than the ratio 1:3.
Therefore, the ratio 3:8 is greater than the ratio 4:12.