which of the following ratios is equivalent to 12/20?
A. 3/10
B. 5:3
C. 120 to 200
D. 60/80
plss helpp!!!
A. 3/10
To find which of the following ratios is equivalent to 12/20, we can simplify the fraction 12/20 to its lowest terms.
Step 1: Find the Greatest Common Divisor (GCD) of 12 and 20.
The factors of 12 are: 1, 2, 3, 4, 6, 12.
The factors of 20 are: 1, 2, 4, 5, 10, 20.
The common factors of 12 and 20 are: 1, 2, 4.
Therefore, the GCD of 12 and 20 is 4.
Step 2: Divide both the numerator and denominator of the fraction 12/20 by the GCD (4).
12/4 = 3
20/4 = 5
Therefore, the simplified fraction 12/20 is equivalent to the fraction 3/5.
Now, let's check which ratio is equivalent to 3/5:
A. 3/10: This ratio is not equivalent to 3/5.
B. 5:3: This ratio is not equivalent to 3/5.
C. 120 to 200: To compare the ratio 120:200 with 3/5, we need to simplify it by dividing both numbers by their GCD. The GCD of 120 and 200 is 40. Dividing both numbers by 40 gives us 3:5. So, this ratio is equivalent to 3/5.
D. 60/80: This ratio is not equivalent to 3/5.
Therefore, the ratio that is equivalent to 12/20 (or 3/5) is C. 120 to 200.
To find the ratio that is equivalent to 12/20, we can simplify the fraction 12/20. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor.
The greatest common divisor of 12 and 20 is 4. Divide both 12 and 20 by 4.
12/4 = 3
20/4 = 5
Therefore, the simplified fraction is 3/5.
Now, let's look at the answer choices:
A. 3/10: This is not equivalent to 12/20.
B. 5:3: This is not a fraction, so it cannot be equivalent to 12/20.
C. 120 to 200: To check if this is equivalent to 12/20, we can simplify the ratio by dividing both numbers by 20.
120/20 = 6
200/20 = 10
Therefore, the simplified ratio is 6 to 10, which can be simplified further to 3 to 5. This is equivalent to 12/20.
D. 60/80: To check if this is equivalent to 12/20, we can simplify the fraction by dividing both numbers by their greatest common divisor. The greatest common divisor of 60 and 80 is 20.
60/20 = 3
80/20 = 4
Therefore, the simplified fraction is 3/4. This is not equivalent to 12/20.
So, the ratio that is equivalent to 12/20 is C. 120 to 200.