Which of the following ratios is equivalent to 12/15
A. 4:5
B. 10:12
C. 60 to 80
D. 60/45
A. 4:5
To determine which of the given ratios is equivalent to 12/15, we need to simplify the fraction 12/15.
The first step is to find the greatest common divisor (GCD) of the numerator and the denominator, which is the largest number that can evenly divide both numbers. In this case, the GCD of 12 and 15 is 3.
To simplify the fraction, we divide both the numerator and the denominator by the GCD:
12 ÷ 3 = 4
15 ÷ 3 = 5
Now that we have simplified the fraction, we see that 12/15 is equivalent to 4/5.
Let's evaluate each given ratio to see which one is equivalent to 4/5:
A. 4:5 - This ratio is indeed equivalent to 4/5, as the two numbers in the ratio match the simplified fraction.
B. 10:12 - To check if this ratio is equivalent to 4/5, we can simplify it. We divide both numbers by their GCD, which is 2:
10 ÷ 2 = 5
12 ÷ 2 = 6
Therefore, 10:12 is not equivalent to 4/5.
C. 60 to 80 - This ratio can also be simplified by finding the GCD:
60 ÷ 20 = 3
80 ÷ 20 = 4
After simplifying, we get 3:4. Since this ratio is not equivalent to 4/5, it is not the correct answer.
D. 60/45 - This is not a ratio, but a fraction. To simplify it, we find the GCD:
60 ÷ 15 = 4
45 ÷ 15 = 3
After simplifying, we get 4/3. Since this is not equivalent to 4/5, it is not the correct answer.
Therefore, the ratio A. 4:5 is the correct answer, as it is equivalent to the fraction 12/15.
To find an equivalent ratio to 12/15, we need to simplify the fraction. We can do this by dividing both the numerator (12) and denominator (15) by their greatest common divisor (GCD).
The GCD of 12 and 15 is 3. When we divide 12 by 3, we get 4, and when we divide 15 by 3, we get 5.
Therefore, the equivalent ratio to 12/15 is 4/5.
Among the given options:
A. 4:5 - This ratio is equivalent to 4/5, which is correct.
B. 10:12 - This ratio is not equivalent to 12/15.
C. 60 to 80 - This ratio is not equivalent to 12/15.
D. 60/45 - This fraction is not equivalent to 12/15.
Therefore, the correct answer is A. 4:5.