The ratio of red candies to green candies in a bag is Start Fraction 4 over 5 End Fraction. Which ratio would form a proportional relationship with this ratio?
A. start fraction 16 over 25 end fraction
B. start fraction 20 over 25 end fraction
C. start fraction 20 over 35 end fraction
D. start fraction 24 over 32 end fraction
A. start fraction 16 over 25 end fraction.
To check if two ratios are proportional, we need to simplify both ratios to their simplest form (also known as finding the lowest terms) and then check if they are equal.
The ratio of red candies to green candies is 4:5. We can simplify this ratio by dividing both the numerator and the denominator by their greatest common factor, which is 1. This gives us the simplest form of the ratio, which is also 4:5.
Now, let's simplify each answer choice:
A. start fraction 16 over 25 end fraction. We can simplify this ratio by dividing both the numerator and the denominator by their greatest common factor, which is 1. This gives us the simplest form of the ratio, which is 16:25.
B. start fraction 20 over 25 end fraction. We can simplify this ratio by dividing both the numerator and the denominator by their greatest common factor, which is 5. This gives us the simplest form of the ratio, which is 4:5. This is already the same ratio as the given ratio, so it is proportional.
C. start fraction 20 over 35 end fraction. We can simplify this ratio by dividing both the numerator and the denominator by their greatest common factor, which is 5. This gives us the simplest form of the ratio, which is 4:7. This is not the same ratio as the given ratio, so it is not proportional.
D. start fraction 24 over 32 end fraction. We can simplify this ratio by dividing both the numerator and the denominator by their greatest common factor, which is 8. This gives us the simplest form of the ratio, which is 3:4. This is not the same ratio as the given ratio, so it is not proportional.
Therefore, the only ratio that is proportional to the given ratio is A. start fraction 16 over 25 end fraction.