The Correct Answer and Explanation is:
The correct answer is 8:3.
To find a ratio that is equivalent to 48:18, the most effective method is to simplify the original ratio to its lowest terms. Two ratios are equivalent if they represent the same proportional relationship. This simplification is achieved by finding the largest number that can divide both parts of the ratio evenly. This number is known as the greatest common divisor (GCD).
First, let’s identify the numbers in the original ratio: 48 and 18. We need to find the GCD of these two numbers. We can list the factors for each number. The factors of 18 are 1, 2, 3, 6, 9, and 18. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. By comparing these two lists, we can see that the largest factor they have in common is 6.
Once the GCD is identified as 6, we divide both parts of the original ratio by it. We calculate 48 divided by 6, which gives us 8. Then, we calculate 18 divided by 6, which gives us 3. This simplifies the ratio 48:18 down to 8:3. This is the simplest form of the ratio, as 8 and 3 do not share any common factors other than 1.
Now, we compare this simplified ratio to the given options.
- 36:6 simplifies to 6:1 (by dividing both numbers by 6).
- 60:30 simplifies to 2:1 (by dividing both numbers by 30).
- 3:1 is already in its simplest form.
- 8:3 is also in its simplest form.
By comparing our simplified ratio of 8:3 with the options, we find an exact match. Therefore, the ratio 8:3 is equivalent to the ratio 48:18.
