The Correct Answer and Explanation is:
Correct Answer: All three options presented, 112:28, 56:14, and 8:2, are equivalent to the ratio 16:4.
Explanation:
To find all the ratios equivalent to 16:4, the most straightforward method is to first simplify the original ratio to its simplest form. Equivalent ratios are simply different ways of expressing the same proportional relationship. By reducing each ratio to its fundamental form, we can easily compare them.
Let’s start with the given ratio, 16:4. To simplify it, we need to find the greatest common divisor (GCD) of both numbers. The largest number that divides both 16 and 4 is 4. We then divide both parts of the ratio by this GCD:
16 ÷ 4 = 4
4 ÷ 4 = 1
So, the simplest form of the ratio 16:4 is 4:1. Now, we must check if the other given ratios also simplify to 4:1.
- 112:28: We can check if this ratio simplifies to 4:1 by dividing both numbers by 28. 28 divided by 28 equals 1. Then we check the first number: 112 divided by 28 equals 4. Since this gives us a ratio of 4:1, the ratio 112:28 is equivalent to 16:4.
- 56:14: Following the same process, we can simplify this ratio. The greatest common divisor of 56 and 14 is 14. Let’s divide both terms by 14:
56 ÷ 14 = 4
14 ÷ 14 = 1
This ratio also simplifies to 4:1, which means it is equivalent to 16:4. - 8:2: For the last option, the greatest common divisor of 8 and 2 is 2. Dividing both numbers by 2 results in:
8 ÷ 2 = 4
2 ÷ 2 = 1
This ratio also simplifies to 4:1.
Because all three of the provided ratios (112:28, 56:14, and 8:2) simplify to the same base ratio of 4:1, they are all mathematically equivalent to 16:4. Thus, selecting all three options is the correct answer.
