Find an equivalent ratio in simplest terms:
81:33
The correct answer and explanation is:
To simplify the ratio 81:33, you need to find the greatest common divisor (GCD) of both numbers and divide each by that number. Here’s how to do it:
- Find the GCD:
The first step is to determine the greatest common divisor of 81 and 33. You can do this by factoring both numbers into their prime factors:- 81 = 3 × 3 × 3 × 3 (which is 343^4)
- 33 = 3 × 11
The GCD of 81 and 33 is 3 because it’s the highest number that divides both 81 and 33.
- Divide both terms by the GCD:
Now, divide both parts of the ratio by 3:- 81 ÷ 3 = 27
- 33 ÷ 3 = 11
So, the simplified ratio is 27:11.
Explanation:
Simplifying a ratio involves finding the largest number that both terms can be divided by, which is the GCD. This allows the ratio to be expressed in its simplest form. By dividing both the numerator and the denominator by their GCD, the ratio is reduced without changing its overall proportion. This ensures that the relationship between the two numbers remains the same, but the numbers are smaller and easier to work with.
In this case, dividing both terms of 81:33 by their GCD (3) reduces the ratio to 27:11. This is the simplest form of the original ratio.