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 81 and 33. This is the largest number that divides both 81 and 33 without leaving a remainder.
Step 1: Find the GCD of 81 and 33
To find the GCD, start by listing the factors of both numbers:
- The factors of 81 are 1, 3, 9, 27, and 81.
- The factors of 33 are 1, 3, 11, and 33.
The greatest common factor is 3.
Step 2: Divide both terms of the ratio by the GCD
Now that we know the GCD is 3, divide both 81 and 33 by 3:
- $81 \div 3 = 27$
- $33 \div 3 = 11$
Step 3: Simplified ratio
The simplified ratio is 27:11.
Explanation
When simplifying ratios, you want to divide both parts of the ratio by their GCD to express the relationship between the two numbers in its simplest form. This ensures that the ratio is represented by the smallest whole numbers that maintain the same proportion as the original.
In this case, by dividing both 81 and 33 by their GCD (3), you reduced the ratio from 81:33 to 27:11, which is the simplest form of the given ratio.