Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 32:36
The Correct Answer and Explanation is:
The ratio 32:36 can be simplified by finding the greatest common divisor (GCD) of 32 and 36.
Step 1: Find the GCD of 32 and 36
To find the GCD, we need to list the factors of each number.
Factors of 32:
1, 2, 4, 8, 16, 32
Factors of 36:
1, 2, 3, 4, 6, 9, 12, 18, 36
The greatest common factor between the two lists is 4. Therefore, the GCD of 32 and 36 is 4.
Step 2: Simplify the ratio
Now, to simplify the ratio 32:36, divide both numbers by their GCD (which is 4).324:364=8:9\frac{32}{4} : \frac{36}{4} = 8 : 9432:436=8:9
Step 3: Final Answer
The simplified ratio of 32:36 is 8:9.
Explanation
Ratios represent a comparison between two or more numbers, and we often simplify them to their lowest terms, just like we do with fractions. Simplifying a ratio involves dividing both terms by their GCD, which is the largest number that divides both terms without leaving a remainder. By simplifying the ratio, we make the comparison easier to understand and work with.
In this case, the GCD of 32 and 36 is 4, meaning that both 32 and 36 can be divided by 4. After performing the division, we end up with 8 and 9, which gives us the simplified ratio 8:9.
In conclusion, when dealing with ratios, the process of finding the GCD and simplifying ensures that we express the ratio in the most efficient form, eliminating any unnecessary complexity and making the relationship between the two numbers clearer.
