36 is what percent of 80?

Introduction / Context:This question is the reverse of the usual percentage calculation. Instead of finding a percentage of a given number, we are asked to determine what percentage one number (36) is of another number (80). This is a fundamental concept in percentage comparisons, frequently used in exam score analysis, growth calculations and ratio interpretation.

Given Data / Assumptions:

The part value is 36.

The base or reference value is 80.

We must find the percentage p such that 36 = p% of 80.

No rounding is necessary because the result is an exact terminating decimal.

Concept / Approach:To find what percent one number is of another, we use the formula p% = (part / whole) * 100. Here, the part is 36 and the whole is 80. So we compute (36 / 80) * 100. Simplifying the fraction first often makes the calculation easier and reduces the chance of mistakes. After simplifying, we convert the result into a percentage value.

Step-by-Step Solution:We want p such that 36 is p% of 80.Use the formula p% = (36 / 80) * 100.First simplify the fraction 36 / 80.Divide numerator and denominator by 4: 36 / 80 = 9 / 20.Now compute (9 / 20) * 100.100 / 20 = 5, so (9 / 20) * 100 = 9 * 5 = 45.Thus, 36 is 45% of 80.

Verification / Alternative check:We can verify by checking if 45% of 80 equals 36. Compute 45% of 80 as (45 / 100) * 80 = 0.45 * 80. Now 0.45 * 80 = 36. Since the original number is recovered, our calculated percentage is confirmed to be correct.

Why Other Options Are Wrong:

54% of 80 is (54 / 100) * 80 = 43.2, not 36.

60% of 80 is 48, which is larger than 36.

64% of 80 is 51.2, still not 36.

50% of 80 is 40, which is also different from 36.

Common Pitfalls:Some learners mistakenly compute 80 as a percent of 36 instead of 36 as a percent of 80, which reverses the ratio. Others incorrectly set up the formula as (80 / 36) * 100. Another error is to forget to multiply by 100 at the end, thus leaving the result as a decimal rather than a percentage. Always remember that the part goes in the numerator, the whole in the denominator, and then multiply by 100 to convert to percent.

Final Answer:Thirty six is 45 percent of 80.