One third of a number is 45. What is 45 percent of that number?

Introduction / Context:
This problem connects fractions and percentages for the same unknown number. It tests the ability to translate given fractional information into the full number and then use that to compute a specified percentage of the number.

Given Data / Assumptions:

• One third of a number is 45.
• We must find 45 percent of that number.

Concept / Approach:
If 1/3 of a number is known, we can recover the full number by multiplying by 3. After that, 45 percent of the number can be computed by multiplying the number by 45/100. Both steps are straightforward applications of fraction and percentage operations.

Step-by-Step Solution:
Let the number be N.Given that (1/3) * N = 45.So N = 45 * 3 = 135.We need to find 45 percent of N.45 percent of N = (45 / 100) * 135.Compute (45 / 100) * 135 = 0.45 * 135.0.45 * 135 = 60.75.

Verification / Alternative check:
We can think of 45 percent as 9/20. Then 9/20 of 135 equals (9 * 135) / 20 = 1215 / 20 = 60.75, which matches the decimal method and confirms the result.

Why Other Options Are Wrong:
Values 58.25, 61.25 and 70.75 arise from arithmetic errors like using the wrong fraction or confusing 45 percent with 45 out of 135 without scaling. Only 60.75 is the correct 45 percent of 135.

Common Pitfalls:
Some candidates mistakenly treat 45 as the original number rather than one third of it, or they compute 45 percent of 45 instead of 135. Carefully follow the order: first reconstruct the number, then apply the percentage.

Final Answer:
45 percent of the number is 60.75.