Express 125% as a fraction in simplest form.

Introduction / Context:
This question checks understanding of converting a percentage into a fraction in simplest form. Knowing how to convert between percentages, fractions, and decimals is a core skill in arithmetic and is frequently used in topics such as ratios, proportions, and probability.

Given Data / Assumptions:

• We are given a percentage: 125%.
• We must express 125% as a proper or improper fraction in simplest form.
• No additional context or conditions are needed.

Concept / Approach:
To convert a percentage to a fraction, we write the percentage as a fraction over 100 and then simplify. For example, X% becomes X / 100. If the resulting fraction is not in simplest form, we reduce it by dividing numerator and denominator by their greatest common divisor. In this problem, 125% will give an improper fraction, which is acceptable as long as it is simplified.

Step-by-Step Solution:
Step 1: Write 125% as a fraction over 100: 125% = 125 / 100. Step 2: Simplify 125 / 100 by dividing numerator and denominator by 25. Step 3: 125 ÷ 25 = 5 and 100 ÷ 25 = 4, so 125 / 100 simplifies to 5 / 4. Step 4: Check if 5 / 4 can be reduced further. Since 5 and 4 have no common factors other than 1, it is already in simplest form. Step 5: Therefore, 125% as a fraction is 5 / 4.

Verification / Alternative check:
We can convert 5 / 4 back into a percentage to check. First, express 5 / 4 as a decimal: 5 / 4 = 1.25. Then multiply by 100 to get 1.25 * 100 = 125%. This confirms that the fraction 5 / 4 exactly represents 125%, so the conversion is correct.

Why Other Options Are Wrong:
1/4 corresponds to 25%, not 125%. 3/4 corresponds to 75%. 7/4 corresponds to 175%. The option 5/2 corresponds to 250%. None of these equal 125%. Only 5/4 reverses correctly back to 125%, so it is the correct answer.

Common Pitfalls:
Some learners mistakenly divide 100 by 125 instead of writing 125 / 100, which inverts the fraction. Others convert to a decimal but misplace the decimal point, for example writing 1.25 as 0.125. It is also easy to forget to simplify a fraction such as 125 / 100 before choosing the final answer. Always remember that X% equals X / 100 and then simplify.

Final Answer:
125% expressed as a fraction in simplest form is 5/4.