4 4/5 of 259.99 is equal to what percentage of 1247.9?

Introduction / Context:
This question involves fractions, decimals, and percentages together. It asks you to find what percentage a multiplied value (4 4/5 of 259.99) is of another number (1247.9). Such problems are important in aptitude exams because they test your ability to handle mixed numbers, convert them into improper fractions or decimals, perform multiplication, and then express the result as a percentage of another quantity.

Given Data / Assumptions:

• We need to compute 4 4/5 of 259.99.
• We then compare this value with 1247.9.
• We must express the computed value as a percentage of 1247.9.
• No rounding instructions are given, so standard reasonable rounding is acceptable.

Concept / Approach:
First, convert the mixed number 4 4/5 into an improper fraction or decimal. 4 4/5 equals 4.8. Then compute 4.8 * 259.99. After obtaining this product, to find what percentage it is of 1247.9, we use the formula: Percentage = (Value / Reference) * 100, where the value is 4.8 * 259.99 and the reference is 1247.9. This will show whether the result is close to 100% or some other option given in the choices.

Step-by-Step Solution:
Step 1: Convert 4 4/5 to decimal form: 4 4/5 = 4 + 4 / 5 = 4 + 0.8 = 4.8. Step 2: Compute 4.8 * 259.99. Step 3: 4.8 * 259.99 ≈ 1247.952 (since 4.8 * 260 ≈ 1248, the exact multiplication is 1247.952). Step 4: Now, we need the percentage of 1247.952 with respect to 1247.9. Step 5: Use Percentage = (Value / Reference) * 100 = (1247.952 / 1247.9) * 100. Step 6: Since 1247.952 is extremely close to 1247.9, their ratio is very close to 1. Step 7: Therefore, the percentage is approximately 100%. Step 8: Hence, 4 4/5 of 259.99 is essentially equal to 100% of 1247.9.

Verification / Alternative check:
We can approximate by rounding 259.99 to 260. Then 4.8 * 260 = 1248. The reference value is 1247.9, which is almost the same as 1248. So the percentage is (1248 / 1247.9) * 100, which is almost exactly 100%. This quick approximation confirms that 100% is the correct choice among the given options.

Why Other Options Are Wrong:
96%, 78%, 88%, and 82% would represent values noticeably lower than the reference 1247.9. For example, 96% of 1247.9 is about 1197, and 88% is about 1098. These are far from 1247.952. Since our computed product is essentially equal to the reference value, only 100% correctly represents the relationship. Thus, all other percentage options are inconsistent with the calculation.

Common Pitfalls:
One common mistake is to misinterpret the mixed number 4 4/5 as 4.45 or 4.05 instead of 4.8. Another pitfall is to round too early or incorrectly, which may give a noticeably different percentage. Students sometimes also invert the percentage formula by computing (Reference / Value) * 100 instead of (Value / Reference) * 100, leading to the reciprocal percentage. Careful conversion and accurate use of the percentage formula prevents these errors.

Final Answer:
4 4/5 of 259.99 is approximately 100% of 1247.9.