In aptitude (fractional simplification), compute the value of (1112 / 139) - 5 by first simplifying the fraction 1112 / 139 and then performing the subtraction to obtain the final result.

Introduction / Context:
This is a straightforward fractional simplification problem. It checks the ability to subtract an integer from a fraction and to recognise when the fraction itself simplifies to an integer plus or minus a smaller fraction. Such questions often appear in the early part of aptitude test papers, where quick mental arithmetic can save valuable time for tougher questions later.

Given Data / Assumptions:
- Expression: (1112 / 139) - 5.
- All numbers are real and standard arithmetic rules apply.
- We may convert 5 into a fraction with denominator 139 to combine the terms more easily.

Concept / Approach:
A simple and effective approach is to express both terms with the same denominator. Since the denominator 139 is already present in the first term, we convert 5 into 5 * 139 / 139 and then subtract numerators. After finding the resulting fraction, we can see whether it simplifies to an integer. Alternatively, we can perform long division to estimate 1112 / 139 and then subtract 5, but the fraction method is cleaner and exact.

Step-by-Step Solution:
Step 1: Start with the expression (1112 / 139) - 5.Step 2: Write 5 with denominator 139: 5 = 5 * 139 / 139 = 695 / 139.Step 3: Now the expression becomes (1112 / 139) - (695 / 139).Step 4: Combine the fractions by subtracting numerators: (1112 - 695) / 139.Step 5: Compute the numerator: 1112 - 695 = 417.Step 6: So the fraction becomes 417 / 139.Step 7: Notice that 417 = 3 * 139, so 417 / 139 = 3.Step 8: Therefore, (1112 / 139) - 5 simplifies exactly to 3.

Verification / Alternative check:
An alternative approach is to perform approximate long division. Compute 1112 / 139: since 139 * 8 = 1112, this shows that 1112 / 139 = 8 exactly. Then the expression becomes 8 - 5 = 3. This confirms the result obtained by the fractional method and proves that the answer is exactly 3, not an approximation.

Why Other Options Are Wrong:
- -3: This would result from reversing the subtraction order and computing 5 - (1112 / 139) instead of (1112 / 139) - 5.
- 8: This is simply 1112 / 139 and ignores the subtraction by 5 entirely.
- 557/67 and 556/67: These are random-looking fractions that do not correspond to any correct simplification of the given expression. They might arise from misusing denominators or from arithmetic mistakes in subtracting numerators or denominators incorrectly.

Common Pitfalls:
Students may incorrectly use 5 / 139 instead of 5 * 139 / 139 when trying to combine fractions, which drastically changes the value. Another error is failing to recognise that 417 is exactly divisible by 139, and leaving the answer as 417 / 139 without simplifying. Paying attention to factorisation and basic multiplication tables helps in spotting such simplifications quickly.

Final Answer:
The expression (1112 / 139) - 5 simplifies to the integer 3.