The Correct Answer and Explanation is:
The correct answer is A. 14.75.
Here is a detailed explanation of how to arrive at this solution.
The problem as written is “Simplify 5.25 ÷ 12.5 : 1.25 – 4 * 1/8”. A literal interpretation, where both the ‘÷’ and ‘:’ symbols represent division, does not lead to any of the multiple choice answers. When calculated strictly as written, the result is a negative number. This suggests there is a typographical error in the problem statement, which is common in test questions. The most likely error is that the first division symbol (÷) was intended to be an addition symbol (+).
Let’s solve the problem with this correction. The intended expression is likely:
5.25 + 12.5 ÷ 1.25 – 4 * (1/8)
To solve this, we must follow the order of operations, often remembered by the acronym PEMDAS or BODMAS. This means we perform operations in the following sequence: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).
- Multiplication and Division:
First, we handle the division and multiplication parts of the expression.- Calculate 12.5 ÷ 1.25. Dividing by 1.25 is the same as multiplying by its reciprocal. Alternatively, you can multiply both numbers by 100 to remove the decimals, making the calculation 1250 ÷ 125, which equals 10.
- Next, calculate 4 * (1/8). This becomes 4/8, which simplifies to 1/2 or 0.5.
- Substitute and Rewrite:
Now we replace these parts of the expression with their results:
5.25 + 10 – 0.5 - Addition and Subtraction:
Finally, we perform the addition and subtraction from left to right.- First, add 5.25 + 10, which gives 15.25.
- Then, subtract 0.5 from this result: 15.25 – 0.5, which equals 14.75.
This final result, 14.75, matches option A.
