What is the cube of -1 1/3?

Appeared in: OSSSC Nursing Officer-2021

Explanation

First, the mixed fraction -1 1/3 is converted to an improper fraction. This is done by calculating (1 * 3 + 1)/3, which equals 4/3, and then reapplying the negative sign to get -4/3.
Next, the improper fraction -4/3 is cubed, which means multiplying it by itself three times: (-4/3) × (-4/3) × (-4/3).
The numerator is calculated as (-4) × (-4) × (-4) = -64.
The denominator is calculated as 3 × 3 × 3 = 27.
Combining the results gives the final answer of -64/27.

Option A: The value 16/9 is the result of squaring -4/3, not cubing it. (-4/3)2 = 16/9.
Option B: The value -16/27 is an incorrect calculation. The numerator is incorrect; it appears to be the result of squaring -4 (which is 16) and then incorrectly applying a negative sign, instead of cubing -4.
Option D: The value 64/27 is the cube of +4/3, not -4/3. This result incorrectly handles the negative sign. The cube of a negative number is always negative.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the cube of a negative mixed fraction as background academic context rather than a clinical decision trigger.
This question tests fundamental mathematical proficiency, which is a critical skill for nurses and other healthcare professionals.
Accurate calculation is essential in clinical practice for tasks such as medication dosage calculation, IV drip rate regulation, and interpreting patient data.
Errors in basic math can have serious consequences for patient safety, making proficiency a core competency.

How to Approach the Question

First, carefully read the question to identify the number (-1 1/3) and the mathematical operation required (cubing).
The first step in handling calculations with mixed fractions is to convert them into improper fractions. Convert -1 1/3 to -4/3.
Recall that cubing a number means raising it to the power of 3.
Calculate the cube of the improper fraction: (-4/3)3.
Remember the rule of signs: a negative number raised to an odd power (like 3) results in a negative number. This helps eliminate positive options.
Calculate the cube of the numerator (43 = 64) and the cube of the denominator (33 = 27).

Concept Tested & Keywords

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