Which of these fractions is the largest?

Appeared in: RRB Staff Nurse Delhi-2015

Explanation

The fraction 7/8 is the largest among the given options.
When converted to a decimal, 7/8 equals 0.875, which is greater than the decimal values of the other fractions: 6/7 (≈0.857), 5/6 (≈0.833), and 4/5 (0.800).
Alternatively, each fraction is of the form (n-1)/n, which is equal to 1 - 1/n. The value is largest when the subtracted part (1/n) is smallest.
Since 1/8 is the smallest unit fraction among 1/5, 1/6, 1/7, and 1/8, the fraction 7/8 (which is 1 - 1/8) is the largest.

Option A: The fraction 6/7 is approximately 0.857, which is less than 0.875 (7/8).
Option B: The fraction 5/6 is approximately 0.833, which is less than 0.875 (7/8).
Option D: The fraction 4/5 is 0.800, which is the smallest value among all the options.

Visual 1: Bar Chart - A bar chart visually comparing the decimal values (0.800, 0.833, 0.857, 0.875) for each fraction. This provides a clear, at-a-glance representation of which value is the largest.
Visual 2: Number Line - A number line from 0 to 1 showing the precise location of 4/5, 5/6, 6/7, and 7/8. This helps visualize that 7/8 is furthest to the right and therefore the largest.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Comparing Fractions as background academic context rather than a clinical decision trigger.
While not a clinical question, a strong understanding of fractions and decimals is a fundamental prerequisite for safe nursing practice.
This mathematical skill is essential for accurate medication dosage calculations, including titrating IV drips, calculating pediatric doses, and verifying pharmacy-prepared medications.
What if? If a nurse misinterprets a fractional dose, for example, confusing 1/4 mg with 1/5 mg, it could lead to a medication error. In this case, 1/4 (0.25) is a larger dose than 1/5 (0.20), and such a mistake could result in an overdose or underdose, potentially harming the patient.

How to Approach the Question

First, identify the task: you need to compare four fractions to find the largest one.
Observe the structure of the fractions. Notice that in each case (4/5, 5/6, 6/7, 7/8), the numerator is one less than the denominator.
Recognize that this pattern allows for a shortcut. Each fraction represents a value slightly less than 1. The largest fraction will be the one that is 'least' less than 1.
Calculate the difference from 1 for each fraction: 1 - 4/5 = 1/5; 1 - 5/6 = 1/6; 1 - 6/7 = 1/7; 1 - 7/8 = 1/8.
Compare these differences. The smallest difference corresponds to the largest original fraction. Since 1/8 is the smallest difference, 7/8 is the largest fraction.
Alternatively, convert each fraction to a decimal and compare the results directly. The largest decimal value corresponds to the largest fraction.

Concept Tested & Keywords

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