Which of the following fractions is the largest?

RRB Staff Nurse Mumbai-2015

Non Nursing Subjects

Hard

Appeared in: RRB Staff Nurse Mumbai-2015

Explanation

To compare fractions, one reliable method is to convert them all to a common denominator. The least common multiple (LCM) of the denominators (8, 16, 40, 80) is 80.
When 7/8 is converted to have a denominator of 80, it becomes 70/80.
The other fractions convert to 65/80 (from 13/16), 62/80 (from 31/40), and 63/80.
By comparing the numerators (70, 65, 62, and 63), it is clear that 70 is the largest. Therefore, 7/8 is the largest fraction.
Alternatively, converting the fractions to decimals (7/8 = 0.875, 13/16 = 0.8125, 31/40 = 0.775, 63/80 = 0.7875) also shows that 7/8 has the highest value.

Option B: The fraction 13/16 is equivalent to 65/80 or 0.8125. This value is less than 7/8, which is 70/80 or 0.875.
Option C: The fraction 31/40 is equivalent to 62/80 or 0.775. This is the smallest value among all the given options.
Option D: The fraction 63/80 is equivalent to 0.7875. This value is smaller than both 7/8 (0.875) and 13/16 (0.8125).

Visual 1: Infographic - A number line marked from 0.75 to 0.90, showing the precise location of each fraction (0.775, 0.7875, 0.8125, and 0.875) to visually confirm that 7/8 (0.875) is the 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 the values of different fractions as background academic context rather than a clinical decision trigger.
Basic arithmetic skills, including comparing fractions, are foundational for safe and accurate medication administration. Nurses frequently perform dosage calculations that involve fractions.
A nurse might need to calculate a partial dose from a scored tablet (e.g., give 3/4 of a tablet) or draw up a fractional amount of a liquid medication. Misinterpreting a fraction could lead to a significant medication error.
What if? If a medication order was for 0.8 mg and the available tablets were 1 mg scored into quarters (0.25 mg each), the nurse would need to administer 3/4 of a tablet (0.75 mg) and understand this is slightly less than the ordered dose, requiring clarification. This demonstrates how fraction-to-decimal conversion is a critical, real-world nursing skill.

How to Approach the Question

First, identify the core task: you need to compare four different fractions and find the one with the greatest value.
Recognize that fractions can be compared directly only when they share a common denominator. Choose a method to achieve this: either finding the least common denominator (LCD) or converting to decimals.
Method 1 (LCD): Find the smallest number that all denominators (8, 16, 40, 80) divide into evenly. In this case, it's 80.
Convert each fraction into an equivalent fraction with the denominator of 80. For example, for 7/8, divide 80 by 8 (which is 10), then multiply the numerator 7 by 10 to get 70. The new fraction is 70/80.
Once all fractions have the same denominator, simply compare their numerators. The fraction with the largest numerator is the largest overall.
Method 2 (Decimals): Use a calculator or long division to convert each fraction to a decimal. Then, compare the decimal numbers to identify the largest value.

Concept Tested & Keywords

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