Simplify $2\frac{3}{5} + 3\frac{1}{2} - \frac{3}{5}$

Appeared in: DSSSB 14 August 2024

Explanation

The expression is $2\frac{3}{5} + 3\frac{1}{2} - \frac{3}{5}$.
The mixed fraction $2\frac{3}{5}$ can be written as the sum $2 + \frac{3}{5}$.
The expression becomes $2 + \frac{3}{5} + 3\frac{1}{2} - \frac{3}{5}$.
The terms $+\frac{3}{5}$ and $-\frac{3}{5}$ cancel each other out.
The remaining expression is $2 + 3\frac{1}{2}$.
Adding the whole number 2 and the mixed number $3\frac{1}{2}$ gives the final answer $5\frac{1}{2}$.

Option A: This answer may result from incorrectly handling the fractions. For example, adding the whole numbers (2+3=5) and then incorrectly adding the numerators and a denominator (3+1+2=6) and simplifying to get 2 1/2, leading to 5 + 2 1/2 = 7 1/2.
Option C: This result might be obtained by incorrectly adding all the fractional parts without considering the subtraction. For instance, calculating $2+3=5$ and then adding all fractions $3/5 + 1/2 + 3/5 = 1.7$, which rounds up, might lead to an estimate near 6 1/2.
Option D: This answer is significantly larger than the correct result and likely stems from a major calculation error, such as adding all numbers present without regard for their place value or fractional nature.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simplification of expressions involving mixed fractions, addition, and subtraction as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, proficiency in arithmetic, including fractions, is a fundamental skill for nurses.
Nurses frequently perform calculations for medication dosages, IV drip rates, and fluid balance, where errors can have serious patient safety consequences.
What if? If the expression was $2\frac{3}{5} - 3\frac{1}{2} - \frac{3}{5}$, the answer would be $2 - 3\frac{1}{2} = -1\frac{1}{2}$. The cancellation of the fraction $\frac{3}{5}$ would still be the first step.

How to Approach the Question

First, read the entire mathematical expression to identify all the numbers and operations involved.
Look for opportunities to simplify the calculation. In this case, notice that the expression contains both a $+ \frac{3}{5}$ (within $2\frac{3}{5}$) and a $- \frac{3}{5}$.
Recognize that these two terms will cancel each other out, simplifying the problem significantly.
Rewrite the expression to make this cancellation clear: $(2 + \frac{3}{5}) + 3\frac{1}{2} - \frac{3}{5}$.
After cancelling the fractions, you are left with a much simpler addition: $2 + 3\frac{1}{2}$.
Perform the final addition to arrive at the correct answer.

Concept Tested & Keywords

Concept Tested: Simplification of expressions involving mixed fractions, addition, and subtraction.
Stem keywords: Simplify, Mixed fraction, Addition, Subtraction
Lead-in keywords: Simplify

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Practise the full DSSSB 14 August 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.