Simplify $\frac{2.46 \times 2.46 - 1.46 \times 1.46}{2.46 - 1.... | Mathematics MCQ | Examoogle

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Simplify $\frac{2.46 \times 2.46 - 1.46 \times 1.46}{2.46 - 1.46}$ and select the most appropriate fraction.

$\frac{392}{100}$

$\frac{392}{10000}$

$\frac{392}{10}$

$\frac{392}{1000}$

Correct Answer

📐 MA • Math Algebraic IdentityMathematicsPrevious Year Paper 2024

Option A

$\frac{392}{100}$

Quick Summary:

Recognize the algebraic identity $a^2 - b^2 = (a-b)(a+b)$ . The $(a-b)$ term cancels out from the numerator and denominator, leaving only $a+b = 2.46 + 1.46 = 3.92$ .

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📐MAMath SolutionAlgebraic Identity

📋 Given

An expression of the form (aa - bb) / (a - b) where a = 2.46 and b = 1.46.

🔢 Formula Used

a2−b2a−b=a+b\frac{a^2 - b^2}{a - b} = a + ba−ba2−b2​=a+b

⚡ Exam Hall Shortcut / Speed Trick

Recognize the algebraic identity $a^2 - b^2 = (a-b)(a+b)$ . The $(a-b)$ term cancels out from the numerator and denominator, leaving only $a+b = 2.46 + 1.46 = 3.92$ .

⚠️ Common Student Trap / Pitfall

Many students attempt to calculate the squares $2.46^2$ and $1.46^2$ manually, which is time-consuming and increases the chance of arithmetic errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify algebraic pattern

Observe that the expression is in the form $\frac{a^2 - b^2}{a - b}$ where $a = 2.46$ and $b = 1.46$ .

a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)a2−b2=(a−b)(a+b)

Simplify the expression

Substitute the identity into the fraction: $\frac{(a - b)(a + b)}{a - b}$ . Canceling $(a - b)$ yields $a + b$ .

(a−b)(a+b)a−b=a+b\frac{(a - b)(a + b)}{a - b} = a + ba−b(a−b)(a+b)​=a+b

Perform final calculation

Add the two values: $2.46 + 1.46 = 3.92$ . Express this as a fraction: $3.92 = \frac{392}{100}$ .

2.46+1.46=3.92=3921002.46 + 1.46 = 3.92 = \frac{392}{100}2.46+1.46=3.92=100392​

✅

A is correct because the expression simplifies to $2.46 + 1.46 = 3.92$ , which is equivalent to $\frac{392}{100}$ .

Core Concepts Used

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Algebraic Identities Fraction Simplification Decimal Addition

💡 EXAM TIP

This type of simplification frequently appears in simplification problems where identifying the difference of squares identity saves significant time.

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