What should be added to $\frac{-5}{9}$ to get $\frac{-5}{6}$? | Mathematics MCQ

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MathematicsPrevious Year Paper 2024

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What should be added to $\frac{-5}{9}$ to get $\frac{-5}{6}$ ?

$\frac{-5}{18}$

$\frac{-5}{9}$

$\frac{-5}{12}$

$\frac{-5}{6}$

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option A

$\frac{-5}{18}$

Quick Summary:

Express both fractions with a common denominator (18). The difference between -15/18 and -10/18 is +5/18.

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📐MAMath SolutionDirect Formula

📋 Given

Initial value = -5/9, Target result = -5/6

🔢 Formula Used

x+−59=−56x + \frac{-5}{9} = \frac{-5}{6}x+9−5​=6−5​

⚡ Exam Hall Shortcut / Speed Trick

Express both fractions with a common denominator (18). The difference between -15/18 and -10/18 is +5/18.

⚠️ Common Student Trap / Pitfall

Failing to account for the negative signs or confusing the order of subtraction (should be Result - Initial).

🔢 Step-by-Step Solution

Set up the equation

Let the value to be added be $x$ . We need to solve for $x$ in the equation: $x + (-\frac{5}{9}) = -\frac{5}{6}$ .

x=−56−(−59)x = -\frac{5}{6} - (-\frac{5}{9})x=−65​−(−95​)

Simplify and find common denominator

The equation becomes $x = -\frac{5}{6} + \frac{5}{9}$ . To add these fractions, we find the Least Common Multiple of 6 and 9, which is 18.

x=−5×318+5×218x = \frac{-5 \times 3}{18} + \frac{5 \times 2}{18}x=18−5×3​+185×2​

Calculate the final value

Perform the arithmetic: $x = \frac{-15}{18} + \frac{10}{18} = \frac{-5}{18}$ .

x=−518x = -\frac{5}{18}x=−185​

✅

A is correct because adding -5/18 to -5/9 results in -15/18 which simplifies to -5/6.

Core Concepts Used

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Fractions Addition Negative Numbers Common Denominators

💡 EXAM TIP

This concept of finding the difference between two rational numbers is fundamental for coordinate geometry and finding distances on the number line.

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