The value of$\frac{3}{7} + \frac{2}{7} + \frac{1}{14} - 3 = ?$ | Mathematics MCQ | Examoogle

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The value of $\frac{3}{7} + \frac{2}{7} + \frac{1}{14} - 3 =?$

$-\frac{27}{14}$

$\frac{13}{14}$

$-\frac{31}{14}$

$\frac{27}{14}$

Correct Answer

📐 MA • Math Fraction ArithmeticMathematicsPrevious Year Paper 2024

Option C

$-\frac{31}{14}$

Quick Summary:

Convert all terms to the common denominator 14: (6/14 + 4/14 + 1/14) - 42/14. Then simply subtract the numerators: (6 + 4 + 1 - 42) / 14 = -31/14.

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📐MAMath SolutionFraction Arithmetic

📋 Given

An expression containing fractions and an integer: 3/7 + 2/7 + 1/14 - 3

🔢 Formula Used

an+bn+cm−d=m×a+m×b+n×c−d×n×mn×m\frac{a}{n} + \frac{b}{n} + \frac{c}{m} - d = \frac{m \times a + m \times b + n \times c - d \times n \times m}{n \times m}na​+nb​+mc​−d=n×mm×a+m×b+n×c−d×n×m​

⚡ Exam Hall Shortcut / Speed Trick

Convert all terms to the common denominator 14: (6/14 + 4/14 + 1/14) - 42/14. Then simply subtract the numerators: (6 + 4 + 1 - 42) / 14 = -31/14.

⚠️ Common Student Trap / Pitfall

Students often make a sign error when subtracting the integer 3, or fail to convert 3 into a fraction with the correct common denominator (i.e., treating it as 3/14 instead of 42/14).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Find common denominator

The denominators are 7, 7, and 14. The Least Common Multiple (LCM) of 7 and 14 is 14. Convert all fractions to have 14 as the denominator.

37=614,27=414,3=4214\frac{3}{7} = \frac{6}{14}, \quad \frac{2}{7} = \frac{4}{14}, \quad 3 = \frac{42}{14}73​=146​,72​=144​,3=1442​

Substitute and Add

Substitute the converted values back into the original expression.

614+414+114−4214\frac{6}{14} + \frac{4}{14} + \frac{1}{14} - \frac{42}{14}146​+144​+141​−1442​

Perform the subtraction

Combine the numerators over the common denominator: $\frac{6 + 4 + 1 - 42}{14}$

11−4214=−3114\frac{11 - 42}{14} = -\frac{31}{14}1411−42​=−1431​

✅

C is correct because the result of the calculation $\frac{3}{7} + \frac{2}{7} + \frac{1}{14} - 3$ is $-\frac{31}{14}$ .

Core Concepts Used

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Fractional Addition Common Denominators Integer Arithmetic

💡 EXAM TIP

Always identify the lowest common denominator first in rational expression problems to simplify calculations quickly and reduce errors.

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