The value of $ \frac{3}{4} \div (\frac{1}{2} + \frac{1}{8}) $ is: | Mathematics MCQ | Examoogle

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MathematicsSimplification

The value of $\frac{3}{4} \div (\frac{1}{2} + \frac{1}{8})$ is:

1.2

0.8

1.5

0.5

Correct Answer

📐 MA • Math LCM MethodMathematicsSimplification

Option A

Quick Summary:

Add the fractions using a common denominator (5/8) then multiply by the reciprocal of the sum.

📐MAMath SolutionLCM Method

📋 Given

Fraction 3/4 divided by the sum of 1/2 and 1/8.

🔢 Formula Used

34÷(12+18)\frac{3}{4}\div\left(\frac{1}{2}+\frac{1}{8}\right)43​÷(21​+81​)

⚡ Exam Hall Shortcut / Speed Trick

Add the fractions using a common denominator (5/8) then multiply by the reciprocal of the sum.

⚠️ Common Student Trap / Pitfall

Often students divide before adding the fractions, giving a wrong result.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Add the fractions in the denominator

Convert 1/2 to 4/8 and add to 1/8 to get 5/8.

12+18=58\frac{1}{2}+\frac{1}{8}=\frac{5}{8}21​+81​=85​

Replace division by multiplication of reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal.

34÷58=34×85\frac{3}{4}\div\frac{5}{8}=\frac{3}{4}\times\frac{8}{5}43​÷85​=43​×58​

Multiply numerators and denominators

Multiply across to obtain a single fraction.

3×84×5=2420\frac{3\times8}{4\times5}=\frac{24}{20}4×53×8​=2024​

Simplify the result

Reduce 24/20 to its lowest terms and convert to decimal.

2420=65=1.2\frac{24}{20}=\frac{6}{5}=1.22024​=56​=1.2

✅

A is correct because the calculation yields $1.2$ .

Core Concepts Used

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💡 EXAM TIP

The same reciprocal‑multiplication technique is used in ratio and proportion problems, helping simplify complex fractional expressions quickly.

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