Evaluate: $\dfrac{3}{4} \div \dfrac{5}{8} \times \dfrac{2}{3}$. | Mathematics MCQ | Examoogle

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Evaluate: $\dfrac{3}{4} \div \dfrac{5}{8} \times \dfrac{2}{3}$ .

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{3}{2}$

$\frac{7}{8}$

Correct Answer

⚙️ TE • Technical BODMAS / Fraction RuleMathematicsArithmetic

Option A

$\frac{4}{5}$

Quick Summary:

Convert division to multiplication by taking the reciprocal of the fraction immediately following the division sign, then cancel common factors across the numerators and denominators to save time.

📐MAMath SolutionBODMAS / Fraction Rule

📋 Given

Given expression to evaluate: $\dfrac{3}{4} \div \dfrac{5}{8} \times \dfrac{2}{3}$

🔢 Formula Used

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}ba​÷dc​=ba​×cd​

⚡ Exam Hall Shortcut / Speed Trick

Convert division to multiplication by taking the reciprocal of the fraction immediately following the division sign, then cancel common factors across the numerators and denominators to save time.

⚠️ Common Student Trap / Pitfall

Students often perform multiplication before division from left to right, or forget to invert the fraction after the division symbol.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Step 1: Understand the Order of Operations

According to the rule of evaluation for operations of the same precedence (multiplication and division), we evaluate from left to right, replacing division with multiplication by the reciprocal.

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

Step 2: Rewrite the Complete Expression

Substitute the inverted division part back into the expression so that all operations are multiplications.

34×85×23\frac{3}{4} \times \frac{8}{5} \times \frac{2}{3}43​×58​×32​

Step 3: Simplify and Cancel Common Factors

Cancel out the common factor $3$ in the numerator and denominator, and simplify $8$ and $4$ : $\dfrac{8}{4} = 2$ .

31×25×23=2×25\frac{\cancel{3}}{1} \times \frac{2}{5} \times \frac{2}{\cancel{3}} = \frac{2 \times 2}{5}13​​×52​×3​2​=52×2​

Step 4: Calculate the Final Value

Multiply the remaining numerator values together and keep the denominator.

45\frac{4}{5}54​

✅

A is correct because evaluating the expression $\dfrac{3}{4} \div \dfrac{5}{8} \times \dfrac{2}{3}$ simplifies to $\dfrac{4}{5}$ .

Core Concepts Used

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Fraction arithmetic Reciprocal operations BODMAS order of operations

💡 EXAM TIP

Mastering fraction simplification and reciprocal rules is crucial for solving algebraic equations and ratio-proportion problems efficiently in competitive exams.

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