Evaluate $(\frac{6}{0.32} \div \frac{2}{0.084})^{-1}$ correct to 1 decimal place.

Step 1: Analyze the question

We need to evaluate the expression $(\frac{6}{0.32} \div \frac{2}{0.084})^{-1}$ and round the result to one decimal place.

Step 2: Explain the concept

To solve this, we follow the order of operations (BODMAS):

1. Solve the divisions inside the parentheses first.
2. Remember that dividing by a fraction is the same as multiplying by its reciprocal (flip the second fraction).
3. Apply the exponent $-1$, which means finding the reciprocal of the final result ($x^{-1} = \frac{1}{x}$).

Step 3: Show the solution

Part A: Simplify the fractions inside the parentheses First, let's simplify the two divisions:

• $\frac{6}{0.32} = \frac{600}{32} = 18.75$
• $\frac{2}{0.084} = \frac{2000}{84} \approx 23.8095$

Part B: Perform the division Now, we divide the first result by the second: $18.75 \div 23.8095$

Using the reciprocal method for accuracy: $\frac{6}{0.32} \times \frac{0.084}{2}$ $= \frac{6}{2} \times \frac{0.084}{0.32}$ $= 3 \times \frac{84}{320}$ $= 3 \times 0.2625 = 0.7875$

Part C: Apply the exponent $-1$ The expression is $(0.7875)^{-1}$, which is $\frac{1}{0.7875}$: $\frac{1}{0.7875} \approx 1.2698$

Part D: Round to 1 decimal place Rounding $1.2698$ to one decimal place gives 1.3.

Step 4: Identify the answer

Comparing our result to the given options, we see that 1.3 matches option A.

Step 5: Exam Tip

When dealing with decimals in JAMB, convert them to whole numbers by multiplying the numerator and denominator by powers of 10 (e.g., $10, 100, 1000$). This eliminates decimal errors and makes the division much easier to handle without a calculator.