To solve the expression \((\frac{1}{0.06} \div \frac{1}{0.042}) - 1\), we will break it down step-by-step. ### Step 1: Simplifying the Division The expression involves dividing two fractions. Recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division as follows: \[ \frac{1}{0.06} \div \frac{1}{0.042} = \frac{1}{0.06} \times \frac{0.042}{1} \] This simplifies to: \[ \frac{0.042}{0.06} \] ### Step 2: Performing the Division Next, we need to calculate \(\frac{0.042}{0.06}\). To do this, we can convert both numbers to fractions: \[ 0.042 = \frac{42}{1000} \quad \text{and} \quad 0.06 = \frac{6}{100} \] Now, we can rewrite the division of these two fractions: \[ \frac{0.042}{0.06} = \frac{\frac{42}{1000}}{\frac{6}{100}} = \frac{42}{1000} \times \frac{100}{6} \] ### Step 3: Simplifying the Fraction Now, we can simplify this expression: \[ = \frac{42 \times 100}{1000 \times 6} \] The \(100\) in the numerator and denominator cancels out: \[ = \frac{42}{1000 \times 6} = \frac{42}{6000} \] Next, we can simplify \(\frac{42}{6000}\): \[ = \frac{42 \div 6}{6000 \div 6} = \frac{7}{1000} \] ### Step 4: Calculating the Value Now, we need to calculate \(\frac{7}{1000}\): \[ \frac{7}{1000} = 0.007 \] ### Step 5: Subtracting 1 Now we return to our original expression: \[ \frac{1}{0.06} \div \frac{1}{0.042} - 1 = 0.007 - 1 \] Calculating this gives: \[ 0.007 - 1 = -0.993 \] ### Step 6: Final Calculation However, we need to ensure we are calculating the correct expression. Let's go back to the division step: Instead of calculating \(\frac{0.042}{0.06}\) directly, we can also calculate \(\frac{1}{0.06}\) and \(\frac{1}{0.042}\) separately: \[ \frac{1}{0.06} = \frac{100}{6} \approx 16.67 \] \[ \frac{1}{0.042} = \frac{100}{4.2} \approx 23.81 \] Now, dividing these: \[ \frac{16.67}{23.81} \approx 0.699 \] Subtracting 1 gives: \[ 0.699 - 1 = -0.301 \] ### Conclusion After reviewing the calculations, it appears that the initial interpretation of the problem was incorrect. The correct answer should be calculated as follows: 1. Calculate \(\frac{1}{0.06} = 16.67\) 2. Calculate \(\frac{1}{0.042} = 23.81\) 3. Divide: \(\frac{16.67}{23.81} \approx 0.699\) 4. Subtract 1: \(0.699 - 1 = -0.301\) ### Summary of the Correct Answer - The correct answer is not among the options provided. - The calculations show that the expression evaluates to approximately -0.301. - The initial assumption of the answer being option A (1.43) was incorrect. ### Revision Summary - Division of fractions can be simplified by multiplying by the reciprocal. - Always simplify fractions before performing calculations. - Double-check calculations to avoid errors in subtraction or division. - Ensure to interpret the problem correctly to avoid miscalculations.