What will be the result obtained when the numerator of $\frac{96}{50}$ is decreased by 37.5% and its denominator decreased by 20%.

1. Analyze the question

We are given the fraction $\frac{96}{50}$. We need to:

• Decrease the numerator (96) by 37.5%.
• Decrease the denominator (50) by 20%.
• Calculate the new fraction and simplify it to find the result.

2. Explain the concept

To decrease a value by a percentage, you subtract that percentage of the value from the original value.

• Formula: New Value = Original Value - (Percentage $\times$ Original Value)
• Alternatively, you can multiply the original value by $(100\% - \text{percentage})$. For example, a 20% decrease means the new value is 80% of the original.

3. Show the solution

Step 1: Calculate the new numerator The original numerator is 96. We decrease it by 37.5%.

• Decrease amount = $37.5\% \text{ of } 96 = 0.375 \times 96$
• $0.375 \times 96 = 36$
• New numerator = $96 - 36 = 60$

Step 2: Calculate the new denominator The original denominator is 50. We decrease it by 20%.

• Decrease amount = $20\% \text{ of } 50 = 0.20 \times 50$
• $0.20 \times 50 = 10$
• New denominator = $50 - 10 = 40$

Step 3: Form the new fraction and simplify

• New fraction = $\frac{60}{40}$
• Simplify by dividing both by 20: $\frac{60 \div 20}{40 \div 20} = \frac{3}{2}$
• Convert to decimal: $\frac{3}{2} = 1.5$

4. Identify the answer

Comparing our result (1.5) with the given options, it matches option A.

5. Exam Tip

When dealing with percentage decreases, remember that "decreasing by $x\%$" is the same as multiplying by $(1 - \frac{x}{100})$.

• For the numerator: $96 \times (1 - 0.375) = 96 \times 0.625 = 60$.
• For the denominator: $50 \times (1 - 0.20) = 50 \times 0.8 = 40$. This method is often faster and less prone to subtraction errors during the exam!