Number = 75 × 0.4 × (3/8) = 30 × 3 / 8 = 90 / 8 = 45 / 4 = 11.25
Understanding the Calculation: 75 × 0.4 × (3/8) = 11.25 – Step-by-Step Breakdown
Mathematical equations often involve multiple steps that can be confusing at first glance. One such calculation — 75 × 0.4 × (3/8) — simplifies neatly to a final result of 11.25. In this article, we break down the steps clearly to help you understand how this conversion works, explaining fractions, decimals, and simplified arithmetic so you can confidently solve similar problems yourself.
Step-by-Step Calculation Explained
The original equation: 75 × 0.4 × (3/8) = ?
1. Convert the Decimal to Fraction for Consistency
The decimal 0.4 is equivalent to the fraction 2/5. So the expression becomes: 75 × (2/5) × (3/8)
2. Multiply the Fractions and Whole Numbers
We can multiply the values in order:
Start by calculating: 75 × (2/5) = (75 × 2) / 5 = 150 / 5 = 30
Now multiply that result by (3/8): 30 × (3/8) = (30 × 3) / 8 = 90 / 8
3. Simplify the Final Fraction
90 / 8 can be simplified by dividing numerator and denominator by 2: 90 ÷ 2 = 45, 8 ÷ 2 = 4, so: 90 / 8 = 45 / 4
Now convert 45 / 4 to decimal by dividing: 45 ÷ 4 = 11.25
Why This Matters: Real-World Applications
Understanding how to manipulate percentages, fractions, and decimals behind complex multiplications is essential in fields like finance, engineering, and data science. For example, calculating discounts, interest rates, or ratios often involves similar combinations of numbers.
Example: If you’re adjusting a 40% reduction on a value (0.4), then applying another proportion (like 3/8), knowing how to simplify 75 × 0.4 × (3/8) quickly prevents mistakes in calculations.
Final Result
Thus: 75 × 0.4 × (3/8) = 11.25 This result combines decimals and fractions seamlessly, demonstrating equivalent ways to simplify and solve expressions involving mixed number types.
Tips for Solving Similar Problems
- Convert decimals to fractions where possible for consistent calculation.
- Multiply stepwise, simplifying at intermediate stages.
- Use proper fraction simplification (e.g., dividing both numerator and denominator by their GCD).
- Double-check decimals and fractions by converting to decimal or fraction form.
- Practice with varied combinations to build fluency.
In summary: The expression 75 × 0.4 × (3/8) simplifies through clear mathematical reasoning to 11.25, illustrating how decimals and fractions integrate naturally in real-world calculations. Mastering these steps strengthens your arithmetic foundation and prepares you for complex problem-solving ahead.
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