Number = 75 × 0.4 × (3/8) = 30 × 3 / 8 = 90 / 8 = 45 / 4 = 11.25 - Coaching Toolbox
Understanding the Calculation: 75 × 0.4 × (3/8) = 11.25 – Step-by-Step Breakdown
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.
Understanding the Context
Step-by-Step Calculation Explained
The original equation:
75 × 0.4 × (3/8) = ?
1. Convert the Decimal to Fraction for Consistency
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Key Insights
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
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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.
