Pregunta
d \( \left(0.125+\frac{4}{8}\right)^{2} \times \frac{64}{125}-1 \)
Ask by Flynn Lee. in Malaysia
Feb 17,2025
Solución de inteligencia artificial de Upstudy
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The result is \( -0.8 \).
Solución
Calculate or simplify the expression \( (0.125+4/8)^2 * 64/125-1 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{\left(0.125+\frac{4}{8}\right)^{2}\times 64}{125}-1\)
- step1: Reduce the fraction:
\(\frac{\left(0.125+\frac{1}{2}\right)^{2}\times 64}{125}-1\)
- step2: Add the numbers:
\(\frac{\left(\frac{5}{8}\right)^{2}\times 64}{125}-1\)
- step3: Multiply the terms:
\(\frac{25}{125}-1\)
- step4: Reduce the fraction:
\(\frac{1}{5}-1\)
- step5: Reduce fractions to a common denominator:
\(\frac{1}{5}-\frac{5}{5}\)
- step6: Transform the expression:
\(\frac{1-5}{5}\)
- step7: Subtract the numbers:
\(\frac{-4}{5}\)
- step8: Rewrite the fraction:
\(-\frac{4}{5}\)
The result of \( \left(0.125+\frac{4}{8}\right)^{2} \times \frac{64}{125}-1 \) is \( -\frac{4}{5} \) or \( -0.8 \).
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Simplifique esta solución The Deep Dive
First, let's simplify the expression inside the parentheses: \( 0.125 + \frac{4}{8} \) can be calculated by converting \( 0.125 \) to a fraction, which is \( \frac{1}{8} \). Thus: \[ \frac{1}{8} + \frac{4}{8} = \frac{5}{8}. \] Now, we square \( \frac{5}{8} \): \[ \left(\frac{5}{8}\right)^{2} = \frac{25}{64}. \] Next, we multiply by \( \frac{64}{125} \): \[ \frac{25}{64} \times \frac{64}{125} = \frac{25 \times 64}{64 \times 125} = \frac{25}{125} = \frac{1}{5}. \] Finally, we subtract 1: \[ \frac{1}{5} - 1 = \frac{1}{5} - \frac{5}{5} = -\frac{4}{5}. \] So, the final answer is: \[ -\frac{4}{5}. \]
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