Pregunta
7. Add or Subtract P\&TY. \( -\frac{2}{7}-0.3+2 \)
Ask by Clark Mejia. in the United States
Feb 05,2025
Solución de tutoría real
Respuesta verificada por el tutor
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The result is \(\frac{99}{70}\) or approximately \(1.4142857\).
Solución
Calculate or simplify the expression \( -\frac{2}{7}-0.3+2 \).
Calculate the value by following steps:
- step0: Calculate:
\(-\frac{2}{7}-0.3+2\)
- step1: Add the numbers:
\(-\frac{2}{7}+1.7\)
- step2: Convert the expressions:
\(-\frac{2}{7}+\frac{17}{10}\)
- step3: Reduce fractions to a common denominator:
\(-\frac{2\times 10}{7\times 10}+\frac{17\times 7}{10\times 7}\)
- step4: Multiply the numbers:
\(-\frac{2\times 10}{70}+\frac{17\times 7}{10\times 7}\)
- step5: Multiply the numbers:
\(-\frac{2\times 10}{70}+\frac{17\times 7}{70}\)
- step6: Transform the expression:
\(\frac{-2\times 10+17\times 7}{70}\)
- step7: Multiply the numbers:
\(\frac{-20+17\times 7}{70}\)
- step8: Multiply the numbers:
\(\frac{-20+119}{70}\)
- step9: Add the numbers:
\(\frac{99}{70}\)
The result of the expression \(-\frac{2}{7}-0.3+2\) is \(\frac{99}{70}\), which can also be written as \(1\frac{29}{70}\) or approximately \(1.4\dot{1}4285\dot{7}\).
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The Deep Dive
To solve the expression \( -\frac{2}{7}-0.3+2 \), let's first convert everything into a fraction. The decimal \( 0.3 \) can be expressed as \( \frac{3}{10} \). To combine fractions, it helps to find a common denominator, which is 70 in this case. Rewriting gives us: \[ -\frac{20}{70}-\frac{21}{70}+\frac{140}{70} = \frac{-20 - 21 + 140}{70} = \frac{99}{70}. \] So, the final result is: \[ \frac{99}{70} \text{ or approximately } 1.414. \] Remember to keep an eye on those signs when working with negatives and positives!
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