To solve the expression \(-1 + \frac{3}{10} + \left(-\frac{4}{15}\right)\), we can break it down step by step.
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First, let's convert \(-1\) to a fraction: \[ -1 = -\frac{10}{10} \] This allows us to have a common denominator between \(-1\) and \(\frac{3}{10}\).
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Now, rewrite the expression: \[ -\frac{10}{10} + \frac{3}{10} - \frac{4}{15} \]
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Next, we need to simplify \(-\frac{10}{10} + \frac{3}{10}\): \[ -\frac{10}{10} + \frac{3}{10} = \frac{-10 + 3}{10} = \frac{-7}{10} \]
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Now we have: \[ \frac{-7}{10} - \frac{4}{15} \]
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To subtract these fractions, we need a common denominator. The least common multiple of \(10\) and \(15\) is \(30\).
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Convert the fractions: \[ \frac{-7}{10} = \frac{-7 \times 3}{10 \times 3} = \frac{-21}{30} \] \[ \frac{-4}{15} = \frac{-4 \times 2}{15 \times 2} = \frac{-8}{30} \]
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Now we can combine the fractions: \[ \frac{-21}{30} - \frac{8}{30} = \frac{-21 - 8}{30} = \frac{-29}{30} \]
So, the final result is: \[ -1 + \frac{3}{10} + \left(-\frac{4}{15}\right) = \frac{-29}{30} \]