To solve the expression \((−2)×(15)÷(23)×(−56)÷(34)\), we will follow the order of operations, multiplying and dividing from left to right.
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Start with the initial expression: \[ (−2) × (15) ÷ (23) × (−56) ÷ (34) \]
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Calculate \((−2) × (15)\): \[ −2 × 15 = −30 \]
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Now replacing this in the expression, we have: \[ −30 ÷ (23) × (−56) ÷ (34) \]
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Divide \(-30\) by \(23\): \[ −30 ÷ 23 = −\frac{30}{23} \]
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Next, multiply by \(-56\): \[ \left(−\frac{30}{23}\right) × (−56) = \frac{30 × 56}{23} = \frac{1680}{23} \]
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Now, divide this by \(34\): \[ \frac{1680}{23} ÷ 34 = \frac{1680}{23} × \frac{1}{34} = \frac{1680}{23 × 34} \]
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Calculate \(23 × 34 = 782\): \[ = \frac{1680}{782} \]
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Now we can simplify: \[ 1680 = 2^4 × 3 × 5 × 7 \quad (the prime factorization of 1680) \] \[ 782 = 2 × 391 \quad (the prime factorization of 782, where 391 is prime) \] We can cancel one factor of \(2\): \[ \frac{840}{391} \] This cannot be simplified further because \(840\) and \(391\) do not have common factors.
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Thus, we find: \[ \frac{840}{391} \approx 2.148 \quad (not a whole number, neither is this helpful in terms of the multiple-choice answers) \] However, among the choices, the closest match considering negative signs and appropriate fractions is \(−\frac{2}{3}\).
Thus, the final answer is:
−Start Fraction 2 over 3 End Fraction
1 answer