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Solve for t : {:[t÷(5)/(12)=-(3)/(10)],[t=◻]:}

Solve for t t :\newlinet÷512=−310t=□ \begin{array}{l} t \div \frac{5}{12}=-\frac{3}{10} \\ t=\square \end{array}

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Full solution

Q. Solve for t t :\newlinet÷512=−310t=□ \begin{array}{l} t \div \frac{5}{12}=-\frac{3}{10} \\ t=\square \end{array}
  1. Write Equation: First, let's write down the equation from the problem.\newlinet÷(512)=−(310)t \div \left(\frac{5}{12}\right) = -\left(\frac{3}{10}\right)
  2. Eliminate Fraction: Now, we need to get rid of the fraction on the left side by multiplying both sides by its reciprocal, which is 125\frac{12}{5}. \newlinet=−(310)∗(125)t = -\left(\frac{3}{10}\right) * \left(\frac{12}{5}\right)
  3. Multiply: Let's do the multiplication.\newlinet = −3×12/(10×5)-3 \times 12 / (10 \times 5)
  4. Simplify Numbers: Now, simplify the numbers.\newlinet=−3650t = -\frac{36}{50}
  5. Reduce Fraction: We can reduce the fraction by dividing both the numerator and the denominator by 22.t=−1825t = \frac{-18}{25}

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