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Solve the equation using the multiplication property\newline215=−y5\frac{2}{15} = -\frac{y}{5}\newline

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Full solution

Q. Solve the equation using the multiplication property\newline215=−y5\frac{2}{15} = -\frac{y}{5}\newline
  1. Isolate variable y: First, we need to isolate the variable yy by getting rid of the fraction on the right side of the equation. We can do this by multiplying both sides of the equation by 55, which is the denominator of the fraction on the right side.\newlineCalculation: (215)⋅5=−(y5)⋅5(\frac{2}{15}) \cdot 5 = -(\frac{y}{5}) \cdot 5
  2. Multiply by 55: After multiplying both sides by 55, the 55 on the right side cancels out with the denominator of the fraction, leaving us with yy alone on the right side.\newlineCalculation: (215)×5=−y(\frac{2}{15}) \times 5 = -y
  3. Perform left side multiplication: Now we perform the multiplication on the left side of the equation.\newlineCalculation: (2×5)/15=−y(2 \times 5) / 15 = -y
  4. Simplify left side: Simplify the multiplication on the left side.\newlineCalculation: 10/15=−y10 / 15 = -y
  5. Simplify fraction: We can simplify the fraction 1015\frac{10}{15} by dividing both the numerator and the denominator by their greatest common divisor, which is 55.\newlineCalculation: (105)/(155)=−y\left(\frac{10}{5}\right) / \left(\frac{15}{5}\right) = -y
  6. Final fraction: After simplifying the fraction, we get:\newlineCalculation: 23=−y\frac{2}{3} = -y
  7. Get rid of negative sign: To solve for yy, we need to get rid of the negative sign. We can do this by multiplying both sides of the equation by −1-1.\newlineCalculation: −1×(23)=−1×(−y)-1 \times (\frac{2}{3}) = -1 \times (-y)
  8. Final value for y: After multiplying both sides by −1-1, we get the final value for yy.\newlineCalculation: −23=y-\frac{2}{3} = y

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