Solve by using the multiplication principle. \( \frac{3}{4}=-\frac{5}{12} y \) The multiplication principle states for any real numbers \( \mathrm{a}, \mathrm{b} \), and c , where \( \mathrm{c} \neq 0 \), the A. \( \mathrm{a}=\mathrm{b} \) is equivalent to \( \mathrm{a} \cdot \mathrm{c}=\mathrm{b} \cdot \mathrm{c} \). B. \( \mathrm{a}=\mathrm{b} \) is equivalent to \( \mathrm{b} \cdot \mathrm{a}=\mathrm{c} \). C. \( \mathrm{b}=\mathrm{c} \) is equivalent to \( \mathrm{a} \cdot \mathrm{c}=\mathrm{b} \cdot \mathrm{c} \). D. \( \mathrm{b}=\mathrm{c} \) is equivalent to \( \mathrm{b} \cdot \mathrm{c}=\mathrm{a} \).
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To solve the equation \( \frac{3}{4} = -\frac{5}{12}y \) using the multiplication principle, we start by isolating \( y \). We can do this by multiplying both sides of the equation by the reciprocal of \(-\frac{5}{12}\), which is \(-\frac{12}{5}\): \[ y = \frac{3}{4} \cdot -\frac{12}{5} \] Calculating this, we get: \[ y = -\frac{3 \cdot 12}{4 \cdot 5} = -\frac{36}{20} = -\frac{9}{5} \] Thus, the solution is \( y = -\frac{9}{5} \). Now, for a fun fact: this manipulation can be visualized as balancing a seesaw! When you multiply both sides by the same value (as long as it isn’t zero), you're ensuring that both sides maintain their "weight" equality—even if they seem to tilt differently at first! For practical purposes, understanding this multiplication principle is vital in everyday situations, like solving proportions in recipes, budgeting, or even calculating distances when using rates. Want to triple that cookie recipe? Just remember to multiply everything by three, so you don’t end up with a cookie disaster!
