To solve each proportion using the multiplication property of equality, we can cross-multiply (multiply the means and the extremes) to find the value of the unknown variable.
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For the proportion \( \frac{3}{2} = \frac{n}{6} \):
Cross-multiply: \[ 3 \cdot 6 = 2 \cdot n \] Simplifying: \[ 18 = 2n \] Now, divide both sides by 2: \[ n = \frac{18}{2} = 9 \]
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For the proportion \( \frac{1}{5} = \frac{t}{3} \):
Cross-multiply: \[ 1 \cdot 3 = 5 \cdot t \] Simplifying: \[ 3 = 5t \] Now, divide both sides by 5: \[ t = \frac{3}{5} \]
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For the proportion \( \frac{g}{3} = \frac{10}{9} \):
Cross-multiply: \[ g \cdot 9 = 3 \cdot 10 \] Simplifying: \[ 9g = 30 \] Now, divide both sides by 9: \[ g = \frac{30}{9} = \frac{10}{3} \]
Thus, the solutions to the proportions are:
- \( n = 9 \)
- \( t = \frac{3}{5} \)
- \( g = \frac{10}{3} \)