Question

Solve each proportion using the multiplication property of equality.
1. 3/2 = n/6
2. 1/5 = t/3
3. g/3 = 10/9

Answer 1

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.

1. **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:
\[
n = \frac{18}{2} = 9
\]

2. **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:
\[
t = \frac{3}{5}
\]

3. **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:
1. \( n = 9 \)
2. \( t = \frac{3}{5} \)
3. \( g = \frac{10}{3} \)