To find the missing value [tex]\( n \)[/tex] in the proportion [tex]\(\frac{3}{15} = \frac{2}{n}\)[/tex], we can use cross-multiplication. Here's a step-by-step approach:
1. Start with the given proportion:
[tex]\[
\frac{3}{15} = \frac{2}{n}
\][/tex]
2. Cross-multiply to eliminate the fractions. This means you multiply the numerator of one fraction by the denominator of the other fraction, and vice versa:
[tex]\[
3 \cdot n = 15 \cdot 2
\][/tex]
3. Simplify the multiplication on the right-hand side:
[tex]\[
3n = 30
\][/tex]
4. Solve for [tex]\( n \)[/tex] by dividing both sides of the equation by 3:
[tex]\[
n = \frac{30}{3}
\][/tex]
5. Simplify the division:
[tex]\[
n = 10
\][/tex]
So, the missing value [tex]\( n \)[/tex] is [tex]\( \boxed{10} \)[/tex].
