To solve for [tex]\(c\)[/tex] given the proportion [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], follow these steps:
1. Start with the given proportion:
[tex]\[
\frac{a}{b} = \frac{c}{d}
\][/tex]
2. Cross-multiply to eliminate the fractions. This involves multiplying the numerator of each fraction by the denominator of the other fraction:
[tex]\[
a \cdot d = b \cdot c
\][/tex]
3. Solve for [tex]\(c\)[/tex] by isolating [tex]\(c\)[/tex] on one side of the equation. You can do this by dividing both sides of the equation by [tex]\(b\)[/tex]:
[tex]\[
c = \frac{a \cdot d}{b}
\][/tex]
Let's demonstrate this using example values for [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(d\)[/tex]:
- Assume [tex]\(a = 6\)[/tex]
- Assume [tex]\(b = 4\)[/tex]
- Assume [tex]\(d = 3\)[/tex]
4. Substitute these values into the equation:
[tex]\[
c = \frac{6 \cdot 3}{4}
\][/tex]
5. Perform the multiplication in the numerator:
[tex]\[
c = \frac{18}{4}
\][/tex]
6. Divide the numerator by the denominator:
[tex]\[
c = 4.5
\][/tex]
Thus, the value of [tex]\(c\)[/tex] is [tex]\(4.5\)[/tex].
