To solve for [tex]\( k \)[/tex] in the equation
[tex]\[
\frac{12}{7} = \frac{k}{8}
\][/tex]
we need to use a method known as cross-multiplication, which allows us to solve the proportion by eliminating the fractions.
Here are the steps to solve for [tex]\( k \)[/tex]:
1. Set up the equation:
[tex]\[
\frac{12}{7} = \frac{k}{8}
\][/tex]
2. Cross-multiply:
This means we multiply the numerator of one fraction by the denominator of the other fraction. Specifically, multiply 12 by 8 and 7 by [tex]\( k \)[/tex]:
[tex]\[
12 \cdot 8 = 7 \cdot k
\][/tex]
3. Perform the multiplication:
[tex]\[
96 = 7k
\][/tex]
4. Isolate [tex]\( k \)[/tex]:
To solve for [tex]\( k \)[/tex], divide both sides of the equation by 7:
[tex]\[
k = \frac{96}{7}
\][/tex]
5. Simplify the fraction:
Finally, perform the division to get the numerical value of [tex]\( k \)[/tex]:
[tex]\[
k = 13.714285714285714
\][/tex]
Therefore, the value of [tex]\( k \)[/tex] is approximately [tex]\( 13.714285714285714 \)[/tex].
