Certainly! Let's simplify the given mathematical expression step by step.
The original expression is:
[tex]\[
-2k \div 12kf
\][/tex]
This can be rewritten as a fraction:
[tex]\[
\frac{-2k}{12kf}
\][/tex]
In this fraction, we have [tex]\(-2k\)[/tex] in the numerator and [tex]\(12kf\)[/tex] in the denominator. Now let's simplify it by following these steps:
1. Factor out common terms:
- [tex]\(k\)[/tex] is present in both the numerator and the denominator. We can cancel [tex]\(k\)[/tex] from both.
[tex]\[
\frac{-2k}{12kf} = \frac{-2}{12f}
\][/tex]
2. Simplify the coefficients:
- The numerator is [tex]\(-2\)[/tex].
- The denominator is [tex]\(12f\)[/tex].
- To simplify [tex]\(\frac{-2}{12}\)[/tex], we need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 2 and 12 is 2.
[tex]\[
\frac{-2}{12} = \frac{-2 \div 2}{12 \div 2} = \frac{-1}{6}
\][/tex]
3. Combine the simplified coefficient with the remaining variable:
Now, we have the simplified fraction:
[tex]\[
\frac{-1}{6f}
\][/tex]
Therefore, the simplified form of the given expression [tex]\(\frac{-2k}{12kf}\)[/tex] is:
[tex]\[
\boxed{\frac{-1}{6f}}
\][/tex]
This completes the step-by-step simplification of the given mathematical expression.
