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9. Simplify the expression:

[tex]\[ -2k \div 12kf = \frac{-2k}{12kf} \][/tex]


Sagot :

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.
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