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Simplify the following expression:

(ii) [tex]\left(\frac{-6+5}{9}\right) \div \frac{(-1)}{6}[/tex]


Sagot :

Sure, let's solve the expression step by step.

First, simplify the fraction in the numerator:

[tex]\[ \frac{-6 + 5}{9} = \frac{-1}{9} \][/tex]

Next, we need to deal with the division by the fraction [tex]\(\frac{-1}{6}\)[/tex]. Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we need the reciprocal of [tex]\(\frac{-1}{6}\)[/tex]:

[tex]\[ \text{Reciprocal of } \frac{-1}{6} \text{ is } \frac{6}{-1} = -6 \][/tex]

Now, we can perform the division by multiplying [tex]\(\frac{-1}{9}\)[/tex] by [tex]\(-6\)[/tex]:

[tex]\[ \frac{-1}{9} \times -6 \][/tex]

Perform the multiplication:

[tex]\[ \left(\frac{-1 \times -6}{9}\right) = \frac{6}{9} = \frac{2}{3} \][/tex]

Thus, the result is:

[tex]\[ \frac{2}{3} \approx 0.6666\ldots \][/tex]

So, the detailed breakdown of the solution gives the final result:

[tex]\[ \left(\frac{-6+5}{9}\right) \div \frac{(-1)}{6} = 0.6666666666666666 \][/tex]