Evaluate the following:
\[\left[ {\left( { - 48} \right) \div \left( { - 6} \right)} \right] \div \left( { - 2} \right)\]

Hint: BODMAS the basic rule for any arithmetic operation. All the arithmetic operations must be done following the BODMAS. This rule is applied irrespective of alignment of numbers, the place value of the numbers or the face value of the numbers. BODMAS is elaborated as Bracket, Order, Division, Multiplication, Addition, and Subtraction.

Complete step by step answer:
We are given with\[\left[ {\left( { - 48} \right) \div \left( { - 6} \right)} \right] \div \left( { - 2} \right)\], we have to simplify this. We must follow the BODMAS rule in order to simplify this correctly despite the sign of the numbers. Now moving along with the BODMAS we have B for Bracket so we will first operate the number within the bracket which is \[\left[ {\left( { - 48} \right) \div \left( { - 6} \right)} \right]\] as \[\left( { - 48} \right)\] and \[\left( { - 6} \right)\]represent the negative of the number so this will not affect the operation within bracket.

We see that there is no operation for O for order or exponents so we will move further.Inside the bracket we got D for division so, we will simplify this as \[\dfrac{{ - 48}}{{ - 6}}\].As the numerator and denominator both have negative sign so the overall sign after dividing will be positive, so on dividing we get
\[\dfrac{{ - 48}}{{ - 6}} = 8\]
Now after this we got the term as
\[\left[ 8 \right] \div \left( { - 2} \right)\]
We see that the numerator is \[8\] which is positive whereas the denominator \[ - 2\] which is negative, which will result in the negative sign of the result.
So on dividing we get \[\dfrac{8}{{ - 2}} = - 4\]

Hence the result will be as \[\left[ {\left( { - 48} \right) \div \left( { - 6} \right)} \right] \div \left( { - 2} \right) = \left( { - 4} \right)\].

Note: In certain scenarios or regions PEMDAS is used, which is the synonym of the BODMAS. PEDMAS is elaborated as Parentheses, Exponents, Multiplication, Addition, and Subtraction. The above question must be solved by following the BODMAS rule else the result will be different and wrong. Operations containing Decimals, fractions also go with the same rule.