Question

Simplify:
\[( - 8) \div (\dfrac{{ - 5}}{{16}})\]

Answer 1

Hint: To simplify the given question, we apply the rule of BODMAS which implies that to solve the arithmetic equation, there is a BODMAS rule. The BODMAS rule says that while solving the arithmetic equation first we solve the bracket, after the bracket we will solve the division, then multiplication, then addition, and at the end subtraction. In this, the sequence goes from left to right. BODMAS says bracket of division, multiplication, addition, and subtraction.

Complete step by step answer:

We can solve \[( - 8) \div (\dfrac{{ - 5}}{{16}})\], by applying BODMAS rule as follows: -
\[ \Rightarrow ( - 8) \div (\dfrac{{ - 5}}{{16}}) = ( - 8) \times (\dfrac{{ - 16}}{5})\]
Here we will interchange the numerator and denominator by replacing the divide sign with multiplication.
After that we will solve bracket in bracket there is fraction value and is not completely divisible so no need to solve that part. Now open the brackets you will get:
$ \Rightarrow ( - 8) \times (\dfrac{{ - 16}}{5}) = - 8 \times \dfrac{{ - 16}}{5}$
$ \Rightarrow ( - 8) \div (\dfrac{{ - 5}}{{16}}) = \dfrac{{ - 8 \times - 16}}{5}$
Here when you multiply minus sign with minus it gets converted to positive and we get,
\[ \Rightarrow ( - 8) \div (\dfrac{{ - 5}}{{16}}) = \dfrac{{128}}{5}\]
You can convert into decimals also we get,
\[ \Rightarrow ( - 8) \div (\dfrac{{ - 5}}{{16}}) = 25.60\]
So, the required answer is 25.60.

Note: Let’s take another example to solve by BODMAS i.e.$ - 12 \times 3 \div 6 \times 48 \div 4 \times (32 - 45 + 72)$
To solve this first of all we will start will bracket but inside bracket there is addition and subtraction but according to BODMAS rule we have to solve bracket first then we get,
$\begin{gathered}
   \Rightarrow - 12 \times 3 \div 6 \times 48 \div 4 \times (32 - 45 + 72) = - 12 \times 3 \div 6 \times 48 \div 4 \times (32 + 72 - 45) \\
   \Rightarrow - 12 \times 3 \div 6 \times 48 \div 4 \times (32 + 72 - 45) = - 12 \times 3 \div 6 \times 48 \div 4 \times (104 - 45) \\
\end{gathered} $
Here in the bracket we have first done the addition as addition comes before subtraction in BODMAS. After this we will perform subtraction under bracket.
$ \Rightarrow - 12 \times 3 \div 6 \times 48 \div 4 \times 59 = - 12 \times \dfrac{1}{2} \times 12 \times 59$
Now after opening the bracket, there is division so we had done division first. After we will do multiplication as follows:
 $\begin{gathered}
   \Rightarrow - 12 \times \dfrac{1}{2} \times 12 \times 59 = - 6 \times 12 \times 59 = - 72 \times 59 \\
   \Rightarrow - 72 \times 59 = - 4248 \\
\end{gathered} $