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Fill in the blanks: $ 80 \div (...) = - 5 $ .

Last updated date: 14th Jul 2024
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Hint: The given questions involve the concepts of arithmetic. We are given a mathematical equation with a blank space in between and we have to fill up the blank space. Now, in order to fill up the blank space, we will use the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.

Complete step-by-step answer:
Now, in the question given to us, we are provided with a mathematical equation.
So, we have, $ 80 \div (...) = - 5 $
Now, the given mathematical equation is about the division of two numbers to give another number as quotient. So, we can also write the equation as $ \dfrac{{80}}{{\left( {...} \right)}} = - 5 $ .
Let the unknown number in the missing place be x.
Then, we have, $ \dfrac{{80}}{x} = - 5 $ .
Now, we have to find the value of x so as to fill up the missing place in the question.
We would use the method of transposition to find the value of x in $ \dfrac{{80}}{x} = - 5 $ . Now, In order to find the value of x, we need to isolate x from the rest of the parameters.
So, $ \dfrac{{80}}{x} = - 5 $
Shifting x to the right side of the equation and all the rest of the parameters to the left of the equation, we get,
  $ \Rightarrow \dfrac{{80}}{{ - 5}} = x $
Carrying out the calculations, we get,
 $ \Rightarrow x = - 16 $
Hence, the value of x in $ \dfrac{{80}}{x} = - 5 $ is $ - 16 $ .
So, the number in missing place in the equation $ 80 \div (...) = - 5 $ is $ - 16 $
So, the correct answer is “-16”.

Note: If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal. The given problem deals with an algebraic equation. There is no fixed way of solving a given algebraic equation. Algebraic equations can be solved in various ways. Linear equations in one variable can be solved by the transposition method with ease.