Question

For the expression, \[\dfrac{4}{-17}\square \dfrac{0}{-17}=\dfrac{4}{-17}\], fill the symbol in the blank as,
(a) +
(b) –
(c) + or –
(d) None

Answer 1

Hint:By using basic arithmetic operations like addition, subtraction, multiplication and division, try substituting in \[\square \]. You should get the answer as \[\left( \dfrac{4}{-17} \right)\].

Complete step-by-step answer:
We have been given the expression \[\left( \dfrac{4}{-17} \right)\] and \[\left( \dfrac{0}{-17} \right)\]. We can write \[\left( \dfrac{4}{-17} \right)\] as \[\left( \dfrac{-4}{17} \right)\]. The negative sign is common to the fraction. Now, \[\dfrac{0}{-17}=0\]. If the numerator of a fraction is zero, then the entire fraction is zero. Thus we can re – write the given expression as,
\[\dfrac{4}{-17}\square \dfrac{0}{-17}=\dfrac{4}{-17}\]
\[\Rightarrow \left( \dfrac{4}{-17} \right)\square 0=\left( \dfrac{4}{-17} \right).....(1)\]
We need to find the arithmetic operation that fits in \[\square \]. We know the basic arithmetic operations as addition (+), subtraction (-), multiplication (\[\times \]) and division (\[\div \]).
Let us undergo the arithmetic operation, addition in (1). Put + in \[\square \].
\[\dfrac{-4}{17}+0=\dfrac{-4}{17}\]
The arithmetic operation addition, combines the two quantities \[\left( \dfrac{-4}{17} \right)\] and zero into a single quantity \ [\left( \dfrac{-4}{17} \right)\]. Thus addition (+), satisfies the expression.
Now let us undergo the arithmetic operation, subtraction in (1). Put in \[\square \].
\[\dfrac{-4}{17}-0=\dfrac{-4}{17}\]
The arithmetic operation subtraction, finds the difference of the two quantities \[\left( \dfrac{-4}{17} \right)\] and zero, to a single quantity \[\left( \dfrac{-4}{17} \right)\]. Thus subtraction (-), satisfies the expression.
Hence both arithmetic operations + and – satisfy the expression.
\[\therefore \] Option (c) is the correct answer.

Note: If we under Multiplication or division, we won’t get the desirable answer. If we undergo multiplication, \[\left( -\dfrac{4}{17} \right)\times 0=0\]. It won’t give the answer \[\left( \dfrac{-4}{17} \right)\]. The case is similar for division.