Question

Find the missing number: \[\left( { - 95} \right) \div \_\_\_\_\_\_ = 95\].

Answer 1

Hint:
Here, we need to find the missing blank. The number in the blank can be positive or negative. We will solve the question by assuming the missing number to be \[x\]. We will use the concept of multiplication and division to find the missing number.

Complete step by step solution:
An integer is a number which is not a fraction. It can be either positive or negative.
For example: \[ - 95\] and 95 are integers.
We will use the multiplication and division of integers to simplify the equation and obtain the missing number.
Let the missing number be \[x\].
Therefore, we can rewrite the given equation in terms of \[x\].
Rewriting the equation \[\left( { - 95} \right) \div \_\_\_\_\_\_ = 95\] in terms of \[x\], we get
\[\left( { - 95} \right) \div x = 95\]
We know that \[a \div b = c\] can be written as \[\dfrac{a}{b} = c\].
Rewriting the equation \[\left( { - 95} \right) \div x = 95\] in the form \[\dfrac{a}{b} = c\], we get
\[ \Rightarrow \dfrac{{ - 95}}{x} = 95\]
Now, we know that the expressions obtained by multiplying or dividing both sides of an equation by the same number are equal.
Therefore, we can multiply or divide both sides of the equation by the same number.
Multiplying both sides of the equation by \[x\], we get
\[ \Rightarrow \dfrac{{ - 95}}{x} \times x = 95 \times x\]
Simplifying the equation, we get
\[\begin{array}{l} \Rightarrow - 95 \times \dfrac{x}{x} = 95x\\ \Rightarrow - 95 \times 1 = 95x\\ \Rightarrow - 95 = 95x\end{array}\]
Now, dividing both sides of the equation by 95, we get
\[ \Rightarrow \dfrac{{ - 95}}{{95}} = \dfrac{{95x}}{{95}}\]
Simplifying the equation, we get
\[\begin{array}{l} \Rightarrow - \dfrac{{95}}{{95}} = \dfrac{{95}}{{95}} \cdot x\\ \Rightarrow - 1 = 1 \cdot x\end{array}\]
Thus, we get
\[ \Rightarrow x = - 1\]

\[\therefore\] The missing number is \[ - 1\].

Note:
We will directly divide both sides of the equation by \[ - 95\] to get the value of the missing number.
Dividing both sides of the equation
\[\dfrac{{ - 95}}{x} = 95\] by \[ - 95\], we get
\[\begin{array}{l} \Rightarrow \dfrac{{\dfrac{{ - 95}}{x}}}{{ - 95}} = \dfrac{{95}}{{ - 95}}\\ \Rightarrow \dfrac{{ - 95}}{{ - 95x}} = \dfrac{{95}}{{ - 95}}\end{array}\]
Simplifying the expression, we get
\[\begin{array}{l} \Rightarrow 1 \times \dfrac{1}{x} = - 1\\ \Rightarrow \dfrac{1}{x} = - 1\end{array}\]
Thus, we get
\[ \Rightarrow x = - 1\]
\[\therefore\] The missing number is \[ - 1\].