Question

Fill in the blank:
$(......) \div ( - 1) = 36$.

Answer 1

Hint: We will firstly let the number in the blank as $x$.
Then, we basically need to find the value of $x$.
We know the following property:
If $a \div b = c$, then,
$a = bc$ for all real numbers $a$, $b$ and $c$.
So, we will take:
$a = x$,
$b = - 1$ and
$c = 36$,
In the above-stated property, to find the value of $x$.

Complete step by step solution:
Let the number in the blank be $x$, that is, we are letting that $x \div ( - 1) = 36$.
We need to find the value of $x$.
We know the following property:
if $a \div b = c$, then
$a = bc$ for all integers $a$, $b$ and $c$.
This is because if we take $b$ on the right-hand side of the equation $a \div b = c$, then, the operation division will be converted to its inverse operation multiplication.
Now, substituting $a = x$,
$b = - 1$ and
$c = 36$,
into the equation $a \div b = c$, we get:
$x \div ( - 1) = 36$.
So, according to the above-stated property, we must have that:
$x = 36 \times ( - 1)$,
because when $ - 1$ is taken to the right-hand side of the equation $x \div ( - 1) = 36$, then the operation division is converted to its inverse operation multiplication and thus, we multiplied the right-hand side, that is, $36$, with $ - 1$.
Now, we know that $a \times ( - b) = - ab$ for all real numbers $a$ and $b$.
So, we can take $a = 36$ and
$b = 1$ in the above-stated property, to simplify the equation:
$x = 36 \times ( - 1)$.
Thus, according to the above-stated property, the value of $x$ is $ - 36$.
Therefore, we finally have that:
$ - 36 \div ( - 1) = 36$.

Note:
When we are supposed to isolate the variable on the left-hand side of an equation, then we take all the terms other than the variable on the right-hand side of the equation and while doing so, we use inverse operations on them on the right-hand side of the equation.