Question

How do you simplify $\left( { - 5} \right) - \left( { - 1} \right)$ ?

Answer 1

Hint: We have to simplify the given expression. We can observe that we have to find the difference of two negative numbers. We can use simple arithmetic properties to solve the problem. After simplification we will get a number as a result which may be positive or negative.

Complete step by step solution:
We have to simplify $\left( { - 5} \right) - \left( { - 1} \right)$.
We can observe that we are given only numbers and arithmetic operators in the expression. Simplification of such expressions means solving the operators to find the resulting number.
We have to find the difference of two negative numbers. $ - 1$ is being reduced from $ - 5$.
First we try to remove the brackets of both the numbers.
When we remove the bracket for $\left( { - 5} \right)$ it will be written simply as $ - 5$ since there are no other numbers or operators before the bracket.
When we are removing the bracket of $\left( { - 1} \right)$ we see that it is preceded by a ‘$ - $ ’ operator. In such a case, we have to convert $ - 1$ to $ + 1$.
Therefore,
$\left( { - 5} \right) - \left( { - 1} \right) = - 5 + 1$
What this means is that reducing a negative number is equal to adding the absolute value of the number. We can also understand it as $' - '\; \times \;' - '\; = \;' + '$.
Now our expression is reduced to addition of a negative number $ - 5$ and a positive number $1$.
Addition is commutative so we can write $ - 5 + 1 = 1 - 5$
$5$ reduced from $1$ gives $ - 4$,
$1 - 5 = - 4$

Hence, $\left( { - 5} \right) - \left( { - 1} \right) = - 4$

Note: We observed that reducing a negative number is equal to addition of absolute value of the number. Simply put, two negatives turn into a positive. For simple arithmetic calculations of addition and subtraction we can also use an imaginary number line, where addition means moving such steps to the right and subtraction means moving such steps to the left to get the result.