Question

How do you simplify $ - 3 - \left(- 7 \right)$ ?

Answer 1

Hint:
In this question, we will use the concept of the product of positive and the negative numbers, that is if the product of the positive and the negative number will always be a negative number while the product of two negative numbers is always a positive number.

Complete step by step solution:
In this question, we have given a set of numbers with some operation operators and we need to simplify the numbers by using the given operators. The given set of number with operation operators is,
$ \Rightarrow - 3 - - 7$
Let us assume a variable to store the result of the operation as,
$ \Rightarrow a = - 3 - - 7$

Now, we will modify the given set of numbers by using the brackets as,
$ \Rightarrow a = - 3 - \left( { - 7} \right)$
As we know that the product of positive and the negative number is always a negative number while the product of two negative number is always a positive number, so apply this concept in the above operation and obtain,
$ \Rightarrow a = - 3 + 7$
Now, as we know that if the operation of sum is performed between two numbers and one of the numbers is positive while the other is negative then the subtraction will take place between these numbers and the sign of the greater number will be used.
Here, as we can see that the greater number is $7$ and the sign is positive, so the numbers are simplified as,
$\therefore a = 4$

Therefore, the simplification of the given set of numbers is $4$.

Note:
In the above solution, we have used the positive sign because $7$ is greater than $3$, now let us take another example for which negative sign will be taken.
Let the given set of number with operation operators is,
$ \Rightarrow - 8 - \left( { - 7} \right)$
Let us assume a variable to store the result of the operation as,
$ \Rightarrow a = - 8 - \left( { - 7} \right)$

Now, we will modify the given set of numbers by using the brackets as,
$ \Rightarrow a = - 8 - \left( { - 7} \right)$
As we know that the product of positive and the negative number is always a negative number while the product of two negative number is always a positive number, so apply this concept in the above operation and obtain,
$ \Rightarrow a = - 8 + 7$
Now, as we know that if the operation of sum is performed between two numbers and one of the numbers is positive while the other is negative then the subtraction will take place between these numbers and the sign of the greater number will be used.
Here, as we can see that the greater number is $8$ and the sign is negative, so the numbers are simplified as,
$\therefore a = - 1$

Therefore, the simplification of the given set of numbers is $ - 1$.