Question

Find the solution of the following without using number line:
\[\left( { + 7} \right) + \left( { - 11} \right)\]

Answer 1

Hint:
Here, we will use the rules of addition without using the number line. Using the rules, we will be able to find the sum of one positive and one negative number. In addition, the sign of the resultant number is equal to the sign of the greater number.

Complete Step by Step Solution:
Given numbers to be added are:
\[\left( { + 7} \right) + \left( { - 11} \right)\]
Now, in order to add these numbers without using a number line, we should keep in mind the following rules of addition without using number line:
1) In order to add a positive number to a positive number, we simply add the two numbers and a positive i.e. the same sign is attached in front of the sum obtained.
2) In order to add a positive number to a negative number, we simply subtract the smaller number from the bigger one and the sign of the bigger number is attached with the answer obtained.
3) In order to add two negative numbers, we simply add both the numbers together and a negative, i.e. the same sign is attached in front of the answer obtained.
In the given question, we can notice that a positive number is being added to a negative number where the positive number is 7 and the number with the minus sign is 11. Clearly, 11 is the bigger number and 7 is the smaller one.
Hence, using the second rule of addition of numbers without using number line,
We will simply subtract the smaller number from the bigger one.
Hence, we can write \[\left( { + 7} \right) + \left( { - 11} \right)\] as: \[11 - 7 = 4\]
But, since, the number with the greater value is having the negative sign in front of it, i.e. \[ - 11\] hence, we will attach a minus sign in front of our answer.
Therefore,
\[\left( { + 7} \right) + \left( { - 11} \right) = - \left( {11 - 7} \right) = - 4\]

Hence, \[ - 4\] is the required answer.

Note:
We can use a number line to visualize how to add and subtract two numbers by thinking of the direction where we are required to move on the number line. But, if in case, the numbers are bigger than usual then, using the number line would not be convenient, and drawing it would be very time consuming and would make the question unnecessarily lengthy. Hence, we should know how to use these rules, and applying them will help us to solve the questions correctly and in less time.