Question

Write down 7 pairs of negative integers whose sum is\[ - 8\].

Answer 1

Hint: In the given question, it is asked to find the 7 pairs of negative integers such that the sum of each pair comes out to be\[ - 8\]. To simplify the solution, we will move forward with the two positive integers whose sum will be\[8\]. And after getting the pairs of positive numbers, we will take their additive inverse as the final answer.

Complete step-by-step answer:
Let\[x\]and\[y\]be the two positive integers.
Therefore, \[ - x, - y\]will be the required pair of negative integers whose sum comes out to be\[ - 8\].
According to the question,
\[
   - x + \left( { - y} \right) = - 8 \\
   \Rightarrow - x - y = - 8 \\
 \]
Multiplying\[\left( { - 1} \right)\]both sides, we get,
\[x + y = 8\] \[ \ldots (1)\]
The sum of two positive integers is (let’s say\[n\]), only and only when both the numbers are less than\[n\].
For equation (1),we have to find the value of two positive integers\[x\]and\[y\]such that their sum comes out to be\[8\]. And it is possible, only and only when both the numbers\[x\]and\[y\]should be less than\[8\].
Therefore, the pairs of positive integers\[x\]and\[y\]will be\[\left\{ {\left( {1,7} \right),\left( {2,6} \right),\left( {3,5} \right),\left( {4,4} \right),\left( {5,3} \right),\left( {6,2} \right),\left( {7,1} \right)} \right\}\].
So, the required pairs of negative integers such that the sum of each pair comes out to be\[ - 8\]will be of the form\[\left( { - x, - y} \right)\].
Hence, the required pairs are\[\left\{ {\left( { - 1, - 7} \right),\left( { - 2, - 6} \right),\left( { - 3, - 5} \right),\left( { - 4, - 4} \right),\left( { - 5, - 3} \right),\left( { - 6, - 2} \right),\left( { - 7, - 1} \right)} \right\}\].

Note: Negative integers are used to denote the values on a scale that are below zero. We often hear negative integers in our daily life. Negative integers are used for weather forecasting. These integers are used to denote the temperature measured on Celsius or Fahrenheit scales.