Question

Add without using a number line.
(i) 11+(-7)
(ii) (-10) + (+19)

Answer 1

Hint: We know that positive multiplied by positive is positive and negative multiplied by positive is negative. So we will use this knowledge to solve these two problems.

Complete step-by-step answer:
Before proceeding with the above question we should understand the concept of plus, minus operations between integers.
Integers are a special group of numbers that are positive, negative and zero, which are not fractions. Rules for addition and subtraction are the same for all, whether it is a natural number or an integer because natural numbers are themselves integers. We just extend the rule and apply it for integers as well.
Addition of integers means there are three possibilities. They are: addition between two positive numbers, addition between two negative numbers; and addition between a positive number and a negative number. Addition of two positive integers always gives a positive-sum. Addition of two negative integers always gives a negative-sum. Addition of a positive and a negative integer give either a positive or negative-sum depending on the value of the given numbers.
(i) \[\Rightarrow 11+(-7)......(1)\]
We know that positive multiplied by negative is negative. So applying this information in equation (1) we get,
\[\Rightarrow 11-7=4\]. Here in this the bigger number is 12 and it has positive sign so hence the answer is also positive.


(ii) \[\Rightarrow -10+(+19)......(2)\]
We know that positive multiplied by positive is positive. So applying this information in equation (2) we get,
\[\Rightarrow -10+19=9\]. Here in this the larger number is 19 and it is positive so hence the answer is also positive.

Note: We have to remember these rules to solve this problem. Also we have to keep in mind that the answer will have positive or negative sign depending on the larger number