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Integers - Lesson Summary

–1, –2, –3, .......are the opposites of the natural numbers and are called the negatives of the natural numbers.
Examples where these negative numbers are used are temperature scale, water level in a lake or river, level of oil tank, debit account and outstanding dues. The collection of natural numbers, zero and negatives of natural numbers that is, … –3, –2, –1, 0, 1, 2, 3, …., is called integers.

Negative integers
The numbers –1, –2, –3, –4…  are called negative numbers. They are also called negative integers.

Positive integers
The numbers 1, 2, 3, 4 …., are called positive numbers. They are also called positive integers.
Integers are represented on the number line as shown in the following figure. When we need to use numbers with a negative sign, we need to go to the left of zero on the number line.

If we stand at the zero mark on the number line, we can either go left towards negative integers or right towards positive integers. When we move left towards zero on the number line, the value of positive integers decreases. When we move left further away from zero on the number line, the value of negative integers decreases.

Two integers that are equidistant from zero and on opposite sides of zero are called opposite numbers.The sum of an integer and its opposite is zero.

Every positive integer is greater than every negetive integer.
Zero is neither positive nor negative. It is greater than every negative integer and less than every positive integer.
The greater the number the lesser is its opposite.

Addition of integers
     •  When two positive integers are added, then the answer is an integer with a positive sign.
           e.g. (+8) + (+6) = + 14
     •  When two negative integers are added, then the answer is an integer with a negative sign. 
           e.g. (–3) + (–5) = –8
     •  When a positive integer is added to a negative integer, then we subtract them and put the sign of the greater integer to the answer. The greater integer can be decided by ignoring the signs of the integers.
           e.g. (+4) + (–9) = –5; (+8) + (–3) = 5

Subtraction of integers
     •  When we subtract a larger positive integer from a smaller positive integer, the difference is a negative integer.
          e.g. (+5) – (+8) = –3
     •  To subtract a negative integer from any given integer, we just add the additive inverse of the negative integer to the given integer.
          e.g. (–5) – (–8) = +3
a and –a are negative or additive inverses of each other. Thus, the subtraction of an integer is the same as the addition of its additive inverse. Both addition and subtraction of integers can be shown on a number line.


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