NCERT Summary: Integers

Integers

• Integers are a type of number that includes all the whole numbers and their negative counterparts, as well as zero. 
• Positive integers are numbers greater than zero, such as 1,2,3,...
• Negative integers are numbers less than zero, such as  -1,-2,-3,....
• Zero is neither positive nor negative.

Predecessor and Successor

•  These are terms used to describe the relationship between numbers in a sequence.
• Predecessor: The predecessor of a number is the number that comes immediately before it in a sequence or number line.
  To find the predecessor of an integer, subtract 1 from it.
  Example 1: The predecessor of 7 is 7-1=6.
  Example 2:The predecessor of -3 is -3-1=-4.
• Successor: The successor of a number is the number that comes immediately after it in a sequence or number line.
  To find the successor of an integer, add 1 to it.
  Example 1: The successor of 5 is 5+1=6.
  Example 2:The successor of -2 is -2+1=-1.

Representation of integers on a number line

• All the positive integers lie to the right of 0 and the negative integers to the left of 0 on the number line.
• In order to mark -5 on the number line, we move 5 points to the left of zero.
• In order to mark +5 on the number line, we move 5 points to the right of zero.

Ordering of Numbers

• On the number line, the number occurring on the right is greater than that on the left and the number on the left is smaller than that on the right. 
• 2> 1, as 2 is to the right of 1.
• 0 >-2, as O is to the right of -2.
• -5>-8, as-5 is to the right of -8.

Addition and Subtraction of Integers

• To add two negative integers, we add the corresponding positive integers and retain the negative sign with the sum. For example: 6 + (-5) = -(6 + 5) = -11
• To add a positive integer and a negative integer, we ignore the signs and subtract integer with smaller numerical value from the integer with larger numerical value and take the sign of the larger one.
• Two integers whose sum is zero are called additive inverse of each other.
• To subtract an integer from a given integer, we add the additive inverse of the integer to the given integer.

Addition of Integers on a Number Line

Let us add 3 and 5 on number line.

On the number line, we first move 3 steps to the right from 0 reaching 3, then we move 5 steps to the right of 3 and reach 8. Thus, we get 3 + 5 = 8.

Subtraction of Integers on a Number Line

• Subtract -4 from -5.

-5 - (-4) is same as -5 + (4), as the additive inverse of -4 is 4. We move 4 steps to the right on the number line starting from -5.