Predecessor and Successor

Predecessor and Successor are the two terms in Mathematics that are most commonly used for series and sequence of whole numbers. Predecessor is known as before numbers (that appear just before) and successor is known as after numbers (that appear just after).

Successor and predecessor are used for the terms/numbers that are just after or just before any term/number, respectively. For example, in the series 1, 2, 3,1 is the predecessor of 2 and 3 is the successor of 2. In this article, we are going to learn about the definitions of successor and predecessor, along with their examples and how to find them. Class 6 students can learn this topic from the chapter whole numbers in a descriptive manner.

What is Predecessor?

As discussed in the introduction, a predecessor is a value that comes right before/immediate before/just before a particular value. Suppose a value is x (where x belongs to any whole number), then the predecessor of x will be x-1. Thus, to find the predecessor of any value we have to subtract the given value from 1.

Examples of Predecessor

  • If x = 5, then predecessor of 5 is 5-1 = 4
  • If x = 10, then predecessor of 10 is 10-1 = 9
  • If x = 20, then predecessor of 20 is 20-1 = 19
  • If x = 50, then predecessor of 50 is 50-1 = 49
  • If x = 100, then predecessor of 100 is 100-1 = 99

Hence, the predecessor of any whole number is one less than the original number.

What is Successor?

Successor is the term that comes right after a particular number or term or a value. Suppose, n is a number, (where n belongs to any whole number), then the successor of n is ‘n-1’. The other terminologies used for successor are just after, immediate after, next number/next value.

Examples of Successor

  • If n = 5, then successor of 5 is 5 + 1 = 6
  • If n = 10, then successor of 10 is 10 + 1 = 11
  • If n = 20, then successor of 20 is 20 + 1 = 21
  • If n = 50, then successor of 50 is 50 + 1 = 51
  • If n = 100, then successor of 100 is 100 + 1 = 101

Therefore, by these examples, we can say, the successor of any whole number is one more than the original number.

Predecessor and Successor of Integers

By the definition of integers we know that, any positive or non-negative natural numbers along with zero are integers. Or we can say, integers are the set of all negative and positive non-fractional numbers.

Z = {….,-5,-4,-3,-2,-1,0,1,2,3,4,5,…}

The predecessor and successor of integers will be one less and one more than the original number. Let us see a few examples here:

Integer Predecessor Successor
-10 -10-1 = -11 -10+1 = -9
-5 -5-1 = -6 -5+1 = -4
-1 -1-1 = -2 -1+1 = 0
0 0 – 1 = -1 0+1 = 1
3 3-1 = 2 3+1 = 4
11 11 – 1 = 10 11+1 = 12

Note: Successor and predecessor are applicable only for perfect numbers (such as natural or whole numbers) but not for fractions.

How to Find Successor and Predecessor?

To evaluate successor and predecessor of any value, we have to apply the basic method of addition and subtraction, respectively. For the successor, we need to add 1 to the given number whereas for the predecessor we have to subtract 1 from the given number. Finding a successor and predecessor is very easy and quick.

  • Successor = Given number + 1
  • Predecessor = Given number – 1

Let us see some solved examples here to understand better.

Solved Examples

Q.1: Find the successor of the following numbers.

  • 12
  • -12
  • -84
  • 90
  • 150
  • 45
  • 89

Solution: The required successors are:

  • 12 → 12 + 1 = 13
  • -12 → -12 + 1 = -11
  • -84 → -84 + 1 = -83
  • 90 → 90 + 1 = 91
  • 150 → 150 + 1 = 151
  • 45 → 45 + 1 = 46
  • 89 → 89 + 1 = 90

Q.2: Find the predecessor of the following numbers:

  • -14
  • -80
  • 45
  • -8
  • 20
  • 199
  • 56

Solution: The predecessors are:

  • -14 → -14 – 1 = -15
  • -80 → -80 – 1 = -81
  • 45 → 45 – 1 = 44
  • -8 → -8 – 1 = -9
  • 20 → 20 – 1 = 19
  • 199 → 199 – 1 = 198
  • 56 → 56 – 1 = 55

Q.3: Write the predecessor and successor of

  1. 19
  2. 1997
  3. 12000
  4. 49
  5. 100000

Solution:

A. 19

Predecessor of 19 → 19 – 1 = 18

Successor of 19 → 19 + 1 = 20

B. 1997

Predecessor of 1997 → 1997 – 1 = 1996

Successor of 1997 → 1997 + 1 = 1998

C. 12000

Predecessor of 12000 → 12000 – 1 = 11999

Successor of 12000 → 12000 + 1 = 12001

D. 49

Predecessor of 49 → 49 – 1 = 48

Successor of 49 → 49 + 1 = 50

E. 100000

Predecessor of 100000 → 100000 – 1 = 99999

Successor of 100000 → 100000 + 1 = 100001

Q.4: What is the successor of the largest 3 digit number?

Answer: The largest 3 digit number is 999. Therefore, the successor of 999 is 1000.

Q.5: What is the predecessor of the smallest 3-digit number?

Answer: The smallest 3-digit number is 100, therefore the predecessor of 100 is 99.

Difference Between Successor and Predecessor

Successor Predecessor
It is the number that comes just next to the original number. It is the number that comes just before the original number.
Successor → Original number + 1 Predecessor → Original number – 1
Example:

Successor of 55 → 56

Example:

Predecessor of 55 → 54

Practice Questions for Class 6

  1. What is the successor of 7148, 8950, 7620, 12499?
  2. What is the predecessor of 321, 4567, 9876, 765?
  3. What is the successor of the smallest 4-digit number?
  4. What is the predecessor of the greatest 4-digit number?
  5. Draw the number line and mention the predecessor and successor of the following numbers: 5, 12, 15, 0

Frequently Asked Questions on Predecessor and Successor

What is the successor of 15?

The successor of 15 is 16.
15 + 1 = 16

What is the successor of 9999?

The successor of 9999 is 10000.
9999 + 1 = 10000

What is the predecessor of 399?

The predecessor of 399 is 398.
399 – 1 = 398.

Is there any natural number that has no predecessor?

Yes, 1 is the natural number that has no predecessor, since we know the series of natural numbers starts from 1.

Is there any natural number which has no successor?

Every natural number has a successor, because there are infinite natural numbers and no last natural number. For example, the successor of 100000000 is 100000001.

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