Successor and Predecessor in Maths: Meaning, Definition, Examples and Rules

What Are Successor and Predecessor?

The successor of a number is the number that comes immediately after it, while the predecessor is the number that comes immediately before it.

The rules are simple:

• Successor = Number + 1

• Predecessor = Number - 1

For example:

• Successor of 8 = 9

• Predecessor of 8 = 7

On a number line, the successor is one step to the right and the predecessor is one step to the left.

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Successor and Predecessor Meaning in Maths

Successor Meaning

The meaning of successor in maths is the number that comes immediately after a given number.

For a number n:

Successor = n + 1

Examples:

• Successor of 5 = 6

• Successor of 20 = 21

• Successor of 99 = 100

• Successor of 0 = 1

• Successor of -18 = -17

Predecessor Meaning

The meaning of predecessor in maths is the number that comes immediately before a given number.

For a number n:

Predecessor = n - 1

Examples:

• Predecessor of 5 = 4

• Predecessor of 20 = 19

• Predecessor of 100 = 99

• Predecessor of 0 = -1

• Predecessor of -18 = -19

What Is a Successor in Maths?

A successor is the number immediately after a given number when numbers are arranged in their usual order.

Successor Formula

Successor of n = n + 1

Successor Examples

Number	Successor	Calculation
7	8	7 + 1 = 8
15	16	15 + 1 = 16
25	26	25 + 1 = 26
100	101	100 + 1 = 101
-6	-5	-6 + 1 = -5
0	1	0 + 1 = 1

What Is the Successor of -18?

Add 1 to -18:

-18 + 1 = -17

Therefore, the successor of -18 is -17.

What Is a Predecessor in Maths?

A predecessor is the number immediately before a given number when numbers are arranged in their usual order.

Predecessor Formula

Predecessor of n = n - 1

Predecessor Examples

Number	Predecessor	Calculation
5	4	5 - 1 = 4
10	9	10 - 1 = 9
20	19	20 - 1 = 19
50	49	50 - 1 = 49
100	99	100 - 1 = 99
-6	-7	-6 - 1 = -7
0	-1	0 - 1 = -1

What Is the Predecessor of Zero?

The predecessor of zero is -1.

Using the formula:

0 - 1 = -1

So:

• Predecessor of 0 = -1

• Successor of 0 = 1

On a number line:

-2 ← -1 ← 0 → 1 → 2

The number immediately before 0 is -1, and the number immediately after 0 is 1.

Check: Consecutive Numbers: Meaning, Types, Formulas and Examples

Difference Between Successor and Predecessor

Feature	Successor	Predecessor
Meaning	Number immediately after a given number	Number immediately before a given number
Operation	Add 1	Subtract 1
Formula	n + 1	n - 1
Number-line direction	One step right	One step left
Example for 10	11	9

A simple way to remember them is:

Successor → after → +1

Predecessor → before → -1

Successor and Predecessor on a Number Line

A number line makes the concept easy to understand.

Consider:

-3, -2, -1, 0, 1, 2, 3

For 0:

• One step to the right = 1, so 1 is the successor.

• One step to the left = -1, so -1 is the predecessor.

For 2:

• Successor = 3

• Predecessor = 1

For -2:

• Successor = -1

• Predecessor = -3

The same rule works for positive numbers, zero and negative integers.

Successor and Predecessor of Integers

Integers include negative numbers, zero and positive numbers:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Every integer has:

• a predecessor that is 1 less

• a successor that is 1 more

Integer	Predecessor	Successor
-10	-11	-9
-5	-6	-4
-1	-2	0
0	-1	1
4	3	5
10	9	11
25	24	26

Successor and Predecessor of Negative Numbers

Negative numbers follow exactly the same rules.

For -7:

Predecessor = -7 - 1 = -8

Successor = -7 + 1 = -6

Therefore:

• Predecessor of -7 = -8

• Successor of -7 = -6

Students can practise number order, successor and predecessor concepts through interactive maths learning resources on CuriousJr.

Successor and Predecessor of Whole Numbers

For non-negative whole numbers, the successor is always one more than the number.

Examples:

• Successor of 0 = 1

• Successor of 1 = 2

• Successor of 25 = 26

• Successor of 99 = 100

The predecessor of a positive whole number is one less.

Examples:

• Predecessor of 1 = 0

• Predecessor of 10 = 9

• Predecessor of 50 = 49

However, -1 is not a whole number, so when discussing the predecessor of 0, it is important to distinguish between the whole-number set and the integers.

Check: Integers: Types, Rules, Properties, and Examples

Successor and Predecessor of Natural Numbers

The exact definition of natural numbers can vary by textbook. Some conventions include 0, while others start with 1.

For positive natural numbers:

• Predecessor of 8 = 7

• Successor of 8 = 9

If a textbook defines natural numbers as 1, 2, 3, ..., then 1 has no predecessor within that set because 0 is not included.

If the set includes 0, then the predecessor of 1 is 0.

The formulas n + 1 and n - 1 still describe the adjacent integers.

Successor and Predecessor Examples

Example 1: Find the successor and predecessor of 27.

Successor:

27 + 1 = 28

Predecessor:

27 - 1 = 26

Answer:

• Successor = 28

• Predecessor = 26

Example 2: Find the successor and predecessor of -4.

Successor:

-4 + 1 = -3

Predecessor:

-4 - 1 = -5

Answer:

• Successor = -3

• Predecessor = -5

Example 3: Find the successor and predecessor of 0.

Successor:

0 + 1 = 1

Predecessor:

0 - 1 = -1

Answer:

• Successor = 1

• Predecessor = -1

Example 4: Find the successor of 3536.

3536 + 1 = 3537

Answer: 3537

Example 5: Find the predecessor of 1000.

1000 - 1 = 999

Answer: 999

Example 6: Find the successor of -18.

-18 + 1 = -17

Answer: -17

Example 7: Find the predecessor of -20.

-20 - 1 = -21

Answer: -21

Find the Numbers After a Given Number

Sometimes a question asks for several numbers after a given number.

Example

Write the numbers after 45 up to 50.

Starting from 45:

46, 47, 48, 49, 50

So the numbers after 45 up to 50 are 46, 47, 48, 49 and 50.

Notice that the successor of 45 is only 46. The other numbers are subsequent numbers, not the successor itself.

Find the Numbers Before a Given Number

Similarly, we can list numbers before a given number.

Example

Write the numbers before 20 down to 15.

19, 18, 17, 16, 15

The predecessor of 20 is 19.

Successor and Predecessor Practice Questions

Try these questions before checking the answers.

Questions

1. Find the successor of 19.

2. Find the predecessor of 19.

3. Find the successor of 99.

4. Find the predecessor of 100.

5. Find the successor of 0.

6. Find the predecessor of 0.

7. Find the successor of -12.

8. Find the predecessor of -12.

9. Find the successor of 500.

10. Find the predecessor of 501.

11. Write the numbers after 28 up to 32.

12. Write the numbers before 15 down to 11.

Answers

1. 20

2. 18

3. 100

4. 99

5. 1

6. -1

7. -11

8. -13

9. 501

10. 500

11. 29, 30, 31, 32

12. 14, 13, 12, 11

Successor and Predecessor for Class 4

Class 4 students commonly use successor and predecessor to understand number order, number lines and place value.

Easy Examples

Number	Predecessor	Successor
9	8	10
20	19	21
45	44	46
100	99	101
250	249	251
999	998	1000

Quick Rule for Class 4

If the question asks for the successor, add 1.

If the question asks for the predecessor, subtract 1.

Example:

Number = 75

Successor = 75 + 1 = 76

Predecessor = 75 - 1 = 74

Common Mistakes

Mistake 1: Adding 1 for the predecessor

Incorrect:

Predecessor of 20 = 21

Correct:

20 - 1 = 19

Mistake 2: Subtracting 1 for the successor

Incorrect:

Successor of 20 = 19

Correct:

20 + 1 = 21

Mistake 3: Getting negative numbers wrong

For -5:

• Successor = -4

• Predecessor = -6

Remember that moving right on a number line increases the value.

Mistake 4: Thinking the successor of 0 is 0

The successor of 0 is 1.

Mistake 5: Confusing “successor” with all later numbers

The successor means the immediate next number, not every number that comes after it.

For example, the successor of 10 is 11, not 12 or 15.

Easy Way to Remember Successor and Predecessor

Use this memory trick:

Successor = Successive/next number = +1

Predecessor = Previous number = -1

Or remember:

After → Add 1

Before → Subtract 1

Quick Revision

• Successor means the number immediately after a given number.

• Predecessor means the number immediately before a given number.

• Successor of n = n + 1.

• Predecessor of n = n - 1.

• Successor of 0 = 1.

• Predecessor of 0 = -1.

• Successor of -18 = -17.

• Predecessor of -18 = -19.

• These rules work for integers, including negative numbers.

• A successor is one step to the right on a number line.

• A predecessor is one step to the left on a number line.