How to Find Successor and Predecessor of a Number with Examples
The concept of successor and predecessor in maths plays a key role in mathematics and helps students understand the order and relationship among numbers. It's a topic that regularly appears in tests, worksheets, and even in real-life scenarios such as counting objects, arranging things, and coding.
What Is Successor and Predecessor in Maths?
A successor in maths is the number that comes immediately after a given number, while a predecessor is the number just before it. For example, in the sequence 7, 8, 9, the successor of 8 is 9, and the predecessor of 8 is 7. You’ll find this concept applied in areas such as counting numbers, sequencing in coding, and calendar dates.
Key Formula for Successor and Predecessor in Maths
Here’s the standard formula that always works for whole numbers:
- Successor of a number = Number + 1
- Predecessor of a number = Number – 1
Why Is Successor and Predecessor Important?
Successor and predecessor in maths are the building blocks of number sense for children. These concepts make it easier for students to understand counting, perform quick mental addition and subtraction, and recognize number patterns. Recognizing before/after relationships in numbers also helps with problem-solving in exams and daily activities.
Step-by-Step Examples
| Number | Successor | Predecessor |
|---|---|---|
| 15 | 16 | 14 |
| 1000 | 1001 | 999 |
| 43 | 44 | 42 |
| 0 | 1 | Not defined for whole numbers |
Worked Out Problem
Question: Find the successor and predecessor of 99999.
1. Given number = 999992. Successor = 99999 + 1 = 100000
3. Predecessor = 99999 – 1 = 99998
Answer: Successor is 100000, Predecessor is 99998.
Successor and Predecessor with Negative Numbers
For integers, the rule of successor (+1) and predecessor (-1) works for both positive and negative numbers. With negative numbers, the successor of –3 is –2, and the predecessor of –3 is –4. However, in the set of natural numbers (1, 2, 3, ...), there is no predecessor for 1, and in whole numbers (0, 1, 2, ...), there is no predecessor for 0.
Real-Life Use Cases & Fun Facts
You see successor and predecessor in maths in action when you:
- Turn the calendar from one day to the next (successor: today + 1 day = tomorrow)
- Check seat numbers (if you are in seat 7, your predecessor sat in seat 6, and your successor will sit in 8)
- Program loops in computer science (next/previous step)
Fun Fact: In Peano’s axioms, the concept of “successor” builds up the entire number system!
Try These Yourself
- What is the successor of 250?
- Find the predecessor of 1200.
- Is there a predecessor for 0 in whole numbers?
- Give the successor and predecessor for –5.
Frequent Errors and Misunderstandings
- Writing the same number as both successor and predecessor.
- Applying the concept to fractions or decimals incorrectly (the next/previous is not always just ±1 for non-integers).
- Forgetting zero has no predecessor in whole numbers.
Relation to Other Number Concepts
The idea of successor and predecessor is strongly linked with number line ordering, even & odd numbers, and arithmetic operations. Understanding this helps with learning addition, subtraction, and comparing numbers. For more on ordering and comparing, try our Greater Than Less Than Calculator.
Classroom Tip
A quick way to remember how to find a successor is to think "add one" to the number, and for predecessor, "subtract one." Vedantu’s experienced teachers often use number lines and simple drawing tricks to make this concept visual and easy in live classes.
More Practice: Worksheets and Activities
Practice is key for mastering successor and predecessor. Download printable worksheets or try online quizzes aligned with CBSE and NCERT standards to test your knowledge. You can also use the Math Basic Calculator for quick checks!
Useful Internal Links for More Learning
- Numbers to Words Converter
- Long Addition Calculator
- Rounding Numbers Tool
- Comparing Fractions Calculator
We explored successor and predecessor in maths — from clear definitions, formulas, and real-life examples, to helpful tricks and links for extra practice. Keep practicing with Vedantu and you’ll soon be a pro at finding successors and predecessors for any number!
FAQs on What Are Successor and Predecessor in Maths?
1. What is the successor of a number in Maths?
In Maths, the successor of a number is the number that comes immediately after it. It's found by adding 1 to the given number. For example, the successor of 5 is 6 (5 + 1 = 6), and the successor of 99 is 100 (99 + 1 = 100).
2. How do you find the predecessor of a given number?
The predecessor of a number is the number that comes immediately before it. You find it by subtracting 1 from the given number. For example, the predecessor of 8 is 7 (8 - 1 = 7), and the predecessor of 1000 is 999 (1000 - 1 = 999).
3. Can a number have more than one successor or predecessor?
No, a number can only have one successor and one predecessor. Successors and predecessors are the numbers directly following or preceding a given number on the number line.
4. What is the predecessor of zero?
In the set of natural numbers, zero has no predecessor. However, in the set of integers, the predecessor of zero is -1.
5. Why are successors and predecessors important in counting?
Successors and predecessors are fundamental to understanding the order of numbers and the concept of counting. They help build number sense and are essential for learning basic arithmetic operations.
6. What is the successor and predecessor of 1000?
The successor of 1000 is 1001 (1000 + 1 = 1001), and the predecessor of 1000 is 999 (1000 - 1 = 999).
7. How do successor and predecessor concepts extend to negative numbers and decimals?
The concept extends similarly to negative numbers; the successor is found by adding 1, and the predecessor by subtracting 1. For decimals, the same rules apply; however, the values are fractional increments or decrements.
8. Why is there no predecessor to 0 in natural numbers but yes in integers?
Natural numbers start from 0 (or 1, depending on the definition); therefore, there's no number before 0 in that set. Integers include negative numbers, so -1 precedes 0.
9. Are successor and predecessor valid for fractions, decimals, and large numbers?
Yes, the concepts apply to fractions and decimals as well, though the successor and predecessor will be values with correspondingly smaller increments. It also applies to large numbers; you still add or subtract 1 to find the successor or predecessor, regardless of the magnitude.
10. What is the role of successor/predecessor in patterns and math coding?
Successors and predecessors are crucial in identifying number patterns and sequences and are fundamental in computer programming, particularly in algorithms involving iterative processes and loops.
11. How are successor and predecessor used in real-life scenarios (e.g., dates, time)?
We use them implicitly when dealing with sequential events like dates (the day after, the day before), time (the next hour, the previous hour), or order in queues (next in line, the person before).
12. What are consecutive numbers?
Consecutive numbers are numbers that follow each other in order, without gaps. For example, 5, 6, and 7 are consecutive numbers. The concept of consecutive numbers is directly related to successors and predecessors.
