What is Subtraction in Maths?
The concept of subtraction plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding subtraction is not only crucial for school exams but also for problem-solving in everyday life, from calculating money to measuring differences in scores or quantities.
What Is Subtraction?
A subtraction is defined as a mathematical operation used to find the difference between two numbers by taking one number away from another. You’ll find this concept applied in areas such as arithmetic, measurement, and data handling. Words like “minus,” “deduct,” “less,” and “take away” all signal subtraction. For example, if you have 15 candies and give away 7, subtraction helps you know how many are left (15 − 7 = 8).
Key Formula for Subtraction
Here’s the standard formula: \( \text{Minuend} - \text{Subtrahend} = \text{Difference} \)
| Term | Meaning | Example (12-5=7) |
|---|---|---|
| Minuend | Number to subtract from | 12 |
| Subtrahend | Number to be subtracted | 5 |
| Difference | Final result (answer) | 7 |
Cross-Disciplinary Usage
Subtraction is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. For example, physicists use subtraction when calculating net forces, and students preparing for JEE or NEET frequently solve equations that require careful subtraction. Logical reasoning problems, such as comparing ages or distances, often involve finding “how much more” or “how many left,” making subtraction an everyday necessity.
Step-by-Step Illustration
- Suppose you have 16 pencils and give 7 to your friend.
Start with 16.
- Subtract the number given away from what you had:
16 - 7 = 9
- The answer, 9, is the number of pencils left with you.
Key Properties and Facts about Subtraction
- Subtracting zero from a number does not change the number. (e.g., 8 − 0 = 8)
- Subtracting a number from itself always gives zero (e.g., 6 − 6 = 0)
- When 1 is subtracted from a number, you get its immediate previous number, called the predecessor (e.g., 10 − 1 = 9)
- Subtraction is not commutative: 7 − 4 ≠ 4 − 7
Subtraction Table for Fast Recall
| − | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 10 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| 9 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | -1 |
| 8 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 | -1 | -2 |
Methods of Subtraction
- Single-digit and Double-digit: For numbers up to 20, subtraction can be done using fingers or mental math.
- Column Subtraction: Place numbers one below the other, align by place value, subtract digit by digit from right to left.
- Subtraction with Regrouping (Borrowing): When a digit in the minuend is smaller than in the subtrahend, borrow from the next place value.
- Number Line: Place the first number and jump backwards as many steps as the number being subtracted.
Speed Trick or Vedic Shortcut
Here’s a quick shortcut to solve subtraction with regrouping:
- When the top digit is smaller, borrow “1” from the next column.
- Add 10 to the top digit, subtract the bottom digit.
- Don’t forget to decrease the next digit by 1.
This Vedic approach helps in solving large number subtraction quickly. Vedantu’s live classes often teach these tricks for speed and confidence in timed tests.
Try These Yourself
- Solve: 74 − 46
- What is the difference between 150 and 79?
- Subtract 1 from 98
- Find the missing number: ___ − 29 = 53
Frequent Errors and Misunderstandings
- Forgetting to regroup (“borrow”) when upper digit is smaller
- Mixing up the minuend (top number) and subtrahend (bottom number)
- Assuming subtraction is commutative (it is NOT: 9 - 2 ≠ 2 - 9)
- Dropping zeros in place value alignment
Relation to Other Concepts
The idea of subtraction connects closely with other operations like addition (its inverse), and properties of subtraction help lay the foundation for subtraction with regrouping and word problems. Mastering subtraction is essential for building skills in fractions, decimals, measurement, and algebra later on.
Classroom Tip
A quick way to remember subtraction is to always “start from the right,” line up digits by their place values, and use number lines or visual aids for tricky sums. Vedantu’s teachers show these steps especially for Class 1 and Class 2, making maths easy and fun for kids.
We explored subtraction—from the definition, formula, and techniques, to common problems and how it links with other maths ideas. Keep practicing with Vedantu's interactive sessions to build your accuracy and confidence in maths!
FAQs on Subtraction – Meaning, Formula, and Examples
1. What is subtraction in Maths?
Subtraction in mathematics is the process of finding the difference between two numbers. It involves taking one number (the subtrahend) away from another number (the minuend) to determine the remaining amount (the difference). Think of it as removing a quantity from a larger quantity. For example, if you have 10 apples and you give away 3, you are left with 7; this can be represented as 10 - 3 = 7.
2. What is the subtraction symbol?
The symbol for subtraction is the minus sign, represented as “–”. This symbol indicates that the number to its right should be subtracted from the number to its left.
3. What are the three parts of a subtraction problem?
The three key parts of a subtraction problem are:
• Minuend: The larger number from which you subtract.
• Subtrahend: The number being subtracted.
• Difference: The result of the subtraction (the answer).
4. What is the subtraction formula?
The basic subtraction formula is: Minuend – Subtrahend = Difference. This formula shows the relationship between the three parts of a subtraction problem.
5. How do you solve subtraction word problems?
Solving subtraction word problems involves these steps:
• Read the problem carefully to understand what it's asking.
• Identify the numbers involved and what they represent (the minuend and subtrahend).
• Determine the operation needed (subtraction).
• Perform the subtraction calculation.
• Write the answer in a sentence, answering the question posed in the word problem. Always check your answer for reasonableness.
6. What is regrouping (borrowing) in subtraction?
Regrouping, also known as borrowing, is a technique used in subtraction when a digit in the minuend is smaller than the corresponding digit in the subtrahend. You 'borrow' a unit from the next higher place value column to make the subtraction possible. For example, when subtracting 28 from 43, you borrow 1 ten from the tens column (making the ones column 13 instead of 3) before subtracting the ones.
7. What are some real-life examples of subtraction?
Subtraction is used frequently in everyday life. Examples include:
• Calculating the change after making a purchase.
• Finding the difference between two amounts of money.
• Determining how many items are left after using some.
• Measuring the difference in height, weight, or distance.
• Calculating elapsed time.
8. What are some common subtraction methods?
There are several methods for subtraction: standard algorithm (column subtraction), using a number line, and various mental math strategies (such as subtracting in parts or using complementary addition). The best method depends on the numbers involved and individual preference.
9. What happens when you subtract a larger number from a smaller number?
Subtracting a larger number from a smaller number results in a negative number (a number less than zero). This is often represented with a minus sign before the result. For example, 5 - 8 = -3
10. Is subtraction commutative?
No, subtraction is not commutative. This means that changing the order of the numbers changes the result. For example, 10 - 5 ≠ 5 - 10. The order matters.
11. How is subtraction related to addition?
Subtraction and addition are inverse operations. This means that they 'undo' each other. You can use addition to check subtraction answers, and vice versa. For example, if 10 - 4 = 6, then 6 + 4 = 10.
12. What are some properties of subtraction?
Key properties of subtraction include:
• Identity property of subtraction: Subtracting zero from a number doesn’t change the number (a - 0 = a)
• Subtraction of zero: Any number minus itself equals zero (a - a = 0)
• Non-commutative property: a - b ≠ b - a (order matters)
