Addition and Subtraction (Definition, Rules and Examples)

Addition And Subtraction

Edited By Team Careers360 | Updated on Jul 02, 2025 05:16 PM IST

Addition and subtraction are part of the calculation in math. Addition and subtraction are opposite of each other. The addition is combining multiple things and counting them as one large group. In mathematics, the process of combining two or more numbers is called addition. The numbers added are addends, and the final answer is called the sum. (It is usually signified by the plus symbol +) Whereas subtract means to take away from a group or number of things. In mathematics, subtracting means the number of things in the group becomes less or reduces. The parts of subtraction are minuend, subtrahend, and difference. (The “-” negative symbol usually signifies it).

This Story also Contains

Addition And Subtraction Sum
Addition, Subtraction And Multiplication
Addition And Subtraction For Classes 4 And 5
Addition To The Kindergarten Class

Addition And Subtraction

Addition And Subtraction Sum

Addition and subtraction are inverse operations of each other. As an illustration, if 9 + 1 = 10, then 10 - 1 = 9. That demonstrates that adding one to 9 shows a result of ten, but subtracting one from 10 shows a result of nine.

A new number is created by adding two or more additional numbers or values. As an illustration, the outcome of adding 2 and 3 is 5.

2 + 3 = 5

Let's now look at the sum of 2 and 3 practically. What number of apples are there in total if we start with two apples in a basket and then add three more?

2 → 1 + 1

3 → 1 + 1 + 1

2 + 3 = 1 + 1 + 1 + 1 + 1

Counting each apple separately yields a total of 5 apples.

If we now count each apple, there are 5 total.

The ability to add to an existing value results in a rise in value.

To subtract is to take away another value to obtain the desired value.

For instance, 2 is the result when 3 is subtracted from 5.

5 - 3 = 2

How many apples are left in the basket if we believe there are 5 apples in it, and we take out 3 of them?

So, the answer is 2 apples.

5 - 3 = 1 + 1 + 1 + 1 + 1 - 1 + 1 + 1 = 2

Addition, Subtraction And Multiplication

As we see above, the four major operations in mathematics are:

Addition
Subtraction
Multiplication
Division

Like addition and subtraction, multiplication and division are also inverse operations of each other.

Let us understand with an example,

If 3 is multiplied by 4,

3 x 4 = 12

So, the answer will be 12.

Now, if 12 is divided by 3,

12 ÷ 3 = 4.

Here, the answer is 4.

Addition And Subtraction For Classes 4 And 5

Grade 4 addition, involves the addition of digits like single digits, two digits, three digits etc. Let's understand more.

Mental Addition-

Mental addition is the calculation (addition) of two different or the same values in mind (directly).

Some examples of mental addition are given below,

Sum of 2-digit numbers

23 + 24 = 47

Here, we can easily do a sum of 23 and 24 in mind.

Sum of three different values( two-digit numbers)

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10 + 11 + 12 = 33

Adding in Columns-

For some additions, we need to do the sum of given values by putting them as Columns; let's see,

Sum of 3 digit numbers

123 + 345 =?

So, for the given addition, we have to put this in the column first

123 + 345 = 468

Another example

456+324 = 780

Here, the sum of the last digits 6 and 4 is 10. So, their sum result is 0 and 1 will be added at the left-sided digit (i.e 5) of 6.

Another example of the addition of three big three-digit numbers is given below,

789+ 687+ 879= 2355

So, 2 + 8 + 8 + 7 = 25. Now the same as above. 5 will be down, and 2 will be added to the left-side column of the digit 8 in 789.

So, the sum of 2 + 7 + 6 + 8 = 23

Now, for the subtraction process, we will take 2, 3, 4, 5, or 6-digit numbers. Let's understand with an example,

Subtraction of 234 and 123

234 - 123 = 111

We’ll take some more examples to understand subtraction.

159 - 031 = 128

Let us understand how the subtraction mechanism works.

For example, 159 - 031,

Now, to find the answer, we’ll write numbers like this,

1 5 9

- 0 3 1

? ? ?

The first step is to subtract from the value's right side. So, we’ll do a subtraction of 9 and 1. So, 9 - 1 = 8.

1 5 9

- 0 3 1

? ? 8

As the next step, we’ll subtract the left side number of 9. So, for 5 and 3, 5 - 3 = 2.

1 5 9

- 0 3 1

? 2 8

Now, at the last step, the left-sided number of 5. So, 1 - 0 = 1.

1 5 9

- 0 3 1

1 2 8

This is how the subtraction mechanism works.

Addition To The Kindergarten Class

Let us understand addition and subtraction,

Addition

The sum of the given value is called addition. See the given images. An apple is good for health

Let us consider that Rahul has 1 apple and Ashok has 1 apple. Now, Ashok gives his 1 apple to Rahul. Then how many apples does Rahul have now? The answer is 2 apples.

Let us learn more with another example.

Eraser is used to remove parts drawn by pencil

https://www.vectorstock.com/royalty-free-vector/cartoon-eraser-vector-5617700

How many erasers are there in the image? Let us count erasers.

Let’s count erasers. There is 1 eraser, then another 1, and then another 1 and then another 1.

So, the numbers of erasers are 1 + 1 + 1 + 1 = 4.

There are 4 erasers in the image.

Now, we learn addition without using images. The followings are the calculations of addition,

1) Addition or sum of 0 and 1

2) Sum of 1 and 2

3) Sum of 3 and 4

So, this is how we can do the sum of two different or the same numbers in mathematics, which is called addition.

Frequently Asked Questions (FAQs)

1. What do you mean by addition and subtraction?

The process in which we add or do a sum of two or more items or numbers of things is called addition. For example, Ayush has 12 bananas, and the prince has 1 banana. So, If the prince gives his banana to Ayush, the total number of bananas Ayush has will be 13. At the same time, the process in which we remove or minus or subtract things or items or numbers is called subtraction. For example, Ayush gives his 12 bananas to the prince. So, now Ayush has 0 bananas.

2. Is addition and subtraction inverse of each other?

Yes, addition and subtraction are inverses of each other. Adding 3 with 2 will gives us an answer as 5 and again subtracting 2 from 5 will gives us an answer as 3. The addition is the process in which two values combine and form a new value. A small value is taken from a bigger value in the subtraction process.

3. Can you subtract a larger number from a smaller one?

Yes, you can subtract a larger number from a smaller one. The result will be a negative number. For example, 5 - 8 = -3. This concept is essential in understanding the properties of real numbers and their operations.

4. How does the commutative property apply to addition but not subtraction?

The commutative property states that changing the order of numbers in addition doesn't affect the result (a + b = b + a). However, this doesn't apply to subtraction. For example, 5 + 3 = 3 + 5, but 5 - 3 ≠ 3 - 5. Understanding this difference is crucial for solving equations and algebraic expressions.

5. What is the relationship between addition and subtraction?

Addition and subtraction are inverse operations. Subtracting a number is the same as adding its opposite (additive inverse). For example, 8 - 3 is the same as 8 + (-3). This relationship is crucial for solving equations and understanding the structure of real numbers.

6. What is the associative property of addition, and why doesn't it apply to subtraction?

The associative property of addition states that the grouping of numbers doesn't affect the sum: (a + b) + c = a + (b + c). This property doesn't apply to subtraction because changing the grouping in subtraction can change the result. For example, (10 - 5) - 3 ≠ 10 - (5 - 3). Understanding this difference is important for algebraic manipulations and problem-solving.

7. How do you add or subtract mixed numbers?

To add or subtract mixed numbers, first convert them to improper fractions. Then, perform the addition or subtraction as you would with regular fractions. Finally, convert the result back to a mixed number if necessary. This process requires understanding the relationship between mixed numbers and improper fractions, as well as fraction addition and subtraction.

8. What is the concept of "additive closure" in real numbers?

Additive closure means that the sum of any two real numbers is always a real number. This property ensures that addition is a well-defined operation within the set of real numbers. Understanding this concept is crucial for grasping the structure and properties of the real number system.

9. What is the concept of "additive identity" in real numbers?

The additive identity for real numbers is zero. Adding zero to any real number leaves that number unchanged: a + 0 = a for any real number a. This property is fundamental to the structure of real numbers and is used in many algebraic proofs and manipulations.

10. How do you add or subtract complex numbers?

To add or subtract complex numbers, you operate on the real and imaginary parts separately. For (a + bi) ± (c + di), the result is (a ± c) + (b ± d)i. This process requires understanding the structure of complex numbers and the principles of addition and subtraction for real numbers.

11. What is the relationship between addition/subtraction and the number line?

On a number line, addition moves to the right, while subtraction moves to the left. The distance moved is equal to the number being added or subtracted. This visual representation helps in understanding the nature of these operations and the concept of signed numbers.

12. What is the concept of "regrouping" in addition, and how does it relate to place value?

Regrouping in addition occurs when the sum of digits in a place value exceeds 9. The excess is "carried over" to the next higher place value. This process is deeply connected to understanding place value and the base-10 number system. It's the reverse of the "borrowing" process in subtraction.

13. How do you add or subtract sets?

Set addition is typically referred to as union (∪), while set subtraction is called difference (-). For sets A and B, A ∪ B includes all elements in either A or B or both, while A

14. What is the difference between addition and subtraction of real numbers?

Addition combines two or more numbers to increase quantity, while subtraction removes one number from another to decrease quantity. With real numbers, these operations can involve positive, negative, and decimal values on a continuous number line.

15. How does adding or subtracting zero affect a real number?

Adding or subtracting zero to any real number doesn't change its value. This is known as the identity property of addition. For any real number 'a', a + 0 = a and a - 0 = a. This property is important in simplifying expressions and solving equations.

16. How do you add or subtract numbers in scientific notation?

To add or subtract numbers in scientific notation, first adjust the exponents so they're the same. Then, add or subtract the coefficients while keeping the exponent the same. Finally, adjust the result if necessary to ensure the coefficient is between 1 and 10. This process requires understanding exponents, scientific notation, and place value.

17. How do you add or subtract fractions with different denominators?

To add or subtract fractions with different denominators, you need to find a common denominator first. This is typically the least common multiple (LCM) of the denominators. Then, convert each fraction to an equivalent fraction with this common denominator. Finally, add or subtract the numerators while keeping the common denominator. This process involves understanding both fraction concepts and LCM.

18. What is the additive inverse of a real number?

The additive inverse of a real number is the number that, when added to the original number, results in zero. For any real number 'a', its additive inverse is '-a'. For example, the additive inverse of 5 is -5, and 5 + (-5) = 0. This concept is fundamental in solving equations and understanding the structure of real numbers.

19. How does the concept of infinity affect addition and subtraction in real numbers?

Infinity is not a real number, but a concept representing unboundedness. Adding or subtracting a finite number to/from infinity still results in infinity. However, subtracting infinity from infinity is undefined. Understanding these concepts is crucial for working with limits and certain areas of calculus.

20. What is the concept of "additive inverse" in modular arithmetic?

In modular arithmetic, the additive inverse of a number is another number that, when added to the original number, results in the modular equivalent of zero. For example, in mod 5, the additive inverse of 3 is 2 because 3 + 2 ≡ 0 (mod 5). This concept is important in number theory and cryptography.

21. What is the concept of "additive manufacturing" and how does it relate to mathematics?

Additive manufacturing, or 3D printing, involves adding material layer by layer to create objects. This process relies heavily on mathematical concepts including geometry, trigonometry, and calculus for designing and optimizing 3D models. Understanding this application introduces students to practical uses of mathematics in modern technology.

22. What is the concept of "additive category" in abstract algebra?

An additive category is a category equipped with a zero object and binary biproducts. This abstract concept generalizes the idea of addition to more complex mathematical structures. While advanced, introducing this concept can help students understand how basic arithmetic operations extend to higher mathematics.

23. How does the concept of significant figures apply to addition and subtraction in logarithmic scales?

When adding or subtracting values on a logarithmic scale (like decibels or pH), you typically convert back to the linear scale, perform the operation, then convert the result back to the logarithmic scale. The number of significant figures should be consistent with the precision of the original measurements. This concept is important in fields like acoustics and chemistry.

24. What is the concept of "borrowing" in subtraction, and how does it relate to place value?

"Borrowing" in subtraction is a method used when the digit in the minuend (the number you're subtracting from) is smaller than the corresponding digit in the subtrahend (the number being subtracted). It involves taking a value from the next higher place value and redistributing it. This concept is deeply connected to understanding place value and the base-10 number system.

25. What is the difference between absolute value addition and regular addition?

Regular addition combines the signs and magnitudes of numbers, while absolute value addition only considers magnitudes. For example, 5 + (-3) = 2, but |5| + |-3| = 8. Understanding this difference is crucial for working with absolute values and solving certain types of equations and inequalities.

26. How does adding or subtracting a negative number relate to its opposite operation?

Adding a negative number is equivalent to subtracting its positive counterpart, and subtracting a negative number is equivalent to adding its positive counterpart. For example, 5 + (-3) = 5 - 3, and 5 - (-3) = 5 + 3. This concept is fundamental to understanding operations with signed numbers and algebraic manipulations.

27. How does the distributive property connect addition and multiplication?

The distributive property states that a(b + c) = ab + ac. This property shows how addition and multiplication interact, allowing us to "distribute" multiplication over addition. It's a fundamental concept in algebra and is crucial for simplifying expressions and solving equations.

28. What is the difference between arithmetic and algebraic addition/subtraction?

Arithmetic addition/subtraction involves specific numbers and produces a numerical result. Algebraic addition/subtraction often involves variables and produces an expression. For example, 5 + 3 = 8 is arithmetic, while x + 3 is algebraic. Understanding this difference is crucial for transitioning from arithmetic to algebra.

29. How do you add or subtract irrational numbers?

Irrational numbers, like π or √2, can't be expressed as exact fractions. When adding or subtracting irrational numbers, we often keep them in their symbolic form or use approximations. For example, π + √2 is left as is or approximated. This concept requires understanding the nature of irrational numbers and their place in the real number system.

30. How do you add or subtract numbers in different bases?

To add or subtract numbers in different bases, you typically convert them to the same base first (often base 10), perform the operation, and then convert the result back to the original base if needed. This process requires understanding place value in different number systems and conversion between bases.

31. How does the concept of significant figures apply to addition and subtraction?

When adding or subtracting measurements, the result should have the same number of decimal places as the measurement with the fewest decimal places. This ensures that the precision of the result reflects the precision of the input measurements. Understanding this is crucial in scientific calculations and data analysis.

32. What is the difference between arithmetic and geometric sequences in terms of addition?

Arithmetic sequences involve adding a constant difference between terms, while geometric sequences involve multiplying by a constant ratio. For example, 2, 5, 8, 11 is arithmetic (add 3 each time), while 2, 6, 18, 54 is geometric (multiply by 3 each time). Understanding this difference is important in sequence and series problems.

33. How do you add or subtract vectors?

Vector addition/subtraction is performed component-wise. For 2D vectors (a,b) and (c,d), their sum is (a+c, b+d) and their difference is (a-c, b-d). This concept extends to higher dimensions and is fundamental in physics and linear algebra.

34. What is the concept of "carrying" in addition, and how does it relate to place value?

Carrying in addition occurs when the sum of digits in a place value exceeds 9. The excess is "carried" to the next higher place value. This process is deeply connected to understanding place value and the base-10 number system. It's the opposite of "borrowing" in subtraction.

35. How does the concept of absolute value affect subtraction?

The absolute value of a difference is not always equal to the difference of absolute values. For example, |5 - 8| = 3, but |5| - |8| = -3. Understanding this distinction is crucial for solving absolute value equations and inequalities.

36. What is the relationship between addition/subtraction and the concept of distance?

The absolute value of the difference between two numbers represents the distance between them on a number line. For example, |5 - 8| = 3 represents the distance between 5 and 8. This concept connects arithmetic operations to geometric interpretations and is fundamental in many areas of mathematics.

37. How do you add or subtract matrices?

Matrix addition/subtraction is performed element by element, and is only defined for matrices of the same dimensions. For example, [a b; c d] + [e f; g h] = [a+e b+f; c+g d+h]. This concept is fundamental in linear algebra and has applications in various fields including computer graphics and data analysis.

38. What is the concept of "additive persistence" in number theory?

Additive persistence is the number of times you need to sum the digits of a number before reaching a single-digit result. For example, 999 has an additive persistence of 2 (9+9+9=27, 2+7=9). This concept introduces students to iterative processes and digit manipulation.

39. How does the concept of significant digits apply to addition and subtraction?

In addition and subtraction, the result should have the same number of decimal places as the least precise measurement used in the calculation. This ensures that the precision of the result accurately reflects the precision of the input data. Understanding this is crucial in scientific and engineering calculations.

40. What is the difference between linear and non-linear addition in mathematics?

Linear addition follows the principle that f(x + y) = f(x) + f(y) for all x and y. Non-linear addition doesn't follow this principle. For example, adding lengths is linear, but adding areas is non-linear. Understanding this difference is crucial in various fields, including physics and economics.

41. How do you add or subtract rational expressions?

To add or subtract rational expressions, you need to find a common denominator first, similar to adding fractions. Then you add or subtract the numerators while keeping the common denominator. This process requires understanding of both fraction arithmetic and algebraic manipulation.

42. What is the concept of "additive smoothing" in statistics and probability?

Additive smoothing involves adding a small constant to frequency counts to avoid zero probabilities. This technique is used in various machine learning and natural language processing applications. Understanding this concept introduces students to practical applications of addition in data science.

43. How does the concept of significant figures apply to addition and subtraction of measurements?

When adding or subtracting measurements, the result should have the same number of decimal places as the least precise measurement used in the calculation. This ensures that the precision of the result accurately reflects the precision of the input data. Understanding this is crucial in scientific and engineering calculations.

44. What is the relationship between addition/subtraction and the concept of net change?

Net change is calculated by subtracting the initial value from the final value. It represents the overall change, taking into account both increases (additions) and decreases (subtractions). This concept is crucial in various fields, including finance and physics.

45. How do you add or subtract polynomials?

To add or subtract polynomials, you combine like terms. Terms with the same variables and exponents are added or subtracted. For example, (3x^2 + 2x - 1) + (x^2 - 3x + 4) = 4x^2 - x + 3. This process requires understanding of algebraic terms and exponents.

46. How does the concept of significant digits apply to addition and subtraction in scientific notation?

When adding or subtracting numbers in scientific notation, the result should have the same number of significant digits as the least precise number in the calculation. This ensures that the precision of the result accurately reflects the precision of the input data. Understanding this is crucial in scientific calculations and data analysis.

47. What is the relationship between addition/subtraction and the concept of equilibrium in physics and chemistry?

In physics and chemistry, equilibrium often involves balancing opposing forces or reactions. This can be represented mathematically as the sum of these forces or reactions equaling zero. Understanding this connection helps students see how mathematical operations apply to real-world phenomena.

48. How do you add or subtract functions?

Function addition/subtraction is performed by adding/subtracting the outputs for each input. For functions f(x) and g(x), (f + g)(x) = f(x) + g(x) and (f - g)(x) = f(x) - g(x). This concept is fundamental in calculus and functional analysis.

49. What is the relationship between addition/subtraction and the concept of conservation in physics?

Conservation laws in physics often involve the idea that certain quantities (like energy or momentum) remain constant in a closed system. Mathematically, this means that the sum of these quantities before and after an event is equal. Understanding this connection helps students see how addition and subtraction apply to fundamental physical principles.