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Multiplication: Definition, Formula, Examples, Rules, Table

Multiplication combines equal groups of numbers, simplifying repeated addition, essential for math concepts like algebra, geometry, and real-world applications. Check this article to know more about multiplication.
authorImageNeha Tanna16 Jun, 2025
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Multiplication

Multiplication: Multiplication is one of the four basic arithmetic operations, representing repeated addition. It involves combining equal groups of numbers to find a total, with terms known as factors and the result called the product.

For example, 4 × 3 means adding 4 three times (4 + 4 + 4), which equals 12. Multiplication is essential in various mathematical concepts, including algebra, geometry, and data analysis. It is fundamental to real-world applications such as calculating areas, scaling quantities, and understanding rates. Mastery of multiplication forms the basis for more advanced math skills like division, fractions, and proportional reasoning. 

Multiplication Definition in Math

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In mathematics, multiplication refers to the process of repeated addition of equal groups. When you multiply two numbers, you are essentially adding one number a specific number of times. For example, multiplying 4 by 3 means adding 4 three times:

4×3=4+4+4=12

This can be visualized as combining equal groups. So, multiplication can be seen as determining how many objects are in a set of equal-sized groups.

Key Terms in Multiplication:

  1. Multiplicand : The number to be multiplied.
  2. Multiplier : The number that tells how many times the multiplicand is to be added.
  3. Product : The result of multiplication.
For example, in the multiplication equation: 4×3=12
  • 4 is the multiplicand.
  • 3 is the multiplier.
  • 12 is the product.
Multiplication is commonly used to solve problems involving repeated addition , such as finding the total number of objects when you have several groups of the same size.

Example

If you have 5 bags, and each bag contains 2 apples, you can multiply the number of bags (5) by the number of apples in each bag (2) to find the total number of apples: 5×2=10 Thus, you have 10 apples in total.

Adding Fractions

Multiplication Examples

See few more examples of multiplication here:
  • Multiplication of 3 and 3 = 3 x 3 = 9
  • Multiplication of 4 by 4 = 4 + 4 + 4 + 4= 16
  • Multiplication of 5 by 5 = 5 + 5 + 5 + 5 + 5 = 25
  • Multiplication of 10 x 10 = 100
  • Multiplication of 8 by 9 = 8 x 9 = 72

Multiplication Symbol

The symbol of multiplication is denoted by a cross sign (×) and also sometimes by a dot (.). Examples:
  • 3 × 11 = 33
  • 5 × 9 = 45
  • 8 × 2 × 10 = 160
  • (9).(10) = 90
  • (7).(8) = 56

Multiplication Formula

The multiplication formula is given by:

Multiplier × Multiplicand = Product

The total number of objects in each group is the multiplicand. The number of equal groupings is the multiplier. The product of multiplier and multiplicand is called the product. Example: If Multiplier = 5 and Multiplicand = 8, then the product is: Product = 5 x 8 = 48

What is Abacus

Properties of Multiplication

The properties of multiplication are:
  • Closure Property
  • Commutative property
  • Associative property
  • Distributive property
  • Identity property
  • Zero property

Closure Property of Multiplication

The closure property of multiplication states that An integer is the product of two numbers (-4 x 3 = -12). A fraction or a whole number can be obtained by multiplying two fractions (1/2 x 2 = 1).

Commutative Property of Multiplication

The commutative property states that the order in which two numbers are multiplied does not affect their product. In other words, changing the position of the factors does not change the result.

A × B = B × A

For example: 2 × 3 = 3 × 2 = 6

Associative Property of Multiplication

The associative property states that when multiplying three or more numbers, the grouping of the numbers (how they are grouped in parentheses) does not affect the product. This means that the result remains the same no matter how the numbers are paired.

A × (B × C) = (A × B) × C

For example: 2 × (3 × 4) = (2 × 3) × 4 = 24

Distributive Property of Multiplication

The distributive property states that multiplication distributes over addition or subtraction. This means that when a number is multiplied by a sum (or difference), you multiply each term inside the parentheses by the number outside.

A × (B + C) = (A × B) + (A × C)

For example: 4 × (2 + 3) = 4 × 2 + 4 × 3 → 20

Identity Property of Multiplication

The identity property of multiplication states that when any number is multiplied by 1, the product is always the number itself. The number 1 is called the multiplicative identity because it does not change the value of the number.

A × 1 = A

For example:
  • 12 × 1 = 12
  • -3 × 1 = -3

Zero Property of Multiplication

The zero property of multiplication states that when any number is multiplied by zero, the result is always zero. This property is often used to simplify complex expressions.

A × 0 = 0

where A is any integer. For example: 9 × 0 = 0

Also Read-

Riddles for Kids Multiplication Indoor Games for Kids
Subtraction Maths Puzzles Laws of Exponents

Rules of Multiplication (How to Multiply)

There are several multiplication rules for numbers. They are as follows: An integer is produced by multiplying two integers. The product of any number with 0 is 0. Any number multiplied by one return to its initial value. The same number of zeros are added to the end of the original number when an integer is multiplied by multiples of 10. For instance, 4 × 1000 = 4000 When multipled together, the numbers' order is irrelevant. As an illustration, 2 × 3 × 4 × 5 = 5 × 4 × 3 × 2 = 3 × 2 × 4 × 5 = 120

Multiplication Signs

The sign rules listed below apply when multiplying two or more numbers with distinct signs (+ and -). The resultant output varies accordingly.
S.No. Operation Result
1. (+ve) × (+ve) +ve
2. (+ve) × (-ve) -ve
3. (-ve) × (+ve) -ve
4. (-ve) × (-ve) +ve

Description:

A multiplication of two positive integers yields a positive result. The result is negative when you multiply one positive integer by one negative integer, or vice versa. A positive integer is produced when two negative numbers are multiplied.

Multiplication Table

The multiplication table for integers 1 through 10 is provided below, both in terms of rows and columns. These tables make it simple and quick to find the product of two numbers between 1 and 10.
× 1 2 3 4 5 6 7 8 9 10
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100

Multiplication of Fractions

When two or more fractions are multiplied then the numerators and denominators are multiplied together, such that: (a/b) × (c/d) = (a×c)/(b×d)
  • Example 1: Multiply ¾ and 5/2.
(¾) × (5/2) = (3×5)/(4×2) = 15/8
  • Example 2: Multiply 4/7 and 21/2
(4/7) × (21/2) = 2 × 3 = 6

Multiplication of Decimals

Multiplying the integers and determining the product of decimals are the same process. Here, the decimal point (.) needs to be carefully considered after multiplication. Let's learn via illustration.
  • Example 1: Find the product of 1.2 and 3.
Sol: 1.2 × 3 = 3.6
  • Example 2: Multiply 4.2 and 1.5
Sol: Let us multiply 4.2 and 1.5 by removing the decimals here and considering them as whole numbers. Hence, 42 × 15 = 630 Now, if we put the decimal back, then the product of the two decimal numbers will have decimal up to two positions from right to left, such that; 4.2 × 1.5 = 6.30

Multiplication Tricks

Single-digit number multiplication is a simple task. However, multiplying a number with more than one digit can be challenging and time-consuming. While locating the product, students can keep in mind these few multiplication tips. Numbers can be multiplied in any sequence. (3 x 4 = 4 x 3) Simply place the number of zeros equal to the multiple of 10 next to the multiplier when multiplying a number by multiples of 10. For example, 6 x 100 = 600. For speedy computation, multiply the little numbers first, and then multiply to the third number, if there are three numbers that need to be multiplied. Write any two- or three-digit values in extended form before multiplying them if they are part of the multiplication. For example, 45 x 9 equals (40 + 5) x 9 or 40 x 9 plus 5 x 9 or 360 + 45 = 405) Observe the sign guidelines provided in the section above.
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Word Problems on Multiplication

Q.1: If Shikha has 10 baskets and each basket has 5 apples. Then find the total number of apples Shikha has.

Sol: Number of baskets Shikha has = 10

Number of apples each basket has = 5 Total number of apples = (Number of baskets) × (Number of apples in each basket) = 10 × 5 = 50 Therefore, Shikha has 50 apples.

Q.2: Sam brings 3 boxes of chocolates from the market. If each box contains 50 chocolates, then how many total chocolates did he has?

Solution: Number of boxes = 3

Number of chocolates in each box = 50 Total number of chocolates = 3 x 50 = 150 Hence, Sam has 150 chocolates.

Q.3: Find the product of 13.99 × 10000.

Sol: 13.99 × 10000

= 139900.00 = 139900  

Multiplication FAQs

What is the multiplication trick?

One of the best and easy multiplication tricks for large numbers is to find the tens of one of the numbers, and multiply with that quickly. Adding the remaining leftovers will be easier to calculate fully. E.g., 22 X 83 can be rewritten as (20 X 83) + (2 X 83) which gives us 1660 + 166 = 1826.

What are the 3 types of multiplication?

There are three properties of multiplication: commutative, associative, and distributive.

What is the law of multiplication?

As per this law, the result of the multiplication of two numbers stays the same, even if the positions of the numbers are interchanged. Hence, A.B = B.A. Examples: 1×2 = 2×1 = 2. 4×5 = 5×4 = 20.

What is the Bodmas rule?

BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. BODMAS stands for B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction.

What is the golden rule of multiplication?

The mathematical golden rule states that, for any fraction, both numerator and denominator may be multiplied by the same number without changing the fraction's value.
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