 # Multiplication

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life. The major application we can see in multiplication tables.

In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another. These numbers can be whole numbers, natural numbers, integers, fractions, etc. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.

Multiplication (denoted by ‘×’) in Maths, is a mathematical operation, apart from addition, subtraction and division. Students learn the four basic arithmetic operations in their primary classes themselves. Here we will learn to solve multiplication problems in an easy and quick way.

## What is Multiplication?

Multiplication is the process of calculating the product of two or more numbers. The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

In Maths, the basic explanation of multiplication is adding a number, with respect to another number, repeatedly.

For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers. ### 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

• Multiplicand is the total number of objects in each group
• Multiplier is the number of equal groups
• Product is the result of multiplication of multiplier and multiplicand

Example: If Multiplier = 5 and Multiplicand = 8, then the product is:

Product = 5 x 8 = 40

## Properties of Multiplication

The properties of multiplication are:

• Closure Property
• Commutative property
• Associative property
• Distributive property
• Identity property
• Zero property

### Closure Property of Multiplication

According to closure property of multiplication,

• Product of two integers is an integer (-4 x 3 = -12)
• Product of two fractions is either a fraction or a whole number (1/2 x 2 = 1)

### Commutative Property of Multiplication

The commutative property of multiplication states, if A and B are any two integers, then:

 A × B = B × A

For example: 2 × 3 = 3 × 2 = 6

### Associative Property of Multiplication

As per the associative property of multiplication, if A, B and C are any three integers, then:

 A × (B × C) = (A × B) × C

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

### Distributive Property of Multiplication

According to distributive property of multiplication, if A, B and C are any three integers, then:

 A × (B + C) = (A × B) + (A × C)

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

### Identity Property of Multiplication

As per the identity property of multiplication, if we multiply any value by 1, then its value remains unchanged, such that;

 A × 1 = A

For example:

• 12 × 1 = 12
• -3 × 1 = -3

### Zero Property of Multiplication

Zero property of multiplication states that any number multiplied by 0 is equal to zero only.

 A × 0 = 0

where A is any integer.

For example: 9 × 0 = 0

## Rules of Multiplication (How to Multiply)

There are various rules to multiply numbers. They are:

• Multiplication of two integers is an integer
• Any number multiplied by 0 is 0
• Any number multiplied by 1 is equal to the original number
• If an integer is multiplied by multiples of 10, then the same number of 0s are added at the end of the original number. Example: 4 × 1000 = 4000
• The order of the numbers, does not matter, when multiplied together. Example: 2 × 3 × 4 × 5 = 5 × 4 × 3 × 2 = 3 × 2 × 4 × 5 = 120

## Multiplication Signs

When two or more numbers are multiplied with different sign (+ and -), then the output result varies, as per the sign rules given below:

 S.No. Operation Result 1. (+ve) × (+ve) +ve 2. (+ve) × (-ve) -ve 3. (-ve) × (+ve) -ve 4. (-ve) × (-ve) +ve

Description:

• When two positive integers are multiplied, then the result is positive
• When one positive integer and one negative integer is multiplied or vice versa, then the result is negative
• When two negative integers are multiplied, then the result is a positive integer

Facts:

 Multiplication of even numbers of negative integers is always positive. (-) × (-) × (-) × (-) = (+)

## Multiplication Table

The table of multiplication for numbers 1 to 10, row-wise and column-wise is given below. With the help of these tables, we can easily find the product of two numbers from 1 to 10 in a quick manner.

 × 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

The method of finding the product of decimals is the same as multiplying the integers. We need to take care here of the position of decimal (.), after multiplication. Let us understand by example.

• 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

Multiplication of single-digit numbers is an easy task. But multiplying two or more digit numbers can be a difficult and time-consuming task. Here are few multiplication tricks that students can remember while finding the product.

• Multiplication of numbers can be done in any order. (3 x 4 = 4 x 3)
• While multiplying a number by multiples of 10, just put the number of zeros equal to multiples of 10, next to the multiplier (Eg. 6 x 100 = 600)
• If there are three numbers to be multiplied, multiply the small numbers first for quick calculation and then multiply to the third number
• If the multiplication includes two-digits or three-digit numbers, then write such numbers in expanded form and then multiply. (Eg: 45 x 9 = (40 + 5) x 9 = 40 x 9 + 5 x 9 = 360 + 45 = 405)
• Follow the sign rule given in the above section

## 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

## Practice Questions on Multiplication

Students can practice these multiplication sums here:

1. Find: 45 × 10
2. Multiply 1.2 × 90
3. Find 8 × 11
4. Find the product of 10 and 78
5. Find the product of 900 and 70
6. Find 0.5 × 100

## Frequently Asked Questions on Multiplication

Q1

### What is multiplication in Maths?

Multiplication is an arithmetic operation, where we find the product of two or more numbers. A times B means, B is repeatedly added A number of times. For example, 5 times of 4 = 4 + 4 + 4 + 4 + 4 = 20

Q2

### What is the symbol for multiplication?

The symbol used to represent multiplication is a cross sign (×). Also, sometimes we use a dot (.) to represent a product of numbers.

Q3

### What is basic multiplication?

Basic multiplication is simply explained for kids, where we find the product of two or more whole numbers by repeated addition.

2 × 3 = 3 + 3 + 3= 6

8 × 4 = 8 + 8 + 8 + 8 = 32

Q4

### What are the rules of multiplication?

The major rules for multiplication are:

Two integers when multiplied by each other results in an integer value

When a value is multiplied by 0, then result is zero

When a value is multiplied by 1, then the result is the same

Order of multiplication of two or more numbers does not matter

Q5

### What are the properties of multiplication?

The properties of multiplication are closure property, commutative property, associative property, distributive property, identity property.

Quiz on Multiplication