 # Multiplication

In mathematics, multiplication (denoted by ‘×’) is a method of finding the product of two or more values. In arithmetic, multiplication of two numbers represents the repeated addition of one number with respect to another. If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.

For example, 3 × 4 means 3 times of 4, such as:

4 + 4 + 4 = 12

In the above example, we have learned to multiply whole numbers. Similarly, we can also multiply fractions and find the product of decimals.

Multiplication is one of the major fundamental topics in Maths, apart from addition, subtraction and division. Students learn the four basic arithmetic operations in their primary classes itself. Here we will learn to solve multiplication problems in an easy and quick way.

## What is Multiplication?

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.

See few more examples here:

• 3 by 3 = 3 + 3 + 3 = 9
• 4 by 4 = 4 + 4 + 4 + 4= 16
• 5 by 5 = 5 + 5 + 5 + 5 + 5 = 25

Multiplication of single digit numbers is an easy task. But multiplying two or more digit numbers, can be a difficult and time consuming task. Find multiplication tricks here to solve multiplication of such big digit numbers in a quick way.

## Symbol

The process 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

## Properties

The properties of multiplication are:

• Commutative property
• Associative property
• Distributive property
• Identity property
• Zero property

### Commutative Property

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

A × B = B × A

• 2 × 3 = 3 × 2 = 6

### Associative property

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

A × (B × C) = (A × B) × C

• 2 × (3 × 4) = (2 × 3) × 4 = 24

### Distributive property

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

A × (B + C) = (A × B) + (A × C)

• 4 × (2 + 3) = 4 × 2 + 4 × 3 → 20

### Identity Property

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

A × 1 = A

• 12 × 1 = 12
• -3 × 1 = -3

### Zero Property

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

A × 0 = 0, where A is any integer.

• 9 × 0 = 0

## Rules of Multiplication

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 and Decimals

Till now we have learned how to multiply two or more integers, whole numbers or natural numbers. Here we will see how to multiply fractions and decimals.

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 upto two positions from right to left, such that;

4.2 × 1.5 = 6.30

## Problems and Solutions

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

Sol: Number of baskets Sita 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, Sita has 50 apples.

Ques.2: Find the product of 13.99 × 10000.

Sol: 13.99 × 10000

= 139900.00

= 139900

### Practice Questions

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

### 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

### 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.

### 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

### 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

### What are properties of multiplication?

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

Quiz on Multiplication