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.
Table of contents: |
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
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;
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
Multiplication Related Articles
- Multiplication Tricks
- Multiplication Chart
- Multiplication And Division Of Integers
- Multiplication of Algebraic Expressions
- Multiplying Polynomials
- Binary Multiplication
- Factors And Multiples
- Matrix Multiplication
- Properties of Multiplication of Integers
Word Problems on Multiplication
Q. 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.
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:
- Find: 45 × 10
- Multiply 1.2 × 90
- Find 8 × 11
- Find the product of 10 and 78
- Find the product of 900 and 70
- 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 the properties of multiplication?
The properties of multiplication are closure property, commutative property, associative property, distributive property, identity property.