Multiplication

Multiplication is one of the basic mathematical operations. The other mathematical operations are addition, subtraction, and division. In math, multiplication is finding the product of two or more numbers.

Multiplication is also known as repeated addition because here the number is repeated added to the number.

For instance, 4 × 4 = 16; that is, 4 + 4 + 4 + 4 = 16. Multiplicand, multiplier, and product are the part of multiplication.

When multiplying 15 × 2 = 30, here 15 is the multiplicand, 2 is the multiplier, and 30 is the product. 

The symbol used in multiplication are ×, *, or a dot (.). 
 

The history of multiplication can be traced back to ancient civilizations. Babylonians were the first to use multiplication tables, they used clay tablets. They used an ideogram: a-du as the symbol of multiplication.

Chinese tables were based on 10, and date back to 305BC.

Egyptians and Greeks developed the first formula multiplication algorithm. 

Around the 12th century, Indians used the lattice method, which involves grids to find the product. 

Fibonacci, Italian mathematician introduced the Hindu-Arabic numeral system to Europe, to make multiplication algorithm easier.

During 19th century multiplication algorithms were introduced in schoolings. 
 

When learning multiplication we should understand the basic properties of multiplication, such as associative, commutative, identity, and distributive property.

• Associative property: The grouping of numbers when multiplying doesn't affect the product.

Such as (2 × 3) 5 = 2 × (3 × 5) = 30

 

•  Commutative property: The order of the numbers when multiplying won’t change the result.

That is 5 × 7 × 6 = 6 × 7 × 5 = 210

 

• Identity property: The product of multiplying a number with 1 will always be the number itself.

That is 5 × 1 = 5; 456 × 1 = 456.

 

• Distributive property: The product of multiplying a number with any addends will be the same when we multiply the number with each addend separately and add it.

Such as 2 × (5 + 2) = 14; (2 × 5) + (2 × 2) = 10 + 4 = 14.
 

There are types of multiplication based on the digits of multiplicand and multiplier, the type of number we multiply. A few of the types of multiplication are: 

 

• Single-digit Multiplication
   
• Multi-digit Multiplication
   
• Multiplying Decimals
   
• Multiplying Fractions
   
• Multiplying Negative Numbers
   
• Multiplying Matrices
   
• Exponentiation
   

Single-digit multiplication is the multiplication of single-digit numbers.

That is 5 × 6 = 30.
 

The multiplication of two or more digit numbers is known as multi-digit multiplication.

For example, 63 × 35 = 2205. 
 

The multiplication of any two or more decimal numbers.

Such as 2.35 × 5.5 = 12.925
 

Multiplying fractions is the process of multiplying the factors.

That is, 2/3 × 5/3 = 10/9
 

The multiplication of negative numbers is -5 × -6 = 30. The sign of the numbers determines the sign of the result.

• The product of two positive numbers and two negative numbers is always positive.

• If one number is negative and the other is positive, then the product is negative. 
   

Multiplying the elements of matrix A with the elements of matrix B which are in the same position.
 

Exponential is the way of writing number as the power of another number. Here the multiplication adding the exponents when the bases are same. In exponential form, a number is written as 34 which is 3 × 3 × 3 × 3 = 81
 

Multiplication is one of the basic operations of math. Here a number is multiplied with other number to find the product. In this section, let's see why multiplication is important for students 

 

• It is one of the basic skills in math, so learning multiplication helps students to complex functions.
   
• It helps students to handle money, as they can easily calculate 
   
• To do complex functions in algebra, statistics, geometry, and so on.
   
• It helps to improve their cognitive skills
   

For making multiplication interesting and easy we use different methods. Such as

 

• Column Multiplication
   
• Grid Method
   
• Lattice Multiplication
   
• Long Multiplication
   
• Cross Multiplication
   

In this method, we write the numbers one above the other and multiply it.

Here, the numbers are multiplied digit by digit. Let’s see how to multiply any two numbers using column multiplication.
 

Multiplying 25 × 35, 
 

In the Grid method, the number is broken down into place values.

The number is arranged in grids based on the place values.

The numbers are multiplied in each grid and the values are added together.

Let's multiply 245 × 25 using Grid method

So, 245 × 25 = 6125
 

A grid or lattice is used to multiply the numbers. Lattice is drawn based on the number of digits.

Draw a diagonal line in each box. One of the numbers is written on the top and another on the right side.

We multiply the number by multiplying every digit that meets. The upper triangle in each grid is for the tens place and the lower for the ones place. Each diagonal in the grid is added.

The product of the number is the number from the top right one to the bottom right one.

Using the lattice method, let's find the product of 12 × 25,
 

Therefore, 12 × 25 = 300
 

The method is used when the number we multiply is large. In this method, the numbers are written in the column method.

In this method, we write the bigger number on the top and the multiplication sign on the left. The number written on the top is the multiplicand and the other is the multiplier.

The one digit in the bottom number is multiplied by the top number. The numbers and the product are divided using a line. Write a 0 in one place the next time. Then we multiply the tens digit in the bottom number.

We add the partial product to get the product.

Cross multiplication is mostly used to multiply the form of a fraction.

In this method, we first multiply the numerator of the first number and denominator of the second number.

That is a / b × c / d = ad = bc
 

Learning multiplication will help students to master many other skills. So let’s learn a few tips and tricks to master multiplication tables. 

• The product of multiplying even numbers will always be even, and the product of odd number is always odd. That is 256 × 68 = 17408, 255 × 55 = 14025.
   
• The table of 2 is adding the number to itself. That is 2 × 5 = 5 + 5 = 10.
   
• Table 4 is doubling the number twice. For example, 4 × 6 = 6 + 6 = 12 + 12 = 24.
   
• The table of 5 either ends in 0 or 5. The multiplies of 5 are 5, 10, 15, 20, 25, 30, … 
   
• The table of 10 always ends in 0, that is 5 × 10 = 50
   
• The product of multiplying any number by 9 is equal to the product of the number with 10 minus the number. That is 9 × 4 = 10 × 4 - 4 = 36. 

In this section let’s learn about the real-world application of multiplication. We use it in different fields.


Shopping: While shopping multiplication is used to calculate the cost, offers, and so on.


Cooking: In cooking multiplication is used to measure the ingredients according to the number of people. It is one of the basic applications of multiplication in real-life 


Construction: In construction, multiplication is used to calculate the area and volume of the rooms.