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Multiplication is an arithmetic operation. It is one of the four basic mathematical operations, the others being, addition, subtraction, and division. It is denoted by the cross symbol (×), the dot symbol (.) and for computers, it is indicated by the asterisk symbol (*).

Repeated addition of a number is called Multiplication. Let’s say we write the number 12 five times. The sum of all the 12s is

12 + 12 + 12 + 12 + 12

Since 12 is added 5 times, the sum is 5 times 12.

5 × 12 = 60



If we have two integers A and B, their Multiplication can be defined as follows:

A × B = B × A

A × (-B) = (-A) × B = -(A × B)

(-A) × (-B) = A × B

Rational Numbers

If we have two fractions A/B and C/D, the Multiplication of these two fractions can be defined as

(A/B) × (C/D) = (A×C)/(B×D)

Complex Numbers

If we have 2 complex numbers z1 and z2, which are given by z1 = x1 + y1i and 

z2 = x2 + y2i, then their multiplication is given by the following statement.

         z1×z2 = (x1×x2 - y1×y2) + (x1×y2 + x2×y1)i


Commutative Property

If you change the order of the numbers that are multiplied, their product remains the same. 

5 × 3 = 3 × 5 = 15

Associative Property

If you change the grouping order or regroup the numbers getting multiplied, their product remains the same. 

5 × (3 × 2) = (5 × 3) × 2 = 30

Identity Property

When a number is multiplied by 1, the product will be the number itself. 

5 × 1 = 5

Hence 1 is called the Multiplicative Identity.

You cannot study advanced concepts in Mathematics without having a strong foundation on the four basic arithmetic operations and their properties. Multiplication is usually introduced to students at a very young age. It is essential to help the students visualise the process and the result of the multiplication.

In this article, we will see a few tips to make the multiplication learning process easier irrespective of the student's age.


A young child’s mind changes its focus from one thing to another frequently. Thus, to get them to focus on an academic topic is very difficult. One of the best ways to introduce a new concept is by conveying it in the form of a story. But this method is not just restricted to a young child. Stories always garner interest, regardless of what is being told and the age of the audience. Starting with a short and informative history lesson could prove to be very useful.

The oldest known tables can be traced back to 350 BC during the era of China’s Warring States period. These tables used a base-ten and were classified as the Chinese Decimal Multiplication Tables. The most exciting part about these tables is that they were written on 21 bamboo strips. When assembled correctly, they represented a decimal multiplication table that could be used to multiply any whole number or half-integer up to 99.5. 

Pythagoras, a Greek Scholar, is sometimes credited for devising the Multiplication table. Another Greco - Roman author Nichomachus (60-120 AD) included a multiplication table in his book called Introduction to Arithmetic. Another fun fact associated with Multiplication Tables is that the oldest surviving Greek Table is on a wax tablet. It is dated to 1 AD and is currently displayed at The British Museum.

As times progressed further, there were more methods devised for the creation of different multiplication tables, which gave rise to the question should the tables be memorized or mastered? The answer to this question is that we must always understand the concept behind anything, and there will be no need to memorise them blindly.


To understand any subject, using physical modes of learning wherein you get to interact a lot is the best way to grasp it. For a student who is just starting her education, working with an Abacus will help in learning how to count.

Abacus was a device that was used before the calculator came into existence. It was used to make mathematical calculations easier before the advent of technology. It is a device that has wires strung with beads. When you move the beads, you can perform simple calculations such as addition, subtraction, and of course, Multiplication.

This method targets a student’s counting and calculating ability while helping them to visualize what is going on. It is a simple way to understand small calculations and condition them for more complex sums. Thus, for young minds who are just starting, this helps to not only clarify their multiplication concepts but also build up their curiosity and cognitive abilities.


There are a variety of multiplication games available online and in-person for making the learning process fun. A student can go for a physical game wherein they get to use blocks, spheres, graphs, charts, and other objects to learn Multiplication.

While a student is looking for a good online resource, it is also important to ensure that it is a good teaching site with legitimate content. Cuemath Live Online Classes provides a wide variety of resources that help in explaining multiplication concepts rather than just memorising multiplication tables. They also provide a Math box which can be used to play physical games and can aid the understanding. They also ensure services from a host of certified tutors to guide you through the learning process.

Cuemath focuses on teaching students in a fun way while clearing all their concepts. Good grades follow as a result. With worksheets, math gyms, and apps, you have a visual and interactive way of understanding Multiplication.

Apart from this, students can also resort to watching informative videos and movies on the topic of Multiplication to enhance their skills. 


Learning is best when it is done together. You can bring in the help of your friends and come up with ways to quiz each other on the different aspects of the topic. 

A guideline that could be used is as follows:

  • Give each individual a topic to prepare on, such as the multiplication table of 6, distributive property, integer multiplication, etc. 
  • Take a day to research the topic.
  • Each individual can come up with questions related to the topic.
  • Choose one person as the referee to whom all the questions will be given, so that he can keep track of whether they are being answered correctly.  
  • Meet each other the next day or have an online session wherein, you have a rapid-fire round. For example, one participant could ask, “Is the product of 5 and 9 equal to 45?” The individual who answers the fastest can pose the next question, and so on. 
  • In the end, the person with the most number of accurate answers wins the game. 

You can have a good time with your friends and develop your academic skills in this subject as well. At the same time, it helps them to develop precision and speed.


To explore more about any subject, the internet always comes in handy. Try to learn about some real-life advantages of Multiplication.

The areas are endless, but some of them are listed as follows:

  • Daily life: You use Multiplication to tally receipts while buying things from a shop. 
  • Computer Science: Multiplication is used as a key to solving complex problems in fields such as Data Analytics. 
  • Architecture: Developing any structure requires the computation of a lot of Geometrical problems. One of the tools used for solving these questions is Multiplication.

Let your imagination run wild. As you gain a holistic understanding of the subject, learning gets simplified, and you can master this topic in no time.


Mathematics is an easy subject if learned the right way. Always believe in yourself and never shy away from taking the help of others to assist in the learning process. Multiplication is used in every possible domain. Be it Physics, Chemistry, Economics, and Business; all subjects require the application of multiplication concepts. In Mathematics itself, algebra, trigonometry statistics, etc. require the use of this. 

Hope you can make use of the methods listed in this article to sharpen your mathematical skills.

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