A Short Note On Multiplication

The basic arithmetic operations, addition, subtraction, multiplication and division play an important part in the field of Mathematics and other related fields of Science since most operations and functions are based on them. Addition and subtraction are represented by + and – signs respectively in both Mathematics and Computer Science. However, in case of multiplication, we use the symbol in Mathematics, whereas the * symbol is used in Computer Science. Similarly, division in Mathematics is represented by the symbol whereas division in Computer Science is represented with the / symbol. Let us know more about the multiplication operation and how it is used. 

What is Multiplication?

In the field of Mathematics, multiplication of two numbers means repeated addition of as many copies of one number as the other one. For two numbers 3 and 7, their multiplication can be defined as 

37=3+3+3+3+3+3+3 = 21

The two numbers that are to be multiplied are known as multiplicand and multiplier respectively and the final output of multiplication is known as the product of the two numbers. The initial two numbers can also be called the factors of the final product. The identity of multiplicand and multiplier can be changed keeping the the product same. Let us assume an example where the multiplicand is 5 and the multiplier is 7. So, consider these cases.

CASE 1: 57=35

CASE 2: 75=35

In Case 1, 5 is the multiplicand and 7 is the multiplier, whereas in Case 2, 7 is the multiplicand while 5 is the multiplier. You will notice that the final product in both cases is same.

How to Write a Multiply Sign?

The Multiply sign is written differently depending on where it is used. If we have to multiply two numbers in Mathematics, we write the multiply sign as . For example, 

3.4=12

However, in case we have to multiply two or more numbers in the field of computer science, we use the * symbol. Every programming language recognizes the  * symbol as the symbol of multiplication as is not present in the keyboard. If you were to depict the multiplication of two numbers in any programming language, it would be written as shown here. 

3*4=12

In some cases, the symbol may also be used to represent multiplication. It is mainly used in Physics to represent the scalar product of two vector quantities. The product in this case has only magnitude and no direction. Sometimes, it might also be used in higher Mathematics to represent the product of two numbers. It must not be confused with the decimal.

At times, if variables are used, we can write them without any symbol at all, but it means multiplication. For example, for variables a and b, 

ab = ab

How to Multiply Two Numbers?

Multiplication can be a very easy process if you follow the correct steps. Let us see how we can multiply 2 numbers, say 24 and 77 in a step-by-step manner. 

• Write the numbers one below the other. It does not matter which number is written above and which one is written below. However, the smaller number is written below to make the calculation easier.

    77

X 24

———–

• Multiply each digit of the number on top with the right-most digit of the number below and write it. If the product of the individual digits is more than 9, we carry it over for addition.

    77

X 24

————-

308

• Leave a place in the ones place and perform the same action as step 2 with the next digit of the number below. Repeat this step until no numbers are left.

    77

X 24

—————

308

154

• Finally, add the lines of numbers to get the final product.

    77

X 24

—————

  308

+154

—————–

 1848

So, the final product of 77 and 24 is 1848.

This is how we multiply two numbers. In case there are more than 2 numbers, we iterate the multiplication process such that the product of the first two numbers is multiplied with the third number and the product is further multiplied with the fourth number and so on.

Conclusion

Now that you know about the multiplication operation, you should be able to perform the operation quiet easily. Often when time is of the essence, like during exams, people tend to follow several tricks and shortcut methods to multiply two numbers. There are various methods other than the traditional one to multiply two numbers, and you can learn about them from various online resources. However, learning is not the end as you would not be able to perform properly unless you practice by yourself. It is important to practice the numbers by yourself so that you can improve your speed and efficiency while performing the multiplication operation.