Multiplication and Division of Decimals

Multiplication and division are important concepts of algebra in mathematics. Multiplication and division operations are quite similar to each other. The division is the inverse operation of multiplication. In division, we divide the numbers into equal parts. In multiplication, we group up numbers together. In multiplication, the answers we get are known as the product and the numbers which we multiply are called factors. The multiplication is denoted by ‘×’. In division, the answer we get after dividing is called the quotient, the number which is being divided is called the dividend, and the number which divides it is called the divisor. The division is denoted by ‘÷’.

Example 1: 4×5= 20

Here 20 is the product, 4, and 5 are the factors.

Example 2: 10÷2= 5

Here 5 is the quotient, 10 is the dividend, and 2 is the divisor.


Decimals

The numbers with a decimal point are called decimals. They can also be represented in the form of a fraction.

For example, the number 3.556 is the decimal number because it has a decimal point in it.

As we add, subtract, multiply, divide the whole numbers similarly we can add, subtract, multiply, and divide the decimals also. Compare to addition and subtraction, multiplication and division are quite difficult.


Multiplication Of Decimals:

In mathematics when we multiply 5 by 2, we get 10 similarly when we add 5 two times that is 5 + 5 we get 10.

In the case of decimals numbers, we get the same value if we multiply 1.2 by 2, we get 2.4 similarly when we add 1.2 two times that is 1.2 + 1.2 we will get 2.4.

So, 1.2 × 2 = 1.2 + 1.2


Example- Find the multiplication of 2.56 and 3.5.

  1. So, in 2.56, the decimal is before two digits and in 3.5 it is before one digit.

  2. Now we will multiply these two numbers without decimals.

  3. 256 × 35 = 8960

  4. Now we will place the decimal here the decimal will be placed before three digits because 2+1=3.

  5. The final answer is 8.960.


Division Of Decimals

Dividing two numbers with decimals is quite difficult and confusing. You can follow these steps in the multiplication of decimal numbers.

There are two methods to do the division of decimals. We will discuss how to do decimal division.


Method 1:

In this method, if we have two decimal numbers, we multiply the numerator and denominator by such a number which on multiplication gives us the whole number in the denominator. So that the calculation becomes easier.

Suppose we have two numbers 30.5 and 0.5 we have to divide it.

So, we will multiply the numerator and denominator by 2 so that we get the whole number in the denominator.

(30.5×2)/ (0.5×2)

= 61/1

= 61


Method 2:

As in method 1, we converted the decimal number into a whole number similarly by using this method also, we can convert a decimal number into a whole number. 

In this method, we will multiply the numerator and denominator by 10, 100, 1000, etc. That is the powers of 10 

We will consider the above example that is 30.5 and 0.5 

Now in 30.5, we have one digit after the decimal point so we will multiply it by 10 and similarly the denominator also.

(30.5×10)/ (0.5×10)

= 305/5

= 61

So, by both the methods, we got the same answer after division.

If there are two numbers after the decimal, we multiply by 100. If three numbers then multiply by 1000 and so on.

FAQ (Frequently Asked Questions)

1. How to Perform Multiplication and Division Operations with Digits Containing Zeros i.e. 10, 100, 1000.

Answer: Now we all are familiar with that decimal numbers are nothing but the form of fractions. By multiplying the fraction or decimals by 10, 100, 1000 multiplication and division become easier and faster. The multiplication of decimals by the power of 10 is easier than by the whole numbers. There are some rules that we need to follow to divide and multiply by 10, 100 and 1000. 

If we multiply the decimal number by 10 then the point moves to the right by one. If we multiply by 100 then the point moves by two to the right, by multiplying by 1000 it moves by three.

Similarly, on dividing by 10, it moves by one to the left.

2. Write the Steps to Perform the Multiplication of Decimals.  

Answer: Steps To Do Multiplication Of Decimals

  1. Consider two numbers: suppose we take 6.55 and 2.

  2. Now we will count the number of digits after the decimal point.

  3. For 6.55 there are 2 digits after the decimal point and 2 is the whole number it does not have a decimal point.

  4. Now we will forget about the decimal point and we will do normal multiplication.

                655 × 2 = 1310

  1. Now we will place the decimal point in the answer which we got after the multiplication.

  2. So, the decimal point was before 2 digits. We will place it before 2 digits in the answer. 13.10

  3. So, this will be the final answer after the multiplication of decimal numbers.

So, by following these simple steps, we can easily do the multiplication. The only thing is first we need to multiply without decimal and then put the decimal in the final answer.