How to Multiply and Divide Decimals with Step by Step Examples and Rules
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.
So, in 2.56, the decimal is before two digits and in 3.5 it is before one digit.
Now we will multiply these two numbers without decimals.
256 × 35 = 8960
Now we will place the decimal here the decimal will be placed before three digits because 2+1=3.
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.
FAQs on Multiplication and Division of Decimals Explained
1. What is multiplication of decimals?
Multiplication of decimals is the process of multiplying numbers that contain decimal points and then placing the decimal correctly in the product. To multiply decimals:
- Ignore the decimal points and multiply as whole numbers.
- Count the total number of decimal places in both factors.
- Place the decimal point in the product so it has the same total number of decimal places.
2. How do you multiply decimals step by step?
To multiply decimals step by step, multiply as whole numbers first and then adjust the decimal places at the end. Follow these steps:
- Step 1: Remove the decimal points temporarily.
- Step 2: Multiply the numbers normally.
- Step 3: Count total decimal places in both numbers.
- Step 4: Place the decimal in the product accordingly.
- 32 × 15 = 480
- Total decimal places = 2
- Final answer = 4.80 or 4.8
3. What is division of decimals?
Division of decimals is the process of dividing numbers with decimal points by converting the divisor into a whole number first. To divide decimals:
- Move the decimal point in the divisor to make it a whole number.
- Move the decimal point in the dividend the same number of places.
- Divide as usual.
4. How do you divide decimals step by step?
To divide decimals, first make the divisor a whole number and then perform long division. Follow these steps:
- Step 1: Shift the decimal in the divisor to the right until it becomes whole.
- Step 2: Shift the decimal in the dividend the same number of places.
- Step 3: Divide normally.
- 72 ÷ 3 = 24
- Final answer = 24
5. Where do you put the decimal when multiplying decimals?
When multiplying decimals, place the decimal in the product based on the total number of decimal places in both factors. Count all decimal places in the numbers being multiplied, then insert the decimal in the answer so it matches that total. For example, in 1.2 × 0.35:
- 12 × 35 = 420
- Total decimal places = 3
- Answer = 0.420 or 0.42
6. How do you divide a decimal by a whole number?
To divide a decimal by a whole number, use long division and place the decimal point directly above its position in the dividend. Steps include:
- Divide as you would with whole numbers.
- Bring the decimal point straight up into the quotient.
7. How do you divide a whole number by a decimal?
To divide a whole number by a decimal, convert the divisor into a whole number by multiplying both numbers by the same power of 10. For example, 6 ÷ 0.2:
- Multiply both by 10 → 60 ÷ 2
- 60 ÷ 2 = 30
8. What are the common mistakes when multiplying and dividing decimals?
The most common mistakes in multiplication and division of decimals involve incorrect placement of the decimal point. Common errors include:
- Forgetting to count total decimal places when multiplying.
- Not moving the decimal in both numbers when dividing.
- Misplacing the decimal in the final quotient.
9. Can you give an example of multiplying and dividing decimals?
Yes, here is a clear example of both multiplying and dividing decimals:
- Multiplication: 0.6 × 0.3
6 × 3 = 18, total decimal places = 2 → 0.18 - Division: 3.6 ÷ 0.9
36 ÷ 9 = 4
10. Why does multiplying by a decimal less than 1 make the number smaller?
Multiplying by a decimal less than 1 makes a number smaller because you are taking a fraction of that number. A decimal like 0.5 means one-half, and 0.1 means one-tenth. For example:
- 8 × 0.5 = 4 (half of 8)
- 10 × 0.2 = 2 (two-tenths of 10)
