Stepwise Strategies for Solving Decimal Problems
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 Made Simple
1. What is the fundamental rule for multiplying two decimal numbers?
The fundamental rule is to first multiply the numbers as if they were whole numbers, ignoring the decimal points. Then, count the total number of digits after the decimal point in both of the original numbers. Finally, place the decimal point in the product so that it has the same total number of decimal places.
2. How do you divide a decimal number by another decimal number?
To divide a decimal by another decimal, the key is to make the divisor (the number you are dividing by) a whole number. You can do this by following these steps:
Move the decimal point in the divisor to the right until it becomes a whole number.
Move the decimal point in the dividend (the number being divided) the same number of places to the right.
Perform the division as you would with whole numbers, placing the decimal point in the quotient directly above its new position in the dividend.
3. What is the shortcut for multiplying or dividing decimals by powers of 10 (e.g., 10, 100, 1000)?
There's a simple shortcut based on moving the decimal point:
For multiplication: Move the decimal point to the right by the same number of places as there are zeros in the power of 10. For example, to multiply by 100, move the decimal two places to the right.
For division: Move the decimal point to the left by the same number of places as there are zeros in the power of 10. For example, to divide by 1000, move the decimal three places to the left.
4. Where are multiplication and division of decimals used in real-world examples?
Decimal operations are essential in many daily activities. For example:
Shopping: Calculating the total cost of multiple items priced with decimals (e.g., 2.5 kg of apples at ₹120.50 per kg).
Finance: Calculating interest, currency conversions, or splitting a bill among friends.
Measurement: Converting units, like inches to centimetres (multiplying by 2.54), or calculating the area of a room with decimal dimensions.
Cooking: Adjusting a recipe, for instance, using 0.5 times the ingredients to make half a batch.
5. Why does dividing by a decimal less than 1 make the answer larger than the original number?
This happens because division is essentially asking 'how many times does the divisor fit into the dividend?'. When you divide by a number smaller than 1 (like 0.5), you are asking how many 'halves' fit into a number. Since there are two halves in every one whole, the answer will be twice the original number. For example, 6 ÷ 0.5 is asking 'how many halves are in 6?', and the answer is 12.
6. What is a common mistake to avoid when placing the decimal point after multiplication?
A common mistake is incorrectly counting the total number of decimal places from the original numbers. Students sometimes only count the places from one number or miscalculate the total sum. Always remember to add the number of decimal places from both numbers being multiplied. For example, in 3.12 (2 decimal places) × 2.4 (1 decimal place), the answer must have 2 + 1 = 3 decimal places.
7. How can you estimate the result before performing decimal multiplication or division?
Estimation is a great way to check if your answer is reasonable. Before calculating, round the decimal numbers to the nearest whole numbers and perform the operation. For example, to calculate 8.9 × 3.2, you can estimate by rounding to 9 × 3 = 27. Your final answer should be close to 27. If your calculated answer is very different, you may have made a mistake in placing the decimal point.
8. Why does the 'move the decimal' trick work when multiplying by powers of 10?
This trick works because our number system is base-10. Multiplying a number by 10 makes each of its place values ten times larger. For example, in 5.23, the '5' is in the ones place and the '2' is in the tenths place. When you multiply by 10, the '5' moves to the tens place and the '2' moves to the ones place, resulting in 52.3. Moving the decimal point one place to the right is a visual shortcut for this shift in place value.
