How to Solve Multiplication and Division Problems
Multiplying and Dividing Decimals
The multiplication division process is a simple step-by-step format used daily in all fields of Mathematics. The multiplication and division of decimals represent the fraction of a number and taking ten as the base of the decimal system of numbers. Point differentiates or decimal notations is an integer part extracted from the part of a fraction. Decimals can undergo addition, subtraction, multiplication, and division. Multiplication and division processes are easier to use with decimals as compared to addition and subtraction. These functions are normally used in computational platforms and tasks.
[Image will be Uploaded Soon]
Multiplication of Decimals
In normal multiplication, the numbers indicate also the addition of the number 20 twice. Similarly, this can be applied to decimals as well. Taking the example of 0.22 x 2 = 0.22 + 0.22, the multiplication of whole numbers and the multiplication of decimal numbers go hand-in-hand. Some simple steps used in the multiplication of decimals are provided below with an example.
Example of Multiplying Decimals
Let’s take the following example to understand how multiplication of decimals is done.
Let us consider the multiplication of two numbers, 4.42 and 2.
Step 1:
Count the total number of digits to the right of the decimal point in both numbers provided. We notice that in 4.42, to the right of the decimal point there are two digits and 4 is a whole number. Therefore, the total number of digits to the right of the decimal is 2.
Step 2:
Without considering the decimal point, multiply the numbers found.
442 x 2 = 884
Step 3:
After multiplication, add the decimal point two places to the right of the answer calculated.
Division of Decimals
The division of decimals is almost similar to the multiplication of decimals. When dividing a decimal directly, it can be confusing where to place the decimal point. But, with a little practice, one can use the same trick of multiplying decimals with ease. When dividing the decimal as a numerator with a whole number as a denominator of two given numbers, it is easier to obtain a result.
Examples of Dividing Decimals By Decimals
There are two methods used to divide a given set of decimal numbers. Let us consider the numbers given below, to understand the mechanism of dividing decimals.
Divide the following decimals 0.398 by 0.20.
Method 1:
Conversion of the decimals to whole numbers by multiplying each with a common factor to make the denominator one. It is important to note that the denominator has to always be a whole number for the division to take place.
0.398 ÷ 0.20 = \[\frac{0.398}{0.20}\] = \[\frac{0.398 \times 5}{0.20 \times 5}\] = \[\frac{1.99}{1}\] = 1.99
(Multiply both the numerator and denominator by 5)
Method 2:
Another method to use is to convert the decimal numbers into whole numbers. This can be done by multiplying with numbers having powers of 10 (10, 100, 1000, etc.).
Let us take the above example and count the number of digits right to the decimal point in the denominator.
The denominator is 0.20 and the number of digits right to the decimal point is 2.
0.398 ÷ 0.20 = \[\frac{0.398}{0.20}\]
The power of 10 is taken common depending on the number of digits present to the right of the decimal point.( 102 = 100)
Multiply both numerator and denominator by 100.
0.398 ÷ 0.20 = \[\frac{0.398 \times 100}{0.20 \times 100}\] = \[\frac{39.8}{20}\] = 1.99
Multiplying and Dividing Decimals Using 10, 100 and 1000
We have read that decimals are a form of expression fractions having their base as 10. Let us consider a couple of examples with fractions of decimals having the base of 100 and 1000. Some rules applied for multiplication and division of decimal numbers by 10, 100, and 1000 are as follows:
FAQs on Multiplication and Division Made Easy
1. What are multiplication and division in simple terms?
In simple terms, multiplication is a quick way of doing repeated addition. For example, instead of adding 4 + 4 + 4, you can multiply 4 × 3 to get the same answer, 12. Division is the process of splitting a number into equal parts or groups. For instance, dividing 12 by 3 (12 ÷ 3) means finding out how many items are in each of the 3 equal groups, which is 4.
2. How are multiplication and division related to each other?
Multiplication and division are inverse operations, which means they are opposites and undo each other. If you know a multiplication fact, you also know the related division facts. This is often called a 'fact family'. For example, if you know that 5 × 6 = 30, you can use the inverse relationship to know that 30 ÷ 6 = 5 and 30 ÷ 5 = 6.
3. What are some everyday examples where we use multiplication and division?
We use these operations frequently in daily life. Here are some examples:
- Multiplication Example: If you buy 5 notebooks and each costs ₹20, you multiply 5 × 20 to find the total cost of ₹100.
- Division Example: If a pizza has 8 slices and you want to share it equally among 4 friends, you divide 8 ÷ 4 to find out that each person gets 2 slices.
4. What is the main difference between long division and short division?
Both long division and short division are methods for dividing numbers, but they differ in how the steps are recorded. Long division is more detailed, as you write down every step, including the subtraction. It is best used for dividing large numbers. Short division is a quicker mental method where you perform the subtraction and carrying over steps in your head. It is ideal for dividing by a single-digit number.
5. What are the common symbols used for multiplication and division?
The common symbols used for these operations are:
- For Multiplication: The cross sign (×), the asterisk (*), or sometimes dots (·) or parentheses () are used to indicate multiplication.
- For Division: The division sign (÷), the slash (/), or a horizontal line (fraction bar) are used to indicate division.
6. Why is multiplication often described as 'repeated addition'?
Multiplication is described as repeated addition because it represents adding the same number to itself a certain number of times. For instance, the expression 7 × 4 is a shortcut for writing 7 + 7 + 7 + 7. Both calculations result in 28. This concept is the foundation of understanding what multiplication achieves: it efficiently calculates the total of many equal groups.
7. What does the commutative property mean for multiplication, and does it apply to division?
The commutative property states that you can change the order of numbers in an operation without changing the result. Multiplication is commutative because the order in which you multiply numbers does not matter (e.g., 8 × 2 = 16, and 2 × 8 = 16). However, division is not commutative. The order is very important. For example, 10 ÷ 2 = 5, but 2 ÷ 10 = 0.2, which are completely different answers.
