How To Multiply And Divide Decimal Fractions With Rules Formulas And Solved Examples
The concept of multiplication and division of decimal fractions plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding how to multiply and divide decimal fractions—also called decimal numbers—lets you solve questions related to money, measurements, and data quickly and accurately. Vedantu covers this key topic for grades 5, 6, and beyond with clear steps and practical examples.
What Is Multiplication and Division of Decimal Fractions?
Multiplication and division of decimal fractions means performing multiplication and division when your numbers include a decimal point (examples: 6.4, 0.12, or 0.5). You’ll find this concept applied in areas such as money calculations, length/weight measurement, and daily data interpretation. Mastering decimal fractions helps you to correctly solve word problems and quick calculations on exams.
Key Formula for Multiplication and Division of Decimal Fractions
Here are the standard formulas:
Multiplying Decimals: Multiply as with whole numbers, then count the total number of decimal places in both numbers. Place the decimal point in the answer accordingly.
Dividing Decimals: If the divisor is a decimal, move the decimal point in both divisor and dividend to the right until the divisor becomes a whole number. Then divide as usual, placing the decimal in the answer.
Step-by-Step Illustration
Multiplying Decimal Fractions Example
Let’s multiply 1.4 × 0.6:
1. First, ignore the decimals and multiply 14 × 6 = 842. Count decimal places: 1 digit in 1.4 and 1 digit in 0.6 (total 2 digits)
3. Place decimal point two places from the right: 0.84
4. Final Answer: 1.4 × 0.6 = 0.84
Dividing Decimal Fractions Example
Let’s divide 6.48 ÷ 0.12:
1. Move decimal two places right (divisor becomes 12), do the same to dividend (648).2. Divide 648 by 12 = 54
3. Place decimal according to steps; answer is 54
So, 6.48 ÷ 0.12 = 54
Key Rules and Properties
- Multiply or divide ignoring decimal points, then adjust the decimal in your answer.
- When multiplying decimals, add the number of decimal places in both numbers for the result.
- When dividing by a decimal, make the divisor a whole number by shifting the decimal, and do the same for the dividend.
- Multiplying/dividing by 10, 100, or 1000 shifts the decimal right (for multiplication) or left (for division) by as many zeros.
Speed Trick or Vedic Shortcut
Here’s a quick shortcut when multiplying decimal fractions by 10, 100, or 1000: simply move the decimal point to the right by as many zeros as there are in the multiplier.
Example Trick: Multiply 5.86 by 100: Move decimal 2 places right to get 586.
This trick helps in exams where time is limited—useful for MCQs and board questions. Vedantu often shares such strategies in live classes and worksheets.
Multiplying/Dividing Decimal Fractions by 10, 100, 1000
| Operation | Decimal Shift | Example |
|---|---|---|
| Multiply by 10 | Right by 1 | 0.74 × 10 = 7.4 |
| Multiply by 100 | Right by 2 | 3.15 × 100 = 315 |
| Divide by 10 | Left by 1 | 74.8 ÷ 10 = 7.48 |
| Divide by 100 | Left by 2 | 315 ÷ 100 = 3.15 |
Decimal Fractions in Real-Life Word Problems
| Problem | Step-wise Solution |
|---|---|
| A pen costs ₹15.75. What is the cost of 3 pens? |
1. Multiply 15.75 × 3 = 47.25 2. Final Answer: ₹47.25 |
| A rope is 8.4 m long. It is divided equally among 7 friends. What length does each get? |
1. Divide 8.4 ÷ 7 = 1.2 2. Final Answer: 1.2 m each |
Frequent Errors and Misunderstandings
- Forgetting to count total decimal places when multiplying decimals.
- Placing the decimal at the wrong place when dividing by a decimal.
- Not shifting the decimal in both dividend and divisor during division.
- Careless copying of numbers in multi-step problems.
Try These Yourself
- Multiply 2.35 × 0.4
- Divide 32.4 ÷ 0.6
- What is 0.25 × 1000?
- Divide 15.8 by 10
Relation to Other Concepts
The idea of multiplication and division of decimal fractions connects closely with topics such as Fraction and Decimals and Decimal Numbers and Standard Form. Mastering decimal operations will also help you understand Fraction to Percent and comparison of decimals and fractions in more complex problems.
Classroom Tip
A quick way to remember decimal placement: multiply as whole numbers, then count all decimal digits from both numbers and put decimal point in the answer that many places from the right. For division, always make the divisor a whole number first. Vedantu teachers use number lines and place value charts to make this visual in live classes.
We explored multiplication and division of decimal fractions—from definition, formula, examples, common mistakes, and links to related topics. Keep practicing with Vedantu lessons and worksheets to get faster, more accurate, and exam-ready every time you work with decimal problems.
Explore More: Decimal Worksheets, Multiplication and Division of Decimals Worksheet, Decimal Expansion of Rational Numbers
FAQs on Multiplication And Division Of Decimal Fractions Explained Clearly
1. What is multiplication of decimal fractions?
Multiplication of decimal fractions means multiplying numbers with decimal points and placing the decimal correctly in the final product.
- Ignore the decimal points and multiply the numbers 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, multiply as whole numbers and then adjust the decimal point based on total decimal places.
- Step 1: Remove decimal points and multiply normally.
- Step 2: Count total decimal places in both numbers.
- Step 3: Insert the decimal point in the product accordingly.
3. What is division of decimal fractions?
Division of decimal fractions means dividing numbers with decimals by converting the divisor into a whole number.
- 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 a decimal by a decimal?
To divide a decimal by a decimal, shift the decimal point in both numbers until the divisor becomes a whole number.
- Identify how many decimal places are in the divisor.
- Multiply both dividend and divisor by 10, 100, etc., to remove the decimal.
- Perform the division normally.
5. What is the rule for placing the decimal point in multiplication?
The rule for placing the decimal point in decimal multiplication is to count the total number of decimal places in both factors.
- Add the decimal places in both numbers.
- Place the decimal in the product so it has that many decimal places.
6. What happens when you multiply decimals less than 1?
When you multiply two decimals less than 1, the product is usually smaller than both numbers.
- This happens because each number represents a fraction of 1.
- Multiplying fractions results in a smaller value.
7. Can you give an example of multiplying and dividing decimal fractions?
Yes, multiplying and dividing decimal fractions follows clear place value rules.
- Multiplication example: 1.2 × 0.3 → 12 × 3 = 36 → Two decimal places → 0.36.
- Division example: 3.6 ÷ 0.9 → Multiply both by 10 → 36 ÷ 9 = 4.
8. What is the difference between multiplying and dividing decimals?
The difference is that multiplication adds total decimal places, while division removes decimals from the divisor first.
- In multiplication, count total decimal places in both numbers.
- In division, make the divisor a whole number before dividing.
9. How do you divide a decimal by a whole number?
To divide a decimal by a whole number, divide normally and place the decimal point directly above in the quotient.
- Set up long division.
- Divide as usual.
- Bring the decimal point straight up into the answer.
10. What are common mistakes in multiplication and division of decimals?
Common mistakes in multiplication and division of decimals usually involve incorrect placement of the decimal point.
- Forgetting to count total decimal places in multiplication.
- Not making the divisor a whole number in division.
- Misplacing the decimal point in the final answer.
