How Do You Multiply and Divide Decimal Fractions? Step-by-Step Methods & Common Mistakes Explained
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: Rules, Steps & Examples
1. What is multiplication and division of decimal fractions in Maths?
Multiplication and division of decimal fractions involve performing these operations on numbers containing a decimal point. It's crucial for solving real-world problems involving money, measurements, and data analysis. The process is similar to working with whole numbers, but requires careful attention to the placement of the decimal point in the final answer.
2. How do you multiply decimal fractions step by step?
To multiply decimal fractions:
- Ignore the decimal points initially.
- Multiply the numbers as if they were whole numbers.
- Count the total number of digits after the decimal points in both numbers.
- In the product, place the decimal point so that the number of digits after it matches the total count from step 3.
Example: 2.5 x 1.2 = 3.00 (2 digits after the decimal point).
3. How to divide decimal numbers by decimals?
Dividing decimals by decimals involves 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 same number of places to the right.
- Perform the division as you would with whole numbers.
- Place the decimal point in the quotient according to the position in the new dividend.
Example: 12.5 ÷ 2.5. Shift decimal in 2.5 one place right (25), and one place in 12.5 (125). 125 ÷ 25 = 5.
4. Why do we shift the decimal point when multiplying or dividing by 10, 100, 1000?
Shifting the decimal point is a shortcut based on the place value system. Multiplying by 10, 100, or 1000 moves the digits to the left (larger values), while dividing by these numbers moves the digits to the right (smaller values). This method efficiently handles the multiplication or division by powers of 10.
5. Can you multiply a fraction with a decimal, and how?
Yes. Convert either the fraction to a decimal or the decimal to a fraction. Then, perform the multiplication as explained above. Example: 1/2 x 0.75. Change 1/2 to 0.5. Then 0.5 x 0.75 = 0.375
6. What happens if you ignore leading or trailing zeros during decimal multiplication?
Ignoring leading zeros (before the first non-zero digit) usually doesn't affect the result, as they only indicate the place value. Ignoring trailing zeros (after the last non-zero digit) can lead to incorrect answers because they are significant digits. Always include significant zeros after the decimal point in your final answer for accuracy.
7. Are there any mental math tricks for quick estimation in decimal multiplication?
Yes. Round the decimals to the nearest whole number or simpler decimal values for estimations. For instance, you can estimate 3.14 x 2.71 as 3 x 3, which gives a close estimate of 9.
8. How can errors in decimal division affect scientific or financial calculations?
Errors in decimal division can lead to significant inaccuracies in scientific or financial calculations. In scientific work, even small errors can affect the accuracy of measurements, and in financial calculations, even small errors can affect large amounts of money leading to severe financial consequences.
9. How are decimal operations different on calculators and in manual methods?
Calculators automatically handle decimal placement. Manual methods need careful attention to decimal point placement during each step of multiplication and division, following the rules previously stated. Calculators offer speed and precision, whereas manual methods help develop a deeper understanding of the process and improve mathematical skills. Understanding both is valuable.
10. When is it necessary to round off answers in decimal operations, and why?
Rounding is necessary when dealing with an infinitely repeating decimal or when the level of precision required by the context is less than the number of digits in the answer. This avoids overly long answers and provides a value that is sufficiently accurate within the required context. Always check the instructions or requirements of a problem to see if rounding is necessary.
11. What are some common mistakes to avoid when multiplying or dividing decimals?
Common mistakes include misplacing the decimal point in the answer, not aligning decimal points correctly when adding or subtracting decimals, or forgetting to account for trailing zeros. Always double-check your work and utilize estimation to verify reasonableness.
