Step-by-Step Guide to Multiplying Whole Numbers with Examples
Learning how to multiply whole numbers is a basic yet essential part of mathematics. This concept is widely used in school exams, entrance tests, and practical life, like calculating costs, quantities, or grouping items. Mastering multiplication builds a strong foundation for higher arithmetic and algebra concepts that you will encounter at every stage of your education.
Understanding Multiplication of Whole Numbers
Multiplication is a mathematical operation that represents the repeated addition of the same number. When you multiply two whole numbers, you are simply adding one number to itself a certain number of times. For example, multiplying 4 × 3 means you are adding 4 three times: 4 + 4 + 4 = 12. Multiplication is fundamental in various topics such as factors, multiples, long multiplication, and number theory, and supports quick calculations in daily scenarios.
Multiplication Properties and Rules
Multiplication of whole numbers follows certain rules and properties:
- Commutative Property: a × b = b × a (Order doesn’t matter)
- Associative Property: (a × b) × c = a × (b × c)
- Identity Property: Any number multiplied by 1 remains unchanged (a × 1 = a)
- Zero Property: Any number multiplied by 0 gives 0 (a × 0 = 0)
These properties make calculations flexible and help in solving bigger problems with ease. For detailed explanation of these properties, you can visit the Properties of Whole Numbers page.
Step-by-Step: How to Multiply Whole Numbers
Here’s a simple way to multiply any two whole numbers, whether single or multi-digit:
- Write the numbers one below the other, aligning the digits to the right.
- Start by multiplying the unit digit of the bottom number with each digit of the top number, moving from right to left.
- If the result is 10 or more, write the unit digit and carry over the tens to the next multiplication.
- If there is more than one digit in the bottom number, multiply the next digit and remember to add a zero for the next line (shift left).
- Add all the results together for the final answer.
For more details, check out our guide on Long Multiplication.
Example: Multiplying Whole Numbers
Let’s multiply 23 × 7:
- 3 × 7 = 21. Write 1, carry over 2.
- 2 × 7 = 14. Add carried 2: 14 + 2 = 16.
- Write 6 next to 1. Answer: 161.
Or for a two-digit by two-digit example: Multiply 14 × 12.
- Multiply 14 × 2 (ones place): 28
- Multiply 14 × 1 (tens place, shift one place left): 14 × 1 = 14, so write 140
- Add results: 28 + 140 = 168
Multiplication Charts and Visual Models
Visual aids like multiplication charts and array/area models make multiplication easier to grasp for many students. For example, a multiplication table from 1–12 helps with quick reference, while an array model (rows and columns of dots) helps you see how multiplication builds on repeated addition. Explore Multiplication Tables for easy memorization.
Special Cases: Multiplying by Zero, One, and Large Numbers
- Any number × 0 = 0
- Any number × 1 = the number itself
- For large numbers, use long multiplication:
Example: 456 × 23
- 456 × 3 = 1368
- 456 × 20 = 9120 (write a zero at the end)
- Add: 1368 + 9120 = 10488
Multiplying Whole Numbers with Decimals and Fractions
| Type | Example | Step | Answer |
|---|---|---|---|
| Decimal | 5 × 0.4 | Multiply as whole numbers, then place decimal (5 × 4 = 20, move decimal left one place) | 2.0 |
| Fraction | 4 × 3/5 | Multiply numerator: 4 × 3 = 12, result is 12/5 | 12/5 or 2.4 |
For more, read Multiplying Fractions and Multiplication with Decimals.
Worked Examples
- 3 × 4 = 12
- 28 × 6 = 168
- 355 × 45:
- 355 × 5 = 1775
- 355 × 40 = 14200
- Sum: 1775 + 14200 = 15975
Practice Problems
- 7 × 8 = ?
- 36 × 12 = ?
- 146 × 7 = ?
- 99 × 100 = ?
- 57 × 0 = ?
- 5 × 1.2 = ?
- 6 × 2/3 = ?
- 234 × 11 = ?
- 50 × 25 = ?
- 78 × 9 = ?
Need more questions? Download a worksheet or practice online at the Vedantu Practice Portal.
Common Mistakes to Avoid
- Adding instead of multiplying by mistake.
- Misaligning digits in multi-digit multiplication, leading to wrong placement values.
- Forgetting to add zeros when shifting lines in long multiplication.
- Not carrying over correctly when sums exceed 9.
- Multiplying by zero or one incorrectly.
Real-World Applications
- Calculating the total cost when buying multiple items.
- Finding area (length × width) of rectangles in geometry and real life.
- Grouping students, distributing items, or forming teams.
- Scaling recipes in cooking or chemistry.
- Estimating large values in business or technology.
Multiplication Table Reference (1 × 1 to 12 × 12)
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
At Vedantu, we make mastering multiplication simple by providing visuals, examples, and practice that help students build math confidence for all exams.
If you want to learn about related topics, explore Whole Numbers, Factors and Multiples, or refine your skills with more complex topics like Multiplying Fractions.
In this topic, we defined multiplication of whole numbers, practiced step-by-step methods, explored real-world applications, and reviewed key tables and tips to avoid mistakes. These skills are crucial for building a strong foundation in mathematics, helping you in school and beyond!
FAQs on How to Multiply Whole Numbers
1. How to multiply whole numbers step by step?
Multiplying whole numbers involves a series of steps. First, align the numbers vertically, ensuring the rightmost digits are aligned. Then, multiply each digit in the top number by each digit in the bottom number, carrying over any tens digit to the next column. Finally, add the partial products to get the final answer. Example: 23 × 7 = 161.
2. How to multiply numbers step by step?
The process of multiplying whole numbers involves sequential steps. Start by writing the numbers vertically, aligning the units digits. Then, multiply the top number's digits individually by each digit in the bottom number, carrying over any tens or hundreds. Finally, add the partial products to obtain the total product. For instance, multiplying 123 by 4 would require you to multiply 4 by 3, then 4 by 2, and then 4 by 1, adding the results according to place value.
3. What is a whole number example?
Whole numbers are non-negative numbers without any fractional or decimal parts. Examples include 0, 1, 2, 3, 10, 100, and so on. They represent complete units and are fundamental in arithmetic operations like addition, subtraction, and multiplication.
4. How to cross multiply whole numbers?
Cross-multiplication isn't directly applicable to multiplying two whole numbers. It's a technique primarily used to solve equations with fractions or proportions. To multiply whole numbers, use standard multiplication methods: align the numbers vertically, multiply each digit, and add the resulting partial products.
5. Multiplying whole numbers examples
Here are some examples of multiplying whole numbers: 5 × 3 = 15; 12 × 6 = 72; 25 × 15 = 375. In each case, the process involves repeated addition or using the standard multiplication algorithm. These examples demonstrate the fundamental concept of multiplying whole numbers, representing repeated addition.
6. Multiplying whole numbers fractions
To multiply a whole number by a fraction, multiply the whole number by the numerator (top number) of the fraction and keep the denominator (bottom number) the same. Then, simplify if needed. For example, 3 x (1/2) = (3 x 1)/2 = 3/2 = 1 1/2 or 1.5.
7. Steps in multiplying whole numbers
Multiplying whole numbers involves these steps: 1. Write the numbers vertically, aligning the units digits. 2. Multiply the top number's digits by each digit in the bottom number, carrying over any tens or hundreds. 3. Add the partial products according to place value. 4. Check your answer. For example, 24 x 5 = 120
8. What happens when multiplying by zero or one?
Multiplying any whole number by zero always results in zero. Multiplying any whole number by one results in the same whole number. These are fundamental properties of multiplication.
9. How do I multiply whole numbers by decimals/fractions?
To multiply a whole number by a decimal, perform standard multiplication, then count the total number of decimal places in the decimal and put the decimal point in the result that many places from the right. To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator the same; simplify if necessary.
10. Why do I get wrong answers?
Errors in multiplication often stem from incorrect carrying, misalignment of digits, or forgetting the zero placeholder when multiplying by tens, hundreds, etc. Carefully review your work step by step, focusing on proper place value. Practice problems of increasing difficulty.
11. How to multiply whole numbers and fractions?
To multiply a whole number by a fraction, first express the whole number as a fraction (e.g., 3 = 3/1). Then, multiply the numerators together and the denominators together. Simplify the resulting fraction if possible. For example, 3 x (2/5) = (3/1) x (2/5) = 6/5 = 1 1/5.
12. Multiply whole numbers by decimals
Multiply whole numbers by decimals as you would multiply whole numbers. Then, count the total number of digits to the right of the decimal point in the original problem. In the result, add a decimal point so that there are this many digits to the right of the decimal point.
13. Multiply whole numbers times fractions
To multiply a whole number by a fraction, multiply the whole number by the numerator of the fraction and place it over the denominator of the fraction. Then simplify the resulting fraction if possible. For example, 4 x (2/3) = 8/3 = 2 2/3. You can also convert the fraction to a decimal and then multiply.
14. Multiply whole numbers worksheet
Many online resources and textbooks provide worksheets with practice problems to enhance multiplication skills. These worksheets often cover various levels of difficulty, from basic single-digit multiplication to more complex multi-digit problems. This is a great way to practice and master the concepts.
15. Multiply whole numbers by 10, 100, and 1000
Multiplying by powers of 10 (10, 100, 1000, etc.) is straightforward. Simply add the same number of zeros to the right of the whole number as there are zeros in the power of 10. For example: 25 x 10 = 250; 25 x 100 = 2500; 25 x 1000 = 25000.
