Quick Multiplication Tricks: Learn to Multiply in Minutes
Mastering Quick Multiplication is a fundamental skill in mathematics that forms the basis for many advanced calculations. While traditional methods of multiplication involve memorizing multiplication tables and performing long multiplication, there are several quick multiplication tricks that can significantly expedite the process. In this article, we will explore various techniques and strategies to learn to multiply in minutes.
1. Quick Multiplication by 10, 100, 1000, etc.:
Multiplying a number by 10, 100, 1000, and so on, involves simply adding zeros to the end of the number. For example:
- 25 x 10 = 250
- 72 x 100 = 7200
- 543 x 1000 = 543000
2. Quick Multiplication by 11:
To multiply a two-digit number by 11, you can add the digits together and place the result between the original digits. For example:
- 34 x 11 = 3 (3+4) 4 = 374
- 67 x 11 = 6 (6+7) 7 = 737
For three-digit numbers, the process is similar but requires carrying over any digits that exceed 9. For example:
- 432 x 11 = 4 (4+3) (3+2) 2 = 4752
3.Quick Multiplication by 9:
To multiply a number by 9, you can use the trick of subtracting the number by 1 and placing the result next to the original number, so the tens place decreases by 1 and the units place increases by 1. For example:
- 36 x 9 = 3 (3-1) 6 = 324
- 82 x 9 = 7 (8-1) 2 = 738
4. Quick Multiplication by 5 and Its Multiples:
Multiplying a number by 5 is simple. Just divide the number by 2 and then add a zero. For example:
- 28 x 5 = (28 ÷ 2) 0 = 140
Similarly, multiplying by multiples of 5 involves multiplying the number by the appropriate multiple and then adding zeros. For example:
- 28 x 15 = 28 x 5 x 3 = 140 x 3 = 420
5. Quick Multiplication Two-Digit Numbers Mentally:
When multiplying two-digit numbers mentally, you can use the “cross-multiplication” method. For example, to multiply 14 by 15:
- First, multiply the tens place of both numbers: 1 x 1 = 1
- Then, multiply the tens place of one number with the units place of the other and add it to the previous result: (1 x 4) + (1 x 5) = 4 + 5 = 9
- Finally, multiply the units place of both numbers: 4 x 5 = 20
Combine the results to get the final answer: 1 (4+5) 0 = 210
6. Using Tables for Quick Multiplication:
Tables can be an excellent visual aid for learning and practicing multiplication. Below is a simple multiplication table up to 10×10:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
Tables like these can help learners visualize multiplication relationships and identify patterns, making multiplication faster and more intuitive.
7. The Distributive Property:
The distributive property states that for any numbers a, b, and c:
a * (b + c) = (a * b) + (a * c)
This property can be useful for breaking down complex multiplication problems into simpler ones. For example:
- 23 * 5 = (20 + 3) * 5 = (20 * 5) + (3 * 5) = 100 + 15 = 115
8. Quick Multiplication by 3:
To multiply a number by 3, you can double the number and then add the original number. For example:
- 14 x 3 = (14 x 2) + 14 = 28 + 14 = 42
9. Quick Multiplication by 4:
To multiply a number by 4, you can double the number twice. For example:
- 17 x 4 = (17 x 2) x 2 = 34 x 2 = 68
10. Quick Multiplication by 6:
To multiply a number by 6, you can multiply the number by 3 and then double the result. For example:
- 9 x 6 = (9 x 3) x 2 = 27 x 2 = 54
Quick Multiplication Two-Digit Numbers:
-
Cross Multiplication Method:
- This method involves multiplying the tens and units place separately and then adding the results together.
- For example, let’s multiply 24 by 35:
- First, multiply the tens place digits: 2 × 3 = 6
- Then, multiply the units place digits: 4 × 5 = 20
- Finally, add the results: 6 (from 2 × 3) and 20 (from 4 × 5) to get 620.
- So, 24 × 35 = 620.
-
Using the Distributive Property:
- Break down one of the numbers into its place value components and distribute the multiplication.
- For example, let’s multiply 24 by 35:
- 24 × 35 = 24 × (30 + 5) = (24 × 30) + (24 × 5)
- Calculate each part separately: (20 × 3) + (20 × 5) + (4 × 3) + (4 × 5) = 600 + 100 + 12 + 20 = 712
- So, 24 × 35 = 712.
-
Shortcut for Multiplying by 11:
- To multiply a two-digit number by 11, simply add the digits together and place the result between the original digits.
- For example, let’s multiply 34 by 11:
- 34 × 11 = 3 (3+4) 4 = 3 7 4.
- So, 34 × 11 = 374.
Quick Multiplication Three-Digit Numbers:
- Using the Distributive Property:
- Apply the distributive property to break down one of the numbers into its place value components and distribute the multiplication.
- For example, let’s multiply 123 by 456:
- 123 × 456 = 123 × (400 + 50 + 6) = (123 × 400) + (123 × 50) + (123 × 6)
- Calculate each part separately: (100 × 4) + (100 × 5) + (100 × 6) + (20 × 4) + (20 × 5) + (20 × 6) + (3 × 4) + (3 × 5) + (3 × 6)
- Simplify to get the final result: 49200 + 6150 + 738 = 56138
- So, 123 × 456 = 56138.
-
Using Cross Multiplication for Three-Digit Numbers:
- For three-digit numbers, you can extend the cross-multiplication method to multiply each digit of one number by each digit of the other number.
- For example, let’s multiply 123 by 456:
- Begin by multiplying each digit of 123 by each digit of 456, starting from the units place.
- Calculate each part separately: (3 × 6), (3 × 5), (3 × 4), (2 × 6), (2 × 5), (2 × 4), (1 × 6), (1 × 5), (1 × 4)
- Add up the results: 18, 15, 12, 12, 10, 8, 6, 5, 4
- Next, adjust the results according to their place values: 18, 15 + 12, 12 + 10 + 8, 6 + 5 + 4
- Finally, simplify and add up the adjusted results to get the final answer: 18, 27, 30, 15
- So, 123 × 456 = 56138.
By using these multiplication tricks, you can efficiently multiply two and three-digit numbers without the need for lengthy calculations, saving time and effort while solving mathematical problems.
Conclusion:
Learning quick multiplication tricks not only saves time but also builds confidence in tackling mathematical problems efficiently. By mastering these techniques and practicing regularly, individuals can enhance their mathematical abilities and approach multiplication with ease. Whether it’s multiplying by single-digit numbers or tackling larger calculations, these tricks provide valuable tools for learners of all ages and skill levels. So, dive into the world of quick multiplication tricks and discover the joy of multiplying in minutes!