Best Multiplication Tricks 2024

Table of Contents

Mastering Multiplication: From Beginner to Advanced Tricks

Multiplication is one of the fundamental building blocks of mathematics. Mastering it not only enhances your computational skills but also opens doors to more complex mathematical concepts. Whether you’re just starting or looking to sharpen your multiplication skills, this guide offers a range of tricks from basic to advanced.

1. The Basics: Understanding Multiplication

Before diving into the tricks, it’s essential to understand what multiplication is. Multiplication is essentially repeated addition. For example, 4 × 3 is the same as adding 4 three times (4 + 4 + 4), which equals 12. This fundamental concept is crucial for grasping more advanced tricks.

2. Beginner Tricks

a. Multiplying by 0 and 1

Multiplying by 0: Any number multiplied by 0 is always 0. For example, 5 × 0 = 0.
Multiplying by 1: Any number multiplied by 1 remains the same. For example, 7 × 1 = 7.

These are the simplest multiplication facts and form the foundation for more complex tricks.

b. The 2 Times Table Trick

Doubling: Multiplying by 2 is just doubling the number. For example, 6 × 2 = 12 (6 doubled is 12). This trick is intuitive and helps in quick mental calculations.

c. The 5 Times Table Trick

Counting by 5s: Multiplying any number by 5 is akin to counting by fives. For example, 4 × 5 is like counting 5, 10, 15, 20, which equals 20. This pattern is easy to remember and can be visualized using fingers.

3. Intermediate Tricks

a. The 9 Times Table Trick

Finger Trick: Hold out all ten fingers. To multiply any single-digit number by 9, fold down the finger that corresponds to the number. For example, to calculate 9 × 4, fold down the fourth finger. You’ll have 3 fingers on the left (representing 30) and 6 fingers on the right (representing 6), giving you 36. This trick works for 9 × 1 to 9 × 10.
Subtracting from 10: Another method is to multiply the number by 10 and subtract the original number from the result. For example, 9 × 7 can be calculated as (10 × 7) – 7 = 70 – 7 = 63.

b. Multiplying by 11

Single-Digit Numbers: To multiply any single-digit number by 11, simply repeat the digit. For example, 11 × 4 = 44.
Two-Digit Numbers: For numbers like 11 × 34, separate the digits (3 and 4). Add them together (3 + 4 = 7) and place the result between the original digits, giving you 374. If the sum is greater than 9, carry over the extra to the first digit.

c. Doubling and Halving

Efficient Multiplication: If one of the numbers is even, you can halve it and double the other number to make the multiplication easier. For example, instead of multiplying 16 × 25, halve 16 to get 8 and double 25 to get 50. Then multiply 8 × 50, which is easier and equals 400.

4. Advanced Tricks

a. Multiplying Large Numbers: The Box Method

Breaking Down Large Numbers: This method, also known as the area model, involves breaking down large numbers into smaller, more manageable parts. For example, to multiply 34 × 56, break down the numbers into 30 + 4 and 50 + 6. Draw a box and label the rows and columns with these numbers. Then, multiply each part:
$30 × 50 = 1500 \\ 30 × 6 = 180 \\ 4 × 50 = 200 \\ 4 × 6 = 24$ $30 \times 50 = 1500 30 \times 6 = 180 4 \times 50 = 200 4 \times 6 = 24$ Add all these products together: 1500 + 180 + 200 + 24 = 1904. This method visually demonstrates the distributive property of multiplication.

b. The Lattice Method

Visualizing Multiplication: This technique involves drawing a grid where the digits of one number are written along the top and the digits of the other number along the side. Each cell is then filled with the product of the corresponding digits, split into tens and ones. The products are added along the diagonals, and the final result is obtained by summing these diagonals.For example, to multiply 23 × 45:
1. Draw a 2×2 grid.
2. Write 23 on the top and 45 on the side.
3. Multiply each digit and fill in the grid.
4. Add along the diagonals to get the final product.
This method, though more complex, can be very effective for visual learners.

c. Multiplying by 15, 25, and 50

Multiplying by 15: Break it down into (10 + 5). For example, 15 × 8 can be done as (10 × 8) + (5 × 8) = 80 + 40 = 120.
Multiplying by 25: Think of it as a quarter of 100. For instance, 25 × 4 can be seen as 100, since 25 is one-fourth of 100.
Multiplying by 50: Multiply by 100 and then halve the result. For example, 50 × 6 can be done as 100 × 6 = 600, then 600 ÷ 2 = 300.

5. Multiplication of Numbers Close to 100

a. Using the Difference from 100

The Formula: If you’re multiplying two numbers close to 100, subtract each number from 100 and multiply the differences. Then subtract this product from 10000 (100 squared). Finally, subtract the sum of the differences from the original numbers. For example:
$97 × 98 = (100 – 97) × (100 – 98) = 3 × 2 = 6$ $97 \times 98 = (100 - 97) \times (100 - 98) = 3 \times 2 = 6$

$Then, 10000 – 6 = 9994 – (3 + 2) = 9994 – 5 = 9989$ $T h e n, 10000 - 6 = 9994 - (3 + 2) = 9994 - 5 = 9989$ The answer is 9506. This method is efficient for numbers near 100, such as 95 to 105.

6. Multiplying Large Numbers Mentally: The Vedic Method

a. Urdhva Tiryak

Step-by-Step Multiplication: This ancient Indian method simplifies the multiplication of large numbers by breaking them down into more manageable steps. For example, to multiply 23 by 34:
$M u l t i p l y 2 \times 3 = 6 (w r i t e d o w n 6) M u l t i p l y d i a g o n a l l y : (2 \times 4) + (3 \times 3) = 8 + 9 = 17$
$Multiply 2 × 3 = 6 (write down 6) \\ Multiply diagonally: (2 × 4) + (3 × 3) = 8 + 9 = 17 (write down 7 and carry over 1) \\ Multiply the last digits: 3 × 4 = 12 + 1 (carried over) = 13$ $M u lt i pl y 2 \times 3 = 6 (w r i t e d o w n 6) M u lt i pl y d ia g o na ll y : (2 \times 4) + (3 \times 3) = 8 + 9 = 17 (w r i t e d o w n 7 an d c a rryo v er 1) M u lt i pl y t h e l a s t d i g i t s : 3 \times 4 = 12 + 1 (c a rr i e d o v er) = 13$ The answer is 782. This method is particularly useful for multiplying large numbers mentally.

7. Conclusion

Mastering multiplication is not just about memorizing times tables; it’s about understanding and applying different techniques to solve problems efficiently. From the basic tricks that build a strong foundation to the advanced methods that challenge your mathematical thinking, each technique serves as a stepping stone towards mathematical proficiency. By practicing these tricks, you can enhance your mental math skills and handle complex calculations with ease.

Whether you’re a student aiming to improve your multiplication skills or an adult looking to sharpen your math abilities, these tricks will make multiplication less intimidating and more manageable. Start with the basics, gradually progress to the advanced techniques, and soon, multiplication will become second nature.

Quick and Effective Tricks to Master Mathematics

Mathematics can sometimes seem like a daunting subject, but with the right strategies and tricks, it can become an enjoyable and manageable challenge. Whether you’re a student trying to improve your grades or someone looking to sharpen your mental math skills, these short tricks will help you tackle mathematical problems with confidence and speed.

1. Mastering Basic Arithmetic

a. Multiplication by 9 Using Your Fingers

Finger Trick: To multiply any single-digit number by 9, hold out both hands with fingers spread. For example, to calculate 9 × 4, fold down the fourth finger. The number of fingers to the left of the folded finger represents tens, and the number to the right represents units. Here, you’ll have 3 fingers on the left and 6 on the right, giving you 36.

b. Doubling and Halving

Efficient Multiplication: If one of the numbers in a multiplication problem is even, halve it and double the other number. This can simplify the calculation. For example, instead of multiplying 16 × 25, halve 16 to get 8 and double 25 to get 50. Now multiply 8 × 50, which is easier and equals 400.

c. Adding Large Numbers Quickly

Round and Adjust: To add two large numbers, round one or both to the nearest ten, hundred, or thousand. Add these rounded numbers, then adjust by adding or subtracting the difference. For example, to add 567 and 289, round 567 to 570 and 289 to 290. Add them to get 860, then subtract the difference of 4 (3 + 1) to get 856.

2. Mental Math for Division

a. Divisibility Rules

Quick Check: Use simple rules to determine if a number is divisible by another:
- 2: The number is even.
- 3: The sum of the digits is divisible by 3.
- 5: The number ends in 0 or 5.
- 9: The sum of the digits is divisible by 9.

b. Estimation for Division

Rounding for Ease: When dividing large numbers, round the divisor and dividend to numbers that are easier to work with. Perform the division and then adjust accordingly. For instance, dividing 563 by 21 can be approximated by dividing 560 by 20, which gives an easier calculation of 28.

3. Algebra Simplified

a. Solving Linear Equations

Balancing Act: To solve equations like 2x + 3 = 11, think of keeping the equation balanced. Subtract 3 from both sides to get 2x = 8, then divide both sides by 2 to find x = 4. The key is to perform the same operation on both sides.

b. Use of Substitution

Plugging In: If you have two equations, solve one equation for one variable and substitute that value into the other equation. For example, if you have x + y = 10 and x – y = 2, solve the first for x = 10 – y, then substitute into the second equation to solve for y.

4. Fractions and Percentages

a. Simplifying Fractions

Divide by Common Factors: To simplify fractions, divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 18/24, divide both by 6 to get 3/4.

b. Converting Fractions to Percentages

Multiply by 100: To convert a fraction to a percentage, multiply by 100. For example, 3/5 as a percentage is (3/5) × 100 = 60%.

c. Quick Percentage Calculations

Use 10% as a Benchmark: To calculate percentages quickly, find 10% of the number (by moving the decimal one place to the left) and use it to estimate other percentages. For example, 15% of 80 can be found by calculating 10% of 80 (which is 8) and then adding half of that (4) to get 12.

5. Geometry and Measurement

a. Area and Perimeter Shortcuts

Rectangles and Squares: For a rectangle, the area is length × width, and the perimeter is 2 × (length + width). For a square, multiply one side by itself for the area and by 4 for the perimeter.

b. Estimating Volume

Round for Simplicity: When estimating the volume of a box (length × width × height), round each dimension to the nearest whole number or easy fraction before multiplying. For example, a box that is 9.8 × 6.2 × 4.7 can be rounded to 10 × 6 × 5 for an approximate volume of 300 cubic units.

6. Handling Powers and Roots

a. Squaring Numbers Ending in 5

Simple Formula: To square a number ending in 5, multiply the first digit(s) by itself plus one, then append 25. For example, 25² = 2 × (2 + 1) = 6, followed by 25, giving 625.

b. Estimating Square Roots

Use Close Squares: If you need to find the square root of a number that isn’t a perfect square, use the square roots of nearby perfect squares to estimate. For example, to estimate √50, note that √49 = 7, so √50 is slightly more than 7.

7. Quick Problem-Solving Strategies

a. Break Down the Problem

Divide and Conquer: When faced with a complex problem, break it into smaller, more manageable parts. Solve each part separately before combining the results. For example, in a word problem involving several steps, handle each step in isolation to avoid confusion.

b. Use Patterns and Sequences

Recognize Patterns: Many mathematical problems follow patterns. For example, in arithmetic sequences, the difference between consecutive terms is constant. Recognizing such patterns can make solving problems much faster.

8. Time-Saving Techniques

a. Mental Math Practice

Daily Drills: Spend a few minutes each day practicing mental math techniques. Start with basic arithmetic, then progress to more complex problems as you improve. This regular practice will boost your speed and accuracy over time.

b. Approximation and Estimation

Good Enough: In many cases, an exact answer isn’t necessary, and an estimate will do. Learn to round numbers and approximate results quickly. This is particularly useful in real-life scenarios like shopping or budgeting.

Conclusion

Mathematics doesn’t have to be a struggle. With these simple tricks and techniques, you can make math more approachable and even enjoyable. Whether you’re simplifying fractions, solving equations, or calculating percentages, these strategies will help you tackle math problems with confidence. Practice regularly, apply these tricks in everyday situations, and watch your math skills improve rapidly.

Best Multiplication Tricks 2024