# 20 Mental Math Tricks

4 min read · Jun 20, 2024

## Table of contents

Mental math tricks can significantly speed up calculations and improve number sense. Here are some strategies for each of the basic arithmetic operations, incorporating a range of techniques designed to enhance calculation skills and number understanding:

## Addition Tricks for Enhanced Mental Math and Arithmetic Skills

**Break Up the Numbers Strategy:**Decompose one addend into expanded form and sequentially add the parts to the other, simplifying through mental processing. This involves analyzing the number by its digits to enhance the addition process. This method is particularly helpful when dealing with big numbers or equations, making it easier to memorize and solve.**Front-End Strategy:**Begin with the largest place values (hundreds, then tens, then ones) to streamline the process. This approach focuses on the digits at the front, facilitating a quicker resolution. It's a top strategy for ensuring accuracy in your calculations.**Compatible Number Strategy:**Identify pairs of numbers that are straightforward to combine, like rounding one number up and the other down to achieve a round number. This method effectively utilizes the digits' value for easier calculations, proving to be a free and easy way to enhance mental math skills.**Balancing Strategy:**Adjust one addend up and the other down to create round numbers for straightforward addition. This method simplifies the process by focusing on the digits' overall impact, making it an instance where mental maths becomes particularly useful.**Special Tens Strategy:**Utilize knowledge of pairs that total ten to simplify addition, a key number strategy for enhancing calculation efficiency. Recognizing these pairs can dramatically speed up the process, teaching us the importance of digit relationships for quick maths.**Compensation Strategy:**Substitute a number close in value for one of the addends, then adjust after calculating to ensure the final answer accounts for the initial adjustment. This strategy showcases the power of decimal understanding in mental arithmetic.**Left to Right Addition:**Approach addition from left to right, reducing dependency on carrying to improve speed and accuracy. This minimizes the need to remember carry digits, making the process smoother and more efficient, illustrating how certain programs can be helpful in practicing these techniques.

## Subtraction Tricks to Boost Mental Math and Memory Skills

**Subtract in Parts:**Break down the number being subtracted into tens and ones and subtract sequentially, applying strategies for better number manipulation. Focusing on each digit individually can make the task more manageable and is a source of simplicity in mental calculation.**Use Basic Subtraction Facts:**Rely on known facts for larger numbers, like understanding that 13 - 8 assists with 93 - 8. This method brings previous knowledge into the current calculation, encouraging us to learn and apply these concepts multiple times for mastery.**Subtract an Easy Number Close to the Subtrahend:**Choose a number near the subtrahend to subtract, then correct the result. This adjustment step ensures the accuracy of the final outcome, allowing for a more intuitive understanding of subtraction.**Think of the Difference:**Rather than subtracting, consider the distance between two numbers, an approach that finds the answer more intuitively. This strategy often leads to a quicker solution, especially in quizzes, and promotes the idea of using subtraction in creative ways multiple times to solidify understanding.

## Multiplication Tricks with Mental Math and Number Strategies

**Base 10 Multiplication:**Tackle multiplication using base 10, breaking down numbers into simpler parts. This method relies heavily on the place value of digits, a critical factor in multiplication, and is often highlighted in research as a method to improve efficiency.**Doubling and Halving:**For even multiplicand and multiplier, halving them simplifies the calculation. This technique effectively reduces the numbers involved, making it a staple strategy in mental maths programs.**Multiplying by 5:**Double the number and then halve the result, a straightforward strategy. The simplicity of this method is its strength, making it easy to apply and a top choice for quick calculations.**Multiplying by 9:**Increase the number by 10 and then subtract the original number, an effective approach for quick calculations. This emphasizes the importance of understanding digit relationships, making it easier to memorize and apply.**Multiplying by 11:**For two-digit numbers, split the digits, sum them, and place the result in between, a technique that improves efficiency. This showcases the power of digit manipulation for faster results, encouraging us to learn and apply these strategies multiple times.

## Division Tricks for Streamlined Mental Math and Arithmetic

**Dividing by 5:**Multiply both the dividend and divisor by 2 to simplify the division. This adjustment is crucial in the strategy, illustrating how learning and applying division strategies multiple times can enhance understanding.**Halving the Dividend and Divisor:**If both numbers are even, halving them gets to smaller figures, a simple technique for easier division. Reducing the size of the digits involved simplifies the calculation, making it an essential strategy in mental math.**Partial Quotients Strategy:**Decompose the dividend into friendlier numbers divisible by the divisor and divide each part, then sum the quotients, a technique that enhances skills in calculation. This strategy allows for step-by-step processing, easing the division task, and is often emphasized in math education research.**Combining Strategies:**Employ a mix of methods to simplify complicated division problems, leveraging for optimal problem-solving. This comprehensive approach often leads to a more accurate answer, demonstrating mastery in calculation skills, and should be practiced multiple times to ensure proficiency.

These techniques can be practiced and mastered over time, leading to faster and more efficient calculations without the need for pen and paper, enhancing both calculation skills and number sense significantly. By incorporating these strategies into daily practice, you can develop a strong foundation that will support your mathematical endeavors for years to come. A solid understanding of these concepts can make a significant difference in your calculation skills, as highlighted throughout this article on mental math tricks.

### About the author

#### Richard Reis

Founder of Mental Math Pro! Also currently doing a fun little "25 AI Startups in 50 Weeks" challenge.