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Numerical thinking, also known as mind math, is a powerful mental skill that enables individuals to perform complex calculations rapidly and accurately, without the use of any external tools. In a world where efficiency and speed are highly valued, cultivating numerical thinking skills can greatly enhance our problem-solving abilities and improve our overall cognitive capabilities. Whether you are a student looking to boost your math performance, a professional aiming to increase your productivity, or simply someone interested in exploring the depths of your own mental capabilities, this guide will provide you with the necessary knowledge and techniques to master the art of calculating numerical thinking. From learning basic strategies to tackle arithmetic operations in your head, to advanced methods for handling more complex calculations, follow along as we delve into the fascinating world of mind math and unlock the potential of your own numerical thinking abilities.
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Numerical thinking or mental math is the ability to use applied algebra, mathematical methods, intelligence, and creativity to solve problems. All details about some of these methods are described in links to other wikiHow articles.
Prerequisite : Know how to memorize basic addition, subtraction, multiplication, and division.
Steps
Addition and subtraction
![Image titled Do Number Sense (Mental Math) Step 1](https://www.wikihow.com/images_en/thumb/7/73/Do-Number-Sense-%28Mental-Math%29-Step-1-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-1-Version-3.jpg)
- For example 88 + 56 = ? ; Rounds 88 to 90.
Add 90 plus 56 = 146
Subtract the number two that is added to 88 (to round to 90).
146 – 2 = 144 ; that’s the answer!
- The process is simply rearranging the problem 56 + (90 -2). Some examples of other uses of this method are: 99 = (100 – 1); 68 = (70 – 2)
- You can also use this rearrangement method for subtraction.
![Image titled Do Number Sense (Mental Math) Step 2](https://www.wikihow.com/images_en/thumb/0/00/Do-Number-Sense-%28Mental-Math%29-Step-2-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-2-Version-3.jpg)
- For example:
7 + 25 + 7 +7 +7 =
will be 25 + (4 × 7) =
25 + 28 = 53
![Image titled Do Number Sense (Mental Math) Step 3](https://www.wikihow.com/images_en/thumb/e/e0/Do-Number-Sense-%28Mental-Math%29-Step-3-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-3-Version-3.jpg)
5 + 4 = 9 is the addition and reverse of -2 -7 = -9
Since they are additive inverses, the actual addition for all four numbers is not necessary; the answer is 0 (zero) after quitting.
- Try this calculation:
4 + 5 – 7 + 8 – 3 + 6 – 9 + 2 =
will become:
(
4+5) –9+ (-7–3) + (8+2) + 6 =By grouping
and remember, don’t add them; just remove the inverse addition from the problem.0 + 0 + 6 = 6
Multiplication
![Image titled Do Number Sense (Mental Math) Step 4](https://www.wikihow.com/images_en/thumb/9/91/Do-Number-Sense-%28Mental-Math%29-Step-4-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-4-Version-3.jpg)
12 × 12 = 144
14400
![Image titled Do Number Sense (Mental Math) Step 5](https://www.wikihow.com/images_en/thumb/4/4e/Do-Number-Sense-%28Mental-Math%29-Step-5-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-5-Version-3.jpg)
- For example:
Instead of taking 14 × 6
divide 14 into 10 and 4, and multiply both by 6, then add them together…
14 × 6 = = 6 ×(10 + 4) = (10 × 6) + (4 × 6) = 60 + 24 = 84.
- For example:
Instead of taking: 35 * 37 = ?
do it this way: 35 × (35 + 2) =
= 35 2 + (2 × 35) = 1225 + 70 = 1295
![Image titled Do Number Sense (Mental Math) Step 6](https://www.wikihow.com/images_en/thumb/4/40/Do-Number-Sense-%28Mental-Math%29-Step-6-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-6-Version-3.jpg)
Apply; 35 2 = ?
3 × 4 = 12
1225
![Image titled Do Number Sense (Mental Math) Step 7](https://www.wikihow.com/images_en/thumb/f/f8/Do-Number-Sense-%28Mental-Math%29-Step-7-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-7-Version-3.jpg)
Apply 41 2 = ? and 39 2 = ?
40 2 = 1600
40 + 41 = 81
40 + 39 = 79.
1600 + 81 = 1.681 —> 41 2 = 1.681
1600 – 79 = 1.521 —-> 39 2 = 1.521
- This method is only suitable for some numbers with one unit above or below the original number.
![Image titled Do Number Sense (Mental Math) Step 8](https://www.wikihow.com/images_en/thumb/8/87/Do-Number-Sense-%28Mental-Math%29-Step-8-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-8-Version-3.jpg)
In this case, the number 45 is the number that is 6 digits away from both numbers.
45 2 = 2025
6 2 = 36
2025 – 36 = 1989
- If you are studying algebra, the formula is expressed as follows:
51 × 39 =
(45 + 6)×(45 – 6) = 45 2 -6 2
( x + y )×( x – y ) = x 2 – y 2
![Image titled Do Number Sense (Mental Math) Step 9](https://www.wikihow.com/images_en/thumb/4/4d/Do-Number-Sense-%28Mental-Math%29-Step-9-Version-3.jpg/v4-728px-Do-Number-Sense-%28Mental-Math%29-Step-9-Version-3.jpg)
25 × 12
1200
1200 4 = 300
25 × 12 = 300
Sources
Calculator’s Cunning: The Art of Quick Reckoning by Karl Menninger
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 20 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 9,694 times.
Numerical thinking or mental math is the ability to use applied algebra, mathematical methods, intelligence, and creativity to solve problems. All details about some of these methods are described in links to other wikiHow articles.
Prerequisite : Know how to memorize basic addition, subtraction, multiplication, and division.
In conclusion, numerical thinking, also known as mind math, is a valuable skill that can be developed through practice and training. By understanding the underlying principles and techniques, individuals can calculate complex mathematical problems quickly and efficiently. The process of calculating numerically involves breaking down complex equations into simpler components and using mental strategies to solve them. Regular practice in numerical thinking can enhance problem-solving abilities, improve mental agility, and boost overall mathematical competence. Moreover, this skill has various real-life applications, from everyday tasks like budgeting and shopping to professional fields such as finance and engineering. Therefore, acquiring the ability to calculate numerically is not only beneficial for academic purposes but also for enhancing critical thinking skills and improving overall cognitive abilities. By incorporating mind math techniques into one’s daily activities and dedicating time to practice, anyone can tap into the power of numerical thinking and witness the transformation it brings to their mathematical problem-solving abilities.
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