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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
- 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.
- For example:
7 + 25 + 7 +7 +7 =
will be 25 + (4 × 7) =
25 + 28 = 53
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
12 × 12 = 144
14400
- 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
Apply; 35 2 = ?
3 × 4 = 12
1225
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.
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
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.
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