《Mental Math》读书笔记思维导图
龙龙哥
2022-11-12
思维导图
《Mental
Math》
读书笔记
简单介绍《Mental Math》读书笔记
树图思维导图提供《《Mental Math》读书笔记思维导图》在线思维导图免费制作，点击“编辑”按钮，可对《《Mental Math》读书笔记思维导图》进行在线思维导图编辑，本思维导图属于思维导图模板主题，文件编号是：e98c0d90c02a9a8558f7c2315249cd91
思维导图大纲
相关思维导图模版
Mental Math思维导图模板大纲
Math in Head
Adding number from Left to Right
Multiplication Table
11 ~ 20 tables
18 X 8 == 80 add 64 = 144
two digit multiple : b/w 11 to 20 only
1st step
Step 2
1 ~ 10 tables
1 & 10 can be 1st eliminated
9 has two theory
1st digit less by 1 of multiplying no
adding product's digits to 9
5 ends with 0 or 5
2 can be done by basic addition
3 & 4 using "Count by 3 / 4 faster n faster"
Reduces to 3 X 3 matrix
Constantly Simplify
Mutliply the Left most number
Calculate left to right
It gives you estimate of answer
Multiply by 11
2 digit by 11
2 digit, with digit's sum more than 9
3 Digit by 11
4 digit by 11
Squaring number
Patterns
Easiest square "5"
Ends with 25
1st digit multiply be "1 digit added 1"
Can be applied for 3 digit numbers too
Addition/Subtraction
Left to Right rule is important
Add the biggest number
Same for bigger numbers too
Using the compliment of Number
Three ways of Subtraction
Subtraction 1
Subtraction 2
Avoid Remainder
Biggest to smallest
Compliments
tens digit add to "9"
ones digit add to "10"
Using compliment to subtract
Compliments have same theory as calculated for 1000, 10000, etc
Remember, when ending with "0" above rule is doesn't hold
Money change calculation
Using compliment
example
Paise adds to "100"
Rupees add to "99"
Go forth & multiply
Simplification is Core
Multiplying 2 / 3 digit numbers 1 digit
Base for 2 by 2 digit / 3by3 digit
Tiangle problem
2by1
3by1
distributive law
Factoring method 2by2
Divide & Conquer
When does number divides evenly
2,5,10
Divisible by 7 is complicated
Whether multiple of 7
Create a zero & kill a zero
Divisible by 4
Divisible by 8
Divisible by 3
Divisible by 9
Divisible by 11
Divisible by 6
Divisible by 12
Division procedure
div by 1
div by 2 : two procedure
Usual Procedure
Negative remainder method - Overshooting
divide n rule
Doubling both num & denom, will keep answer same
Double & kill 0
Playing with decimal numbers
Converting fraction to decimal
When denominator is below 11 it is easy
fraction of 7 is trickiest
1/7 = 0.142857 (repeated
This is damn interesting
Further support for above circle to locate start point
Decimal expansion: 2, 3, 4, 5
Expansion of 6, 8
For 10, it is automatic
If 1/9 = 0.111 remaining follow
similar to 9, 1/11 = 0.0909
Guesstimation
Rounding procedure
Helpful in grocery store
Both for adding & subtracting
Rounding to 1000s or 100s
Precision increases
Multiplication
General rule of thumb
Product of initial digit decides the answers
no of digits
Using Words to get Digits
Division
Order of Magnitude
To find the exact no of digit, compare the 1st digits of the number
If the 1st Digits are same, then 2nd digit needs comparison
Example : Light's Speed
Physical Estimation
It is better to know your body dimensions
Tax calculation when tax% is not whole #
Guestimate for whole# tax%
Then divide answer by 8
15% restaurant tip
Calculate 10% then divide it by 2
Add that to get 15%
Pinky to Thumb = 20 cm or 8 inch
Measuring a table dimension with your fingers
Error Estimation using x X y / z, refer course for problem
Money Estimation
EMI Calc
Formula for accurate calc
Symbols
Quite a huge explanation, but here is a formula
Rule of 70
70 / 3
where 3% is the rate
Square root estimation
Perfect Vs Imperfect Squares
Some applications
Triangle Hypotnuse
Margin of Error in Satistics
Finding Square roots
Locating the approximate square root
Then increasing precision
Finalising answer
Math on Paper
Adding column of Numbers
Right to Left
Ability to chek : bottom to top
Subtracting with compliments
Do the Cents & then Dollars
1st Usage of Compliment : in "E-services"
2nd Usage of Compliment : "Odd & Ends"
mutliplying on Paper
It takes 5 Steps for 3 digit No pair
Casting Out nines
Can be used to check additions/Multiplications/subtraction
Remove 9's wherever you see
Close together method
How far each number is from 100
Procedure above 100
If below 100 then
abv n blw 100
It can be near any number with "0" at end
Close 2 1000 , multiply
It takes 7 steps for a 4 digit no pair
all digits in each number is multiplied atleast once
It was introduced by Fibbonacci
Digit Sum Check
Vedic Division
Carry over issue
Mental Multiplication
Addition Method
Subtraction Method
Factoring Method
There are multiple ways to factor
Using Math of Least resistance
Close-together Method
Squaring
Vedic Division
Mathematical & Algebraic Shortcuts
Digits in Answer generates further digits
4 methods
Long Division : Usual Method
Vedic Division
Best number suitable is number ending with "9"
Memory Division : Divide n Conquer Lecture
Short Division : Not thought in Schools
Shrort division
Example
Vedic Division Divided by number ending with "9"
Used when the divisor ends with high numbers
Procedure
Adding/subtracting the Quotient
Reminder Step
If the quotient has carry
Number that ends with other numbers
Instead of adding the quotient directly, we have multiplier
depending whether you go down or up, the adding or subtracting needs to be done
The divisor is rounded to nearest number ending with "0"
Calendar Calculation
There is a code for each part of the date
Code for Year 2000 : 0
- Your B'day adds by one every another year
- For the leap year you jump to next number
- Since we are subtracting multiples of 7 in
Code for the month
Exceptions
Mnemonics & Major System
Major System
Mnemonics
1st half year
2nd half year
Code for Week is
How days got their name
Formula for Day calculation
another example
Finding the 1st monday
Advanced Multiplication
Squaring 3 digit no
Be ready with 2 digit squares upto 50
Easiest 3 Digit no : 108
Slightly Tougher 3 digit squaring
Very Tough 3 digit Squaring
Getting the UP/Down no in this method
4 digit Squaring
In Cls together method you will not push away more than 500
Always say out the biggest number after 1st step of this method
Bring in mnemonics
Excellent approximation of Cube of 43
Estimate by 40 X 40 X 40 : not very better
Balanced cube approximation
You can go down also
Cube requirement can arise @ unlikely places
You can multiplication methods to simplify squaring
Masters of Mental Math
Benford's Law
The prevalence of finding #1
All numbers are not created equal
The course made you to give numbers extra thought
Cubes 1~10
will help you find cube root of numbers
Look @ 1000s
Look at last digit of the #
To get into guiness book, 13th root of 100 digit number needs to be calculated
查看更多
相似思维导图模版
首页
我的文件
我的团队
个人中心