《Mental Math》读书笔记思维导图

11 ~ 20 tables

1 ~ 10 tables

Mutliply the Left most number

Calculate left to right

It gives you estimate of answer

2 digit by 11

2 digit, with digit's sum more than 9

3 Digit by 11

4 digit by 11

Patterns

Easiest square "5"

Subtraction 1

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

Using compliment

example

Paise adds to "100"

Rupees add to "99"

Base for 2 by 2 digit / 3by3 digit

Tiangle problem

2by1

3by1

distributive law

2,5,10

Divisible by 4

Divisible by 8

Divisible by 3

Divisible by 9

Divisible by 11

Divisible by 6

Divisible by 12

div by 1

Doubling both num & denom, will keep answer same

Double & kill 0

Playing with decimal numbers

When denominator is below 11 it is easy

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

Helpful in grocery store

Both for adding & subtracting

General rule of thumb

Product of initial digit decides the answers no of digits

Using Words to get Digits

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

It is better to know your body dimensions

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

EMI Calc

Quite a huge explanation, but here is a formula

Rule of 70

70 / 3

where 3% is the rate

Perfect Vs Imperfect Squares

Right to Left

Ability to chek : bottom to top

Do the Cents & then Dollars

1st Usage of Compliment : in "E-services"

2nd Usage of Compliment : "Odd & Ends"

It takes 5 Steps for 3 digit No pair

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

Carry over issue

There are multiple ways to factor

Using Math of Least resistance

Long Division : Usual Method

Memory Division : Divide n Conquer Lecture

Short Division : Not thought in Schools

Example

Used when the divisor ends with high numbers

The divisor is rounded to nearest number ending with "0"

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

Code for Week is

another example

Finding the 1st monday

Be ready with 2 digit squares upto 50

Easiest 3 Digit no : 108

Slightly Tougher 3 digit squaring

Very Tough 3 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

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

The prevalence of finding #1

will help you find cube root of numbers

Look @ 1000s

Look at last digit of the #