Mind Sharpener - Easy Math for Hard Life Problems

Foreword

The creators of AI have accomplished an impressive feat. Many people are worried that human intelligence has been surpassed by artificial intelligence. However, there are two important elements that robots can never comprehend: suffering and hope. These two elements are inherent in our life problems.

Solving life problems requires some math ability to tackle the so-called word problems.

The topic of word problems is well-known, with numerous manuals and methods written to develop the ability to solve them.

However, our approach is somewhat different because the problems we present are actual life problems, and their solutions, much like in reality, in most cases, are closely tied to money. Life's problems are related to HEALTH, WEALTH, and LOVE, but undoubtedly, money is the bottom line.

This book is not for mathematicians, but for anybody willing to practice how to handle various problems in life. And these problems imply, among other things, some simple math, primarily involving basic arithmetic.

However, it is advisable to perform the calculations mentally, as in real situations.

The most important strategies for solving word problems:

1.  Extract the essential information

A general recommendation for any word problem is to ignore unimportant information and focus only on what is essential—usually quantities and relevant details about those quantities.

2.  Convert words into mathematical operations

In order to solve a word problem, one needs to translate words into a mathematical expression.

-  Example: three actions times two – should be written as 3a * 2, which eventually equals 6a

3.  Apply estimation to anticipate answers

Use rounded numbers to approximate the result: for instance 298 – 102 is close to 300 – 100 = 200.

Mental math

Tips for performing mental calculations

We will present some ideas about mental calculations.

In real-life situations, it's advantageous to be able to perform quick calculations mentally.

For many people mental math is a pain. But it’s a good idea to practice from time to time. It strengthens the brain muscle and prevents Alzheimer's.

There are various algorithms, methods, and styles, but we will focus only on the simplest additions, subtractions, multiplications, divisions, and also percentages.

Additions

one digit: this should have been already memorized. Most people can handle one digit addition like 3+5 or 8 +7. If you don’t, the only solution is to practice.

two digits: in a 2-digit number the first digit is the number of tens and the last digit is the units.

To calculate mentally an addition of two digit numbers, add firstly the tens, then the units and add them together. For instance: 32 + 43.

-  Add first 30 + 40 = 70,

-  then the units: 2 + 3 = 5,

-  and finally 70 + 5 = 75.

Another example, a bit more difficult is: 28 + 57

-  add first the tens: 20 + 50 = 70.

-  then the units 8 +7 = 15

-  and finally 70 + 15 = 85

three digits: same principle applies - add the hundreds, then tens, units and finally add the results together. It’s more difficult because we have to hold the three results in our short memory. Here is an example: 234 + 521.

-  200 + 500 = 700

-  30 + 20 = 50

-  4 + 1 = 5

-  finally the sum (700 + 50 + 5) equals 755

2. Subtractions

you digit numbers - in two steps, i.e 43 - 25

-  first we subtract 20 from the first number

43 - 20 = 23

-  and then 23 - 5 = 18