Cracking the Mental Math Code

By Yash Chandak

From those who read a poster asking them to join the school’s Number Sense team to the seasoned competitor eyeing State medals, this book serves as a guide and as inspiration, to not only pique interest but to build a foundation on.

You’ll find in this book a step-by-step guide on how-to solve Number Sense problems and prepare you for any mental math competitions. There are over 80 mental math techniques are explained in this book, and over 750 problems to learn, train, and improve with. Just a note: as fun as it is to learn new tricks and techniques on PEMDAS, Squares, GCD & LCM, Remainder, Higher Order Exponents, Roots, Primes & Divisors, Roman & Complex Numbers, Factorials & Combinations, Sequences, Memorization, Fractions, Decimals, Bases, Linear & Quadratic Equations, Sets, Logarithms, Matrices and many more.  It’s just as important to master them and implement them in full-length tests!

I wish you all the best of luck, and happy computing!

• Language: English
• Publisher: MINDPOP
• Release date: Nov 14, 2017
• ISBN: 9781386590828

Yash Chandak

Yash Chandak is a high school senior with a passion for mathematics. Training on mental math for 8 years, Yash has gained an expertise on the subject, winning competitions at regional and state levels. His passion for helping others led him to write this compendium of tricks and techniques, hoping that he can inspire the next generation of mental mathematicians to learn the beauty of the discipline.

Book preview

PEMDAS

1.1  Fast Addition and Subtraction

Most all tricks in this book will require you to be quick in basic operations. Given that you only have 7.5 seconds to read, solve, and write the answer for each question, you don’t get much time for the intermediate steps. So, let’s teach you a trick on arguably the simplest topic in mathematics: addition and subtraction.

Basic addition involves adding one digit at a time moving right to left. To get the answer faster, however, you can add two digits at a time, write the answer for that, and maintain the carries. Let’s see a couple of examples.

Note: it’s almost always advantageous to subtract before you add. Dealing with smaller numbers is usually easier.

Practice Problem Set 1.1

1)  4703+3211=

2)  864+579=

3)  357+864-135=

4)  3205-3088=

5)  2024-3026=

6)  2010+201+20=

7)  1234+123+12+1=

8)  2134-1123=

9)  1914 - 3229 =

10)  2468-9753=

11)  2551+125-51+2=

12)  975+318-642=

13)  289+33445-291=

14)  4110-4128+2008=

15)  16183-14135+230=

16)  437-734=

17)  537-33+284=

18)  2016-424+508=

19)  78-3457+230=

1.2  PEMDAS Approximations

Almost every Number Sense test will have an approximation question that is solely addition and subtraction, usually 5 or 6 digits long. Since you can be within 5% of the actual answer and still get the question correct, it is advantageous for you to only do the operations for the highest 2 place values and round appropriately rather than trying to chug through all the digits.

To solve this question, I would use the ten-thousands and thousands digits to determine an approximate value.

My answer: 96,000

Range: 91,545 to 101,181

Most times, rounding in these questions is beneficial because the ranges are quite large and the problem can become quite easier to solve. However, if you round up on one number a substantial amount (relative to the number of course), it’s good to round down on another to balance out the error.

It’s important to be both quick and accurate when rounding. You don’t want to waste time on easy questions trying to choose how to round. Just do what feels right and start calculating!

Practice Problem Set 1.2

1)  314+272-31-27=

2)  2101+3202-2323=

3)  9876+1234-50=

4)  57346-45634+34365=

5)  753+2468-901+2005=

6)  449*9+451=

7)  789-3120+645=

8)  2345-456+3298-264=

9)  376-1785+63=

10)  2585+20345+245+23=

11)  4554-5665-6776=

12)  74859-27384+2604=

13)  3131-311+133-33=

14)  3091+2512+7896=

1.3  Multiply by 11 and like

The one thing more common than addition on a Number Sense test is multiplication. I cannot emphasize how drastically multiplication speed affects your score. It goes without saying that with a lot of multiplication comes a lot of multiplication tricks. The easiest and most common trick is multiplying by 11.

I could try to explain this trick in words for you, but that would be quite confusing and lengthy, so let’s use an example.

Let’s use the original way of multiplying to see the trick.

It looks like all we did was add the two digits (3+5=8) and put that sum in the middle of that