SHORT STEP MAGIC MATHS

1) Multiplying by 5: A. This method will instruct you to write the answers from right to left. 1. When multiplying by 5, it is easier to divide by 2 and multiply by 10. 2. If the number you are multiplying is odd, then the last number will be a 5 (sce Ex [2]), otherwise the last number is O. B. Examples: Ex [1] 5 x 142 = _ a) 142 / 2 = 71. Write 71. b) Since 142 is even the last number is 0. Write 0. c) The answer is 710. Ex [2] 5 x 142857 = a) 142857  / 2 = 71428 with a remainder of 1. Write 71428. b) Since there is a remainder of 1, the last number is 5. Write 5. c) The answer is 714285. **Note: This trick works because 5- = 10 / 2.  

  4) FINDING THE SUM OF ALL EVEN NUMBERS STARTING FROM 2 RULE:   ( MULTIPLY THE AMOUNT OF NUMBERS IN THE GROUP BY ONE MORE THAN THEIR NUMBER ) We shall use this rule to find the sum of all even numbers from 1 to 100. Hall of the numbers will be even and half will be odd, which means there are 50 even numbers  from 1 to 100. Applying the rule, 50x 51 = 2,550 Thus the sum of all even numbers from 1 to 100 is 2,550.In Short Cut 2 the sum of all the numbers from 1 to 99 is found to be 4,950 : consequently the sum of all numbers from 1 to 100 is 5,050.In Short Cut 3 the sum of all odd numbers from 1 to 100 is found to be 2,500.Our answer for the sum of all the even numbers   from 1 to 100 is therefore in agreement Sum of all numbers 5,050 – Sum of all odd numbers 2,500 = Sum of all even numbers 2,550

FINDING THE SUM OF ALL ODD NUMBERS STARTING FROM 1 Rule : Square the amount of numbers from 1 to 100  will be calculated. There are 50 odd numbers in this group. Therefore 50 x 50 = 2,500 Answer This is the sum of all odd numbers from 1 to 100. As a check , we can compare this  answer with the answers found in Short Cuts 2 and 4.

Consider the problem of adding a group of consective numbers such as: 1, 2, 3, 4, 5, 6, 7, 8, and 9.  How would you go about  finding their sum ?  This group is certainly easy enough to add the usual way.  But if you're really clever you might notice that the first number, 1, added to the last number , 9, totals 10 and the second number, 2, plus the next to last number,  8,  also totals  10.  In fact, starting from both ends and adding pairs, the total in each case is 10. We find there are four pairs, each adding to 10; there is no pair for the number 5.   Thus 4 x 10 =  40 ;   40 + 5 = 45 Going a step further, we can develop a method for finding the sum of as many numbers in a row as we please   Going a step further, we can develop a method for finding the sum of as many numbers in a row as we please Rule : Muliply the amount of numbers in the group by one more than their number , and divide by 2. As an example , suppose we are asked to find the sum of all numbers from 1 to 99. Th

                         ADDING CONSECUTIVE NUMBERS Rule: (Add the smallest number in the group to the largest number in the group, multiply the result by the amount of numbers in the group, and divide the resulting product by 2.) Suppose we want to find the sum of all numbers from 33 to 41. First, add the smallest number to the largest number. 33 + 41 =    74 Since there are nine numbers from 33 to 41, the next step is 74 x 9 = 666 Finally, divide the result by 2. 666 / 2 = 333 Answer The sum of all numbers from 33 to 41 is therefore 333.

  INTRODUCTION CUTTING CORNERS Whether  due to curiosity or sheer  laziness , man has always  been  expeimenting , searching  for and stumbling  up on ways of making  work easier for himseif . That anony mous caveman who chipped  the corners  off a flat rock and invented the wheel started this tradition .   Most  of man’ s efforts in the past were directed at con- serving or increasing his muscle power’ but as time went  on some  were  aimed at saving  weat  and teat on another vital organ; his brain. It followed naturally that his attention turned to reducing such laborious  tasks as calculating.        WHAT SHORT CUTS ARE Short cuts in mathematics are ingenious little tricks in calculating that can save enormous amounts of time and labour _ not to mention paper – in solving otherwise complicated problems. There are no magical powers connected with these tricks: each is based on sound mathematical principals growing out of the very properties of numbers themselves .The results they pr