BLOG 1 - playing with numbers - LETTERS FOR DIGITS IN ADDITION

BLOG 1 - playing with numbers - LETTERS FOR DIGITS IN ADDITION

GOOD MORNING BOYS,,,,,

                                                 LETTERS FOR DIGITS(PART I)

LEARNING OUTCOMES 
By the end of the lesson you will be able  to find the " DIGIT" to the " LETTER" IN THE ARITHMETIC SUM PROBLEM and hence  solve the puzzle 

CLICK HERE TO GET AN INTRODUCTION ON THE PLAYING WITH NUMBERS FOR ADDITION

HERE are two rules we follow while doing such puzzles

(1)Each ALPHABET in the puzzle must stand for just one digit.Each DIGIT  must be represented by just ONE DIGIT.

(2)The first digit of a number cannot be ZERO.Thus, we write the number  fifty nine as " 59". and NOT AS "059" or "0059"

Q1 :    Find the values of the letters in the following and give reasons for the             steps involved


Answer : 

The addition of A and 5 is giving 2 

i.e., a number whose ones digit is 2. 

This is possible only when digit A is 7. 

In that case, the addition of A =7 and 5 will give 12 and thus, 1 will be the carry for the next step. 

In the next step,  

1 + 3 + 2 = 6  

Therefore, the addition is as follows.    Clearly,   B is 6.  

Hence, A and B are 7 and 6 respectively.  

Q2 :   Find the values of the letters in the following and give reasons for the steps involved.   

                                              

Answer : 

The addition of A and 8 is giving 3 i.e., a number whose ones digit is 3. 

This is possible only when digit A is 5. 

In that case, the addition of A and 8 will give 13 and

 thus, 1 will be the carry for the next step.

 In the next step,  

1 + 4 + 9 = 14  

Therefore, the addition is as follows.  

Clearly, B and C are 4 and 1 respectively.  

Hence, A, B, and C are 5, 4, and 1 respectively.  

Q.4

   

Find the values of the letters in the following and give reasons for the steps involved.  

Answer : 

The addition of A and 3 is giving 6. There can be two cases.  

(1)  First step is not producing a carry  

In that case, A comes to be 3 as 3 + 3 = 6. 

Considering the first step in which the addition of B and 7 is giving A (i.e., 3), B should be a number such that the units digit of this addition comes to be 3. It is possible only when B = 6. In this case, A = 6 + 7 = 13. However, A is a single digit number. Hence, it is not possible.  

(2)  First step is producing a carry 

In that case, A comes to be 2 as 1 + 2 

In that case, A comes to be 2 as 1 + 2 + 3 = 6. 

Considering the first step in which the addition of B and 7 is giving A (i.e., 2), 

B should be a number such that the units digit of this addition comes to be 2. 

It is possible only when B = 5 and 5 + 7 = 12.   

Hence, the values of A and B are 2 and 5 respectively.

  Q10 : 

   

Find the values of the letters in the following and give reasons for the steps involved.  

ANSWER;

The addition of A and B is giving 9

 i.e., a number whose ones digits is 9. 

The sum can be 9 only as the sum of two single digit numbers cannot be 19. 

Therefore, there will not be any carry in this step.  

In the next step, 2 + A = 0  

It is possible only when A = 8        

1  + 8 = 10 and 1 will be the carry for the next step.  

1 + 1 + 6 = A  

Clearly, A is 8. We know that the addition of A and B is giving 9. As A is 8, therefore, B is 1.  

Therefore, the addition is as follows.  

Hence, the values of A and B are 8 and 1 respectively.   

HOME WORK 

NCERT PAGE 256  QUES 8 and QUES 9

THAT' S ALL FOR TODAY