Tricks With Digits
Tricks With Digits
Trick 1:
Adding the number and its reverse number.
Step 1: Choose a 2 digit number. Let us take 34
Step 2: Now reverse the digits. We get 43
Step 3: Add the two digits . we get 34 + 43 = 77
Step 4 : Divide the sum by 11. We get 77 11 = 7
Step 5 : The quotient will always be equal to the sum of digits that is 3 and 4 in this case
Justification:
Consider a two digit number having ones and tens digits as b and a respectively. On reversing the digits of this number , we obtain a two digit number
.
In expanded form, we have
and,
Adding (i) and (ii) , we get
Thus, is completely divisible by 11 and the quotient is a+b.
Also, it is divisible by a+b and in that case the quotient is 11.
In other words, the sum of any two digit number and the number
by reversing its digits is completely divisible by
(i) the sum a+b of its digits and the quotient is 11.
(ii) 11 and the quotient is a+b i.e., the sum of its digits.
Trick 2:
Subtracting the number and its reverse number.
Step 1: Choose a 2 digit number. Let us take 28
Step 2: Now reverse the digits. We get 82
Step 3: Subtract the smaller number from the bigger number . We get 82 - 28= 54
Step 4 : Divide the difference by 9. We get 54 9 = 6
Step 5 : The quotient will always be equal to the difference of the greater digit and the smaller digit that is 8 and 2 in this case. 8 -2 = 6
Justification:
Consider a two digit number having ones and tens digits as b and a respectively. On reversing the digits of this number , we obtain a two digit number
.
In expanded form, we have
and,
Subtracting (ii) from (i) , we get
Thus, is exactly divisible by 9 and the quotient is a- b i.e. the difference of the digits.
Also, is exactly divisible by a- b (difference of digits) and the quotient is 9.
Illustration 1: Without performing actual addition and division find the quotient when the sum of 79 and 97 is divided by (i) 16 (ii) 11.
Solution: The two numbers 79 and 97 are such that one can be obtained reversing the digits of the other.
Therefore, their sum when divided by the sum of the digits i.e. 7 + 9 = 16, we obtain 11 as the quotient .
If the sum of these two numbers is divided by 11, we get 7 + 9 ( sum of the digits) =16 as the quotient.
Illustration 2 : Without performing actual calculation find the quotient when the difference of 73 and 37 is divided by (i) 4 (ii) 9.
Solution: The two numbers 73 and 37 are such that one can be obtained reversing the digits of the other.
Therefore, their difference 73 - 37 = 36 when divided by the difference of the digits i.e. 7 - 3 = 4, we obtain 9 as the quotient .
If the difference 73 - 37 = 36 is divided by 9, we get 7 - 3 ( difference of the digits) = 4 as the quotient.
Without performing actual calculation find the quotient when the difference of 71 and 17 is divided by 9. | |||
| Right Option : D | |||
| View Explanation | |||
Without performing actual addition and division find the quotient when the sum of 72 and 27 is divided by 11 | |||
| Right Option : B | |||
| View Explanation | |||
Without performing actual addition and division find the quotient when the sum of 28 and 82 is divided by 10. | |||
| Right Option : A | |||
| View Explanation | |||
Students / Parents Reviews [10]
My experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
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10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
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