Page 45 - SM inner class 8.cdr

Example 13. Is 314159 divisible by 9? the numbers must be divisible by 3 (divisibility
rule of 3)
Solution: 314159 has a digit sum of 3 + 1 + 4 +
For 136 5785x to be divisible by 3, 1 + 3 + 6 +
1 + 5 + 9 which is 23. 2 + 3 has a digit sum of 5,
x + 5 + 7 + 8 + 5 must be divisible by 3
And, since this single digit is not 9,
Þ 35 + x must be divisible by 3
Then 314159 is not a multiple of 9. No x =1 satisfies this condition

Example 14. If the 8 digit no 136x5785 is least value of x =1
divisible by 15 find the least value of x.
Solution: If the number is divisible by 15 it is
also divisible by 3. To be divisible by 3, sum of

E xercise 5.3

1. Check whether the given numbers are divis i ble by ‘2’ or not ?
(i) 273432 (ii) 100533 (iii) 784076 (iv) 24684
2. Check whether the given numbers are divis i ble by ‘3’ or not ?
(i) 3024 (ii) 1000 (iii) 412 (iv) 56240
3. Check whether the given numbers are divis i ble by ‘9’ or not ?
(i) 4808 (ii) 11124 (iii) 1089 (iv) 76728
4. 50B is a number divis i ble by 5, what might be the value of B ?
5. 2P is a number which is divis i ble by 2 and 3, what is the value of P?

6. A 3-digit number 4A3 is added to another 3-digit number 964 to give four digit number 13B7, which is
divisible by 9. Find (A + B).

7. Find all the possi ble values of y for which 43y2 is divis i ble by 3.

Summary
m Writing and understanding a 3-digit number in expanded form 100a + 10b + c. Where a, b, c digits a ­ 0, b, c
is from 0 to 9
m The given number is divisible by 5, only if the unit’s digit c = 0 or 5
m Cryptarithms are a type of mathematical puzzle in which the digits are replaced by symbols.
m If the given number is divisible by 2, it is possible only if the unit’s digit c = 0 or 2 or 4 or 6 or 8 ( even
number).

Review Exercise

1. If 5 A + B 3 = 65, then find the value of A and B.
2. If 6 A ´ B = A 8 B, then find the value of A – B.
3. Find the least value that must be given to number ‘a’ so that the number 91876a2 is divis i ble by 38.
4. If 1AB + CCA = 697 and there is no carry–over in addi tion, find the value of A + B + C.
5. 212 ´ 5 is a multi ple of 3. Find the value of x.
6. A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divis i -
ble by 9. Find the value of b – a.
7. Find the value of the letters in each of the follow ing ques tions.
85 C B A AB
(i) + A (ii) + C B A (iii) ´ 6
4
BC 3 1 A30 C 68

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Mathematics In Focus - 8