ML Aggarwal Playing with Numbers Exe-5.3 Class 8 ICSE Ch-5 Maths Solutions. We Provide Step by Step Answer of Exe-5.3 Questions for Playing with Numbers as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-8.
ML Aggarwal Playing with Numbers Exe-5.3 Class 8 ICSE Maths Solutions
| Board | ICSE |
| Publications | Avichal Publishig Company (APC) |
| Subject | Maths |
| Class | 8th |
| Chapter-5 | Playing with Numbers |
| Writer | ML Aggarwal |
| Book Name | Understanding |
| Topics | Solution of Exe-5.3 Questions |
| Edition | 2023-2024 |
Playing with Numbers Exe-5.3
ML Aggarwal Class 8 ICSE Maths Solutions
Page-93
Question 1. Which of the following numbers are divisible by 5 or by 10:
(i) 87035
(ii) 75060
(iii) 9685
(iv) 10730
Answer :
A number is divisible by 5 if its unit digit is 5 or 0.
A number is divisible by 10 if its unit digit is 0.
So, 87035, 75060, 9685, 10730 are all divisible by 5.
75060 and 10730 are divisible by 10.
Question 2. Which of the following numbers are divisible by 2, 4 or 8:
(i) 67894
(ii) 5673244
(iii) 9685048
(iv) 6533142
(v) 75379
Answer :
A number is divisible by 2 if its unit digit is 2, 4, 6, 8 or 0.
A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
So Number 67894, 5673244, 9685048, 6533142 are divisible by 2.
Numbers, 5673244, 9685048 are divisible by 4 and numbers 9685048 is divisible by 8.
Question 3. Which of the following numbers are divisible by 3 or 9:
(i) 45639
(ii) 301248
(iii) 567081
(iv) 345903
(v) 345046
Answer :
A number is divisible by 3 if the sum of its digits is divisible by 3.
A number is divisible by 9 if the sum of its digits is divisible by 9.
So the numbers 45639, 301248, 567081, 345903 are divisible by 3.
And 49639, 301248, 467081 are divisible by 9.
Question 4. Which of the following numbers are divisible by 11:
(i) 10835
(ii) 380237
(iii) 504670
(iv) 28248
Answer :
A number is divisible by 11 if the difference of the sum of digits at the odd places and sum of the digits at even places is zero or divisible by 11.
So the numbers 10835, 380237, 28248 are divisible by 11.
Question 5. Which of the following numbers are divisible by 6:
(i)15414
(ii) 213888
(iii) 469876
Answer :
A number is divisible by 6 if it is divisible by 2 as well as by 3.
So the numbers 15414 and 213888 are divisible by 6.
Question 6.
(i) If 34x is a multiple of 3, where x is a digit, what is the value of x?
(ii) If 74×5284 is a multiple of 3, where x is a digit, find the value(s) of x.
Answer :
(i) 34x is a multiple of 3
If 3 + 4 + x = 7 + x is divisible by 3
x + 7 = 9
x = 9 – 7
= 2
∴ x = 2, 5, 8
(ii) 74 × 5284 is divisible by 3
7 + 4 + x + 5 + 2 + 8 + 4 is divisible by 3
30 + x is divisible by 3
∴ x = 0, 3, 6, 9
Question 7. If 42z3 is a multiple of 9, where z is a digit, what is the value of z?
Answer :
42z3 is a multiple of 9
4 + 2 + z + 3 is divisible by 9
9 + z is divisible by 9
So either 9 + z = 9 or 9 + z = 0
z = 9 + 9 = 18, or z = 9 – 9 = 0
∴ z = 0, 9
Question 8. In each of the following replace * by a digit so that the number formed is divisible by 9:
(i) 49 * 2207
(ii) 5938 * 623
Answer :
(i) 49 × 2207 is divisible by 9
4 + 9 + x + 2 + 2 + 0 + 7 is divisible by 9
24 + x is divisible by 9
24 + x = 27
x = 27 – 24
= 3, which is divisible by 9
∴ x = 3
(ii) 5938 × 623 is divisible by 9
5 + 9 + 3 + 8 + x + 6 + 2 + 3 is divisible by 9
36 + x is divisible by 9
So, 36 + x = 36 or 45
x = 36 – 36 = 0 or x = 45 – 36 = 9
∴ x = 0, 9
Question 9. In each of the following replace * by a digit so that the number formed is divisible by 6:
(i) 97 * 542
(ii) 709 * 94
Answer :
(i) 97 × 542
Divisible by 6
It is divisible by 2 and 3
Since its unit digit is 2
∴ It is divisible by 2.
Divisible by 3
its sum of its digits 9 + 7 + 5 + 4 + 2 = 27 [which is divisible by 3]
27 + ‘*’ = 27, or 30, 33, 36
∴ The ‘*’ place can be replaced by 0 or 3 or 6 or 9.
(ii) 709 × 94
Divisible by 6
It is divisible by 2 and 3
We know that its unit digit is 4
∴ It is divisible by 2
Divisible by 3
its sum of its digits = 7 + 0 + 9 + 9 + 4 + * = 29 + * [which is divisible by 3]
29 + * = 30, or 33, or 36
∴ The ‘*’ place can be replaced by 1 or 4 or 7.
Playing with Numbers Exe-5.3
ML Aggarwal Class 8 ICSE Maths Solutions
Page-94
Question 10. In each of the following replace * by a digit so that the number formed is divisible by 11:
(i) 64*2456
(ii) 86*6194
Answer :
(i) 64 × 2456
Divisible by 11
The difference between the sum of digits of odd places and sum of digits of even place is divisible by 11or it is zero.
6 + 4 + * + 6 – 5 + 2 + 4 [which is divisible by 11]
16 + * – 11 is divisible by 11
5 + x is divisible by 11
∴ * is 6.
(ii) 86 × 6194
Divisible by 11
The difference between the sum of digits of odd places and sum of digits of even places is divisible by 11 or it is zero.
4 + 1 + * + 8 = 13 + *
9 + 6 + 6 = 21
21 – (13 + *) is divisible by 11
21 – 13 – * is divisible by 11
8 – * is divisible by 11
∴ * is 8.
— : End of ML Aggarwal Playing with Numbers Exe-5.3 Class 8 ICSE Maths Solutions :–
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