Joy of Mathematics Class 6 Solutions Chapter 2

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Joy of Mathematics Class 6 Solutions Chapter 2 Number System

Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Joy of Mathematics Class 6 Book, Chapter 2 Number System. Here students can easily find step by step solutions of all the problems for Number System. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Students will get chapter 2 solutions. Here students will find exercise wise solutions for chapter 2 Exercise 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 and 2.9

Number System Exercise 2.1 Solution : 

Question no – (1)

Solution :

(a) 56,004 = Fifty six thousand four.

Fifty six thousand four.

(b) 8,05,065 = Eight lakh five thousand sixty five.

Eight hundred five thousand sixty five.

(c) 56,23,008 = Fifty six lakh twenty three thousand eight.

Five million six hundred twenty three thousand eight.

(d) 5,60,002 = Five lakh sixty thousand two.

Five hundred sixty thousand two.

(e) 32,10,10,010 = Thirty two crore ten lakh ten thousand ten.

Three hundred twenty one million ten thousand ten.

Question no – (2)

Solution :

(a) 70000000 + 6000000 + 300000 + 400 + 80 + 9

= 76030489.

∴ Seven crore sixty lakh thirty thousand four hundred eighty nine.

(b) 6,4005,061 = Six crore forty lakh five thousand sixty one.

(c) 90,07,06052 = Ninety crore seven lakh six thousand fifty two.

(d) 20,40,08,999 = Twenty crore forty lakh eight thousand nine hundred ninety nine.

Question no – (3) 

Solution :

(a) 1,00202,550

(b) 1,005,010,005

Question no – (4)

Solution :

Required numbers are, 306, 603, 360, 630.

Question no – (5)

Solution :

Numbers are, 404, 414, 424, 434, 444, 454, 464, 474, 484, 494.

Question no – (6)

Solution :

1^st term = 105

Difference = 5

∴ It occurs 40 times.

Question no – (7)

Solution :

The required numbers are,

666, 665, 660, 600, 650, 605, 606, 656, 555, 556, 550, 566, 500, 560, 506, 505, 565

Question no – (8)

Solution :

The required numbers are,

111, 113, 115, 155, 133, 153, 151, 135, 131, 333, 335, 331, 355, 311, 351, 315, 353, 313, 555, 551, 553, 511, 513, 533, 531, 535.

Question no – (9)

Solution :

Largest number is = 95432

Smallest number is = 23459

Question no – (10)

Solution :

Smallest = 203579

Largest = 975320

Question no – (11)

 

Solution :

(a) Place value of 4 is 4000000

(b) Place value of 4 is 40000000

(c) Place value 0f 4 is 400

(d) Place value of 4 is 400000000

Question no – (12) 

Solution :

(a) Sum = (200000 + 2) = 200002

(b) Sum = (20000 + 2) = 20002

(c) Sum = (20000 + 2) = 20002

(d) Sum = (2000 + 2) = 2002

Question no – 13

Solution :

Product = (600000 × 600)

= 360000000

Question no – 14

Solution :

Largest number is = 98765432

Smallest number is = 10234567

Number System Exercise 2.2 Solution : 

Question no – (1)

Solution :

(a) Successor is (2000569 + 1)

= 2000570

(b) Successor is = (5648392 + 1)

= 5648393

(c) Successor is = (743659520 + 1)

= 743659521

(d) Successor is = (569354525 + 1)

= 569354526

Question no – (2)

Solution :

(a) Predecessor is = (9000009 – 1)

= 9000008

(b) Predecessor is = (593946539 – 1)

= 593946538

(c) Predecessor is = (727272727 – 1)

= 727272726

(d) Predecessor is = (305645321 – 1)

= 305645320

Question no – (3)

Solution :

(a) All natural numbers between 100 and 120 are,

101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119.

(b) Between 10 and 15 numbers are 11, 12, 13, 14.

(c) Between 405 and 409 are 406, 407, 408.

(d) Numbers are 501, 502, ….., 600

Question no – (4)

Solution :

(a) Three consecutive numbers are 199, 200, 201.

(b) Consecutive numbers are 347, 346, 345, 344.

Question no – (5)

Solution :

= (632 – 621) = (12 × 100) Rs.

= 1200 Rs.

Question no – (6)

Solution :

(a) 12562 < 13265

(b) 312643 > 126656

(c) 734999 > 87100

(d) 129999 < 210000

Question no – (7)

Solution :

In descending order, 8, 7, 5, 4, 0.

Question no – (8)

Solution :

In Ascending order,

6397, 53800, 112535, 361745, 699451

Question no – (9)

Solution :

(a) The numbers are total is 9.

(40 – 30) – 1

= 10 – 1

= 9

(b) Numbers are = 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40

Total = 11

Question no – (10) 

Solution :

(a) Given statement is – True

(b) Given statement is – False

(c) Given statement is – True

(d) Given statement is – False

(e) Given statement is – True

Number System Exercise 2.3 Solution : 

Question no – (1) 

Solution :

(a) 45 + 37 = 37 + 45

(b) 6 + 0 = 0 + 6 = 6

(c) 55 + 25 = 25 + 55

(d) (1 + 2) + 7 = 1 + (2 + 7)

(e) (31 + 36) + 13 = 31 + (36 + 13)

(f) (9 + 10) + 11 = 9 + (10 + 11)

Question no – (2) 

Solution :

(a) 425 + 375

= 800

And, 375 + 425

= 800

∴ Both are equal.

(b) 111 + 333

= 444

and, 333 + 111

= 444

(c) 99 + 101

= 200

and, 101 + 99

= 200

(d) 73 + 137

= 210

and, 137 + 73

= 210

(e) 25 + 27

= 52

and,27 + 25

= 52

(f) 69 + 131

= 200

and, 131 + 69

= 200

Question no – (3)

Solution :

(a) 38, 347, 62

= 347 + (62 + 38)

= 347 + 100

= 447

(b) 75 + (107.9 + 121)

= (75 + 1200)

= 1275

(c) (129 + 421) + (37 + 113)

= 550 + 150

= 700

(d) (17 + 23) + (227 + 413)

= 100 + 640

= 740

Question no – (4)

Solution :

(a) 45 + 37 = x + 45

=> x = 37

(b) x + 35 = 35 + 49

=> x = 49

(c) 37 + 0 = 45 + x = 45

=> x = 45 – 45

= 0

(d) (41 + 19) + 140 = x + (19 + 140)

=> 60 + 140 = x + 159

=> x = 200 – 159

= 41

Question no – (5)

Solution :

(a) Commutative property

(b) Commutative property

(c) Additive Identity

(d) Associative property

(e) Commutative property

(f) Associative property.

Question no – (6)

Solution :

(a) Given statement is – False

(b) Given statement is – True

(c) Given statement is – False

(d) Given statement is – True

(e) Given statement is – False

(f) Given statement is – False

Number System Exercise 2.4 Solution : 

Question no – (1) 

Solution :

(a) 341

– 255
———————–
86

(b) 5764

– 3223
———————–
2541

(c) 7896

– 3959
———————–
3937

(d) 719

– 162
———————–
557

(e) 8432

– 4558
———————–
3874

Question no – (2)

Solution :

Difference = (100000 – 99999)

= 1

Question no – (3)

Solution :

Difference = (1000000 – 99999)

= 900001

Question no – (4)

Solution :

Money left

= (32500 – 9999) Rs

= 22499 Rs

Question no – (5)

Solution :

Money left = 2500 – (1000 + 560 + 800)

= 2500 – 2360

= 140

Question no. – 6

Solution :

Number of females will be,

= (6,83,562 – 4,32169)

= 251393

Question no – (7)

Solution :

= (975689 + 4563 – 8976)

= 971276

Question no – (8)

Solution :

Watch movie channels

= 6900 – (1200 + 3157)

= 6900 – 4357

= 2543

Question no – (9)

Solution :

Other number will be,

= (9395 – 1999)

= 7396

Question no – (10)

Solution :

Number will be,

= (48367 – 1349)

= 47018

Question no – (11)

Solution :

No. is = (45967 – 29461)

= 16506

Question no – (12) 

Solution :

(a) The statement is – False

(b) The statement is – True

(c) The statement is – True

(d) The statement is – False

(e) The statement is – False

(f) The statement is – True

Number System Exercise 2.5 Solution : 

Question no – (1)

Solution :

(a) 49 by 1003

= (50 – 1) × 1003

= (1003 × 50) – (1003 × 1)

= 50150 – 1003

= 49147

(b) 49 × 998

= 49 × (1000 – 2)

= (49 × 1000) – (49 × 2)

= 49000 – 98

= 48902

(c) 87 by 101

= 87 × (100 + 1)

= (87 × 100) + (87 × 1)

= 8700 + 87

= 8787

(d) 87 × 99

= 87 × (100 – 1)

= (87 × 100) – (87 × 1)

= 8700 – 87

= 8613

Question no – (2)

Solution :

(a) (4 × 357 × 25)

= (4 × 25) × 357

= 100 × 357

= 35700

(b) (8 × 1635 × 125)

= (8 × 125) × 1635

= 1000 × 1635

= 1635000

(c) 625 × 312 × 80

= (625 × 80) × 312

= 50,000 × 312

= 15600000

(d) 25 × 6 × 5 × 8

= (25 × 8) × (6 × 5)

= 200 × 30

= 6000

Question no – (3)

Solution :

(a) 273 × 8 + 2 × 273

= 273 (8 + 2)

= 273 × 10

= 2730

(b) 112 × 97 + 3 × 112

= 112 (97 + 3)

= 112 × 100

= 11200

(c) 9876 × 6789 – 9876 × 5789

= 9876 (6789 – 5789)

= 9876 × 1000

= 9876000

(d) 4897 × 999 + 4897

= 4897 (999 + 1)

= 4897 × 1000

= 4897000

Question no – (4)

Solution :

(a) (9999 × 100)

= 999900

(b) (9999 × 999)

= 9999 × (1000 – 1)

= (9999 × 1000) – (9999 × 1)

= 9999000 – 9999

= 9989001

Question no – (5)

Solution :

(a) 4355 × 365 = 365 × 4355

(b) 10 × 100 × 100 = 100000

(c) 49 × 63 + 63 × 51 = 63 × (49 + 51)

(d) 835 × 98 + 2 × 835 = 835 × (98 + 2)

(e) 891 × 99 + 891 = 891 (99 + 1)

(f) 222 + 333 + 444 = 111 × (2 + 3 + 4)

(g) 4 × 8444 = 16 × (200 + 111)

(h) 45 × 500 × 301 × 0 = 0

Question no – (6)

Solution :

Total cost = (32615 × 99) Rs/-

= 32615 × (100 – 1) Rs

= 32615 × 100 – 32615

= 3261500 – 32615

= 3228885 Rs/-

Question no – (7)

Solution :

Total Amount = 197 × 125

= (200 – 3) × 125

= (125 × 200) – (125 × 3)

= 25000 – 375

= 24625 Rs

Question no – (8)

Solution :

Total Amount paid,

= (20 × 18 + 20 × 17) Rs

= (360 + 340)

= 700 Rs

Question no – (9)

Solution :

Product of two whole no is zero. Because one of the no is zero so,

a × 0 = 0 always.

Question no – (10)

Solution :

The no.’s are (1 × 1) = 1

Number System Exercise 2.6 Solution : 

Question no – (1) 

Solution :

(a) 2436 ÷ 7

∴ Now, (7 × 348)

= 2436

(b) 97629 ÷ 23 

Now, (23 × 423)

= 9729

(c) 52029 ÷ 123

∴ (423 × 123)

= 520

(d) 40180 ÷ 164 

Now, (245 × 164)

= 40180

(e) 34750 ÷ 139 

Now, (139 × 250)

= 34750

(f) 7303 ÷ 109 

Now, (109 × 69)

= 7303

Question no – (2)

Solution :

No, it is not true for any distinct whole numbers.

Question no – (3)

Solution :

(a) 425 ÷ 1

= 425

(b) 0 ÷ 425

= 0

(c) 315 + 850 ÷ 85

= 315 + 10

= 325

(d) 601 – 600 ÷ 600

= 601 – 1

= 600

(e) 312 ÷ 312 – 213 ÷ 213

= 1 – 1

= 0

(f) 1200 – 200 × (150 ÷ 75)

= 1200 – 200 × 2

= 1200 – 400

= 800

Question no – [4]

Solution :

Students in each row,

= (1680 ÷ 35)

= 48 students

Question no – [5]

Solution :

Bags required,

= (840 ÷ 20)

= 42 bags.

Question no – (6)

Solution :

∴ The required number is 20

(1000 – 20)

= 980

Question no – (7)

Solution :

Now, (35 – 20) = 15

∴ The required number is 15.

Question no – (8)

Solution :

Now, (75 – 25) = 50

∴ The least number is

= (10000 + 50)

= 10050

Question no – (9)

Solution :

∴ Required Number will be,

= (99999 – 25)

= 99975

Question no – (10)

Solution :

Divided = 35 × 30 + 12

= 1050 + 12

= 1062

∴ Number is 1062

Question no – (11)

Solution :

Senior citizens = 975176 ÷ 15

= 65011.73

= 65011

Question no – (12)

Solution :

(a) This statement is – False

(b) This statement is – False

(c) This statement is – False

(d) This statement is – True

(e) This statement is – False

(f) This statement is – True

(g) This statement is – False

Number System Exercise 2.7 Solution : 

Question no – (1)

Solution :

Total friends = 20

Items price = 50 Rs (Let)

∴ Total expenditure,

= (50 × 20) Rs

= 1000 Rs

Question no – (2)

Solution :

(a) 4990 + 605

= 5000 + 600

= 5600

(b) 9945 – 390

= 9950 – 400

= 9550

(c) 449 × 29

= 450 × 30

= 13500

Question no – (3) 

Solution :

Total population = 5000

Daily, wheat = 300gm × 7 = 2100gm

Rice = 100g × 7 = 700gm

Sugar = 50g × 7 = 350gm

Pulses = 50g × 7 = 350gm

∴ Wheat total

= (2.1 × 5000)

= 10500kg

= 105 quintal

Rice total, 

= (0.7 × 5000)

= 3500

= 35 quintal

Sugar,

= (0.350 × 5000)

= 17500

= 18 quintal

Pulses,

= 18 quintal

Number System Exercise 2.8 Solution : 

Question no – (1) 

Solution :

The next two terms are

= 123456 × 8 + 6

= 987654

and, 1234567 × 8 + 7

= 9876543

Question no – (2)

Solution :

The next two terms are,

1 + 3 + 5 + 7 + 9 + 11

= 36

= 6 × 6

1 + 3 + 5 + 7 + 9 + 11 + 13

= 49

= 7 × 7

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15

= 64

= 8 × 8

Next Chapter Solution :  

👉 Chapter 3 👈