# Joy of Mathematics Class 6 Solutions Chapter 3

## Joy of Mathematics Class 6 Solutions Chapter 3 Integers

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 3 Integers. Here students can easily find step by step solutions of all the problems for Integers. 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 3 solutions. Here students will find exercise wise solutions for chapter 3 Exercise 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6

Integers Exercise 3.1 Solution :

Question no – (1)

Solution :

(a) + 15° C

(b) – 20° C

(c) – 700 Rs

(d) + 5000 m

(e) + 500 Rs

(e) – 50 m

Question no – (2)

Solution :

(a) +7

(b) -3

(c) +5

(d) 0

Question no – (3)

Solution :

(a)

 City : Temperature : Delhi + 23 °C Shimla – 2 °c Srinagar – 7°c Darjeeling – 3° c Chennai + 32°c

(b) Srinagar

(c) Srinagar < Darjeeling < Shimla < Delhi > Chennai

Question no – (4)

Solution :

 Integer 4 Integer 12 Integer 0 Integer – 5 Integer 0 Integer 1 Integer 45 Integer 1

Question no – (5)

Solution :

(a) – 3 < 2

(b) 0 < 5

(c) – 6 < 0

(d) – 5 < 0

(e) – 1 < 1

(f) 1 < 2

(g) – 6 < 0

(h) – 4 < 0

Question no – (6)

Solution :

(a) 2 > 1 > 0 > – 2 > – 3

(b) 5 > 4 > 3 > 2 > 1 > – 3

(c) 3 > 2 > 1 > 0 – 1 > – 2 > – 3

(d) 0 > – 1 > – 2 > – 3 > – 4 > – 5

(e) 3 > 2 > 1 > 0 > – 1

(f) 4 > 3 > 2 > 1

(g) 0 > – 1 > – 2 > – 3 > – 4 > – 5 > – 6

Question no – (7)

Solution :

Integers are,

= – 14, – 13, – 12, – 11, – 10

Integers are,

= – 16, – 17, – 18

Question no – (8)

Solution :

(a) Absolute value of 10 is 10

(b) Absolute value of – 10 is 10

(c) Absolute value of 0 is 0

(d) Absolute value of – 1 is 1

(e) Absolute value of 5 is 5

(f) Absolute value of – 12 is 12

Question no – (9)

Solution :

(a) 0 < 8

(b) – 5 < 5

(c) 8 > – 30

(d) – 10 – 16

(e) – 10 < – 5

(f) 0 > – 16

Question no – (10)

Solution :

(a) |4 + 3| = |7| = 7

(b) |- 8| = |8| = 8

(c) |6 + 2+ 5| = |13| = 13

(d) |8 – 4| = 4

(e) | – 8| – |- 3|

= 8 – 3

= 5

(f) |8| + |- 6| – |- 1|

= 8 + 6 – 1

= 13

Question no – (11)

Solution :

(a) Statement is – False

(b) Statement is – True

(c) Statement is – True

(d) Statement is – False

(e) Statement is – True

(f) Statement is – True

(g) Statement is – True

Question no – (12)

Solution :

(a) In an ascending order,

= -6, -3, 5, 10, 1 -121

(b) In an ascending order,

= -6, -5, 0, 7, 12

(c) In an ascending order,

= -11, -13, 3, 1 -71, 11

(d) In an ascending order,

= -30, -25, 0, 15, 50

Integers Exercise 3.2 Solution :

Question no – (1)

Solution :

(a) 5 + (– 5)

= 5 – 5

= 0

(b) 12 + 5

= 17

(c) – 15 + 6

= – 9

(d) – 15 + ( – 5)

= – 15

= – 20

(e) – 122 + (- 52)

= – 122 – 52

= – 174

(f) – 112 + 37

= – 75

Question no – (2)

Solution :

(a) -5 + 8

(b) 4 + (-8)

(c) – 4 + (- 7)

= – 4 – 7

= – 11

(d) 2 + (- 3) + 3

= 2 – 3 + 3

=- 1 + 3

= 2

Question no – (3)

Solution :

(a) 315 + 210 + (- 315)

= 535 – 315

= 220 …..(Associative)

(b) 222 + 0

= 222 …..(Identity property)

(c) 125 + 327 + 75

= 200 + 327

= 527 …..(Associative)

(d) 637 + 363 + 429

= 100 + 429

= 1429 ……(Associative)

(e) – 111 + 0 + 111

= – 111 + 1111

= 1000 ….(Identity)

(f) – 427 + 977 + 523

= 550 + 523

= 1023 ….(Associative)

Question no – (4)

Solution :

(a) 100 + (- 55) + (- 45)

= 100 – 55 – 45 (Associative)

= 45 – 45 (Identity)

= 0

(b) 1237 + (- 63) + ( – 937) + 547

= 1237 – 63 + (- 937) + 547

= 1174 – 937 + 547

= 237 + 547

= 784

(c) – 531 + (- 36) + 31 + (- 142)

= – 531 – 36 + 31 – 142

= – 567 + 31 – 142

= – 678

(d) – 53 + 40 + (- 402) + (- 68)

= – 13 – 402 – 68

= – 415 – 68

= – 483

(e) 271 + 100 + (- 17)

= 317 – 17

= 300

(f) – 45 + ( – 37) + (- 8) + 100

= – 82 + 92

= 10

Question no – (5)

Solution :

(a) The integer is = + 64

(b) The integer is = – 35

(c) The integer is = + 5

(d) The integer is = + 1

(e) The integer is = – 1

(f) The integer is = – 10

Question no – (6)

Solution :

(a) 3 × 2

= 2 × 3 + 3 × 2 + (- 2)

= 6 + 6 – 2

= 10

(b) 8 × (- 3)

= 2 × 8 + 3 × (- 3) + (3)

= 16 – 9 + 3

= 7 + 3

= 10

(c) – 3 × 5

= 2 × (- 3) + 3 × (5) + ( – 5)

= – 6 + 15 – 5

= 9 – 5

= 4

(d) 5 × 0

= 2 × 6 + 3 × 0 + (- 0)

= 10 + 0 – 0

= 10

Question no – (7)

Solution :

Distance,

= (+ 50 – 40)

= 10 km from starting point finally

Question no – (8)

Solution :

(a) Greater sum is 6.

(b) Pair of integer are,

= (- 3, 3) , (3 – 3), (2, – 2), (- 6 – 2, 2)

= (- 1, 1,) (1, – 1), (0, 0)

(c) Pair of integer are

= (- 1, -4), (- 3, – 2, (- 2, – 3), (3, 2), (2, 3)

Question no – (9)

Solution :

(a) False

(b) True

(c) False

(d) False

(e) False

Question no – (10)

Solution :

(a)

Integer is = 3

(b)

Integer is = – 5

(c) Move in Right side,

(d) Move in left Side,

Integers Exercise 3.3 Solution :

Question no – (1)

Solution :

(a) + 7 – (- 4)

= 7 + 4

= 11

(b) – 2 – 915)

= – 2 – 15

= – 17

(c) 10 – (25)

= 10 + 25

= 35

(d) 0 – (- 15)

= 0 + 15

= 15

(e) – 20 – 0

= – 20

(f) 7 – 12

= – 5

(g) 12 – 7

= 5

(d) – 15 – (- 12)

= – 15 + 12

= – 3

Question no – (2)

Solution :

(a) 2 from 8

= 8 – 2 = 6

(b) 8 from -2

= – 2 – 8

= – 10

(c) = – 3 – (- 5)

= – 3 + 5

= 2

Question no – (3)

Solution :

(a) – 7 – 8 (- 20)

= – 7 – 8 + 20

= – 15 + 20

= 5

(b) – 10 + 20 – 8 + (- 1)

= – 10 + 20 – 8 – 1

= 10 – 8 – 1

= 2 – 1

= 1

(c) – 7 (- 8) + 15

= – 7 – 8 + 15

= – 15 + 15

= 0

(d) 10 – (10) – (- 2)

= 10 + 10 + 2

= 22

Question no – (4)

Solution :

(a)  – 5 + (- 7) = – 12

(b) (- 239) + 216 = – 23

(c) 0 – (+ 176) = – 176

(d) – 26 + 26 = 0

(e) 425 – (425) = 0

(f) 728 + (- 372) = 356

Question no – (5)

Solution :

(a) Successor,

= 356 + 1

= 357

Predecessor,

= 356 – 1

= 355

(b) Successor

= – 342 + 1

= – 341

Predecessor –

= – 342 – 1

= – 343

(c) Successor,

= 960 + 1

= 961

Predecessor

= 960 – 1

= 959

(d) Successor,

= 0 – 1

= – 1

Predecessor,

= 0 + 1

= 1

(e) Successor

= 1 – 1

= 0

Predecessor

= 1 + 1

= 2

(f) Successor,

= (- 1 – 1)

= – 2

Predecessor,

= (- 1 + 1)

= 0

Question no – (6)

Solution :

Lost = – 1500 Rs

Gain = + 1200 Rs
————————————
= – 300 Rs

Loss = 300 Rs

Question no – (7)

Solution :

Other integer = 75 – (- 30)

= 75 + 30

= 105

Question no – (8)

Solution :

Sum = (19) + (- 11)

= – 19 – 11

= – 30

Now, (- 30) – 30

= – 30 – 30

= – 60

Question no – (9)

Solution :

= – 18 – ( – 53)

= – 18 + 53

= 35

Question no – (10)

Solution :

(a) – 26 – (- 14)

= – 26 + 14

= – 12

(b) – 21 – (- 24)

= – 21 + 24

= 6

(c) – 12 – (- 18)

= – 12 + 18

= 6

(d) 7 – (9)

= 7 + 9

= 16

(e) 20 – (- 4)

= 20 + 4

= 24

(f) – 12 – (- 20) – 5 + (- 7)

= – 12 + 20 – 5 – 7

= 8 – 5 – 7

= – 4

Question no – (11)

Solution :

(a) Statement is – True

(b) Statement is – False

(c) Statement is – False

(d) Statement is – True

(e) Statement is – True

Integers Exercise 3.4 Solution :

Question no – (1)

Solution :

(a) 4 × (- 15)

= – 60

(b) 12 × (- 4)

= – 40

(c) 5 × (- 6) × 7

= – 210

(d) (- 5) × 30 × – 6)

= 900

(e) (- 5) ×(- 5) × (- 5)

= – 125

(f) (- 4) × (- 5) × (- 6) × (- 7)

= (+ 20) × (+ 42)

= 840

Question no – (2)

Solution :

(a) (- 5) × 0 × (65) × (- 65)

= 0

(b) 356 × 430 – 356 × 432

= 356 (430 – 432)

= 356 × (- 2)

= – 712

(c) 312 × 212 + 218 × 88

= 212 (312 + 88)

= 212 × 400

= 84900

(d) 1846 × [154 – (- 1846)]

= 1846 × [154 + 1846]

= 1846 × [2000]

= 3692

(e) ( – 5) × (- 4) × (- 1) × (- 5)

= + 20 × (+ 5)

= 100

(f) – 30 × (- 5 + 25)

= – 30 × (20)

= – 600

Question no – (3)

Solution :

(a) The integer is 30

(b)  The integer is – 56

(c) The integer is – 1

(d) The integer is 0

Question no – (4)

Solution :

(a) L.H.S

= |(- 6) × 8]

= 1 – 48

= 48

R.H.S

= | 6 | × | 8|

= 6 × 8

= 48

LHS = RHS

(b) L.H.S = |( – 5) × (- 9)|

= | + 45|

= 45

R.H.S = |- 9| × |- 5|

= | + 45|

= 45

Question no – (5)

Solution :

(a) +

(b) +

(c) –

(d) +

Question no – (6)

Solution :

(a) (18 + 12) × 20

= 30 × 20

= 600

And, 18 × (12 – 20)

= 18 × (- 8)

= – 144

∴ (18 + 12) × 20 is greater

(b) In 1st product sign is negative

In 2nd product sign is positive

So, 6 × (9 × 15) is greater

(c) [(- 5) – 6] × ( – 8)

= [- 11] × (- 8)

= 88

And, (- 5) × (- 8) × (- 6)

= – 240

[(5 – 5) – 6] × ( – 8) is greater

Question no – (7)

Solution :

 x 3 2 1 0 -1 -2 -3 3 9 6 3 0 -3 -6 -9 2 6 4 2 -2 -4 -6 1 3 2 1 0 -1 -2 -3 0 0 0 0 0 0 0 0 – 1 – 3 -2 -1 0 1 2 3 – 2 – 6 -4 -2 0 2 4 6 -3 – 9 -6 -3 0 3 6 9

(a) Get 4 times

(b) Get 4 times

(c) The pair of integers are,

= (0, 3), (0, 2), (0, 1), (0, 0), (0, – 1), (0, – 2)

= (0, – 3), (3, 0), (2, 0), 91, 0), (- 1, 0), (- 2, 0), (- 3, 0)

Question no – (8)

Solution :

(a) The statement is – True

(b) The statement is – True

(c) The statement is – True

(d) The statement is – False

(e) The statement is – True

Question no – (9)

Solution :

Temperature change in 7 hours.

= {7 × (- 2)} °C

= – 14°C

Integers Exercise 3.5 Solution :

Question no – (1)

Solution :

(a) 48 ÷ (- 30

= – 16

(b) (- 125) ÷ (- 25)

= – 125/-25

= 5

(c) 120 ÷ 30

= 4

(d) – 75 ÷ (- 25)

= – 75 – 25

= 3

(e) 320/80

= 4

(f) – 440/11

= 40

(g) (- 525) ÷ (- 25)

= 525/25

(h) 180 ÷ ( 6)

= 180/- 6

= – 300

Question no – (2)

Solution :

(a) ?/- 12 = 4

=? = (4 × – 12)

= – 48

(b) ?/- 10 = 36

= ? = (36 × – 10)

= 360

(c) – 25/? = 1

= ? = – 25

(d) 0 ÷ ( – 36) = 0

(e) 63 ÷ – 7 = – 9

(f) 12 ÷ (- 3) = – 4

(g) 882 ÷ 21 = 42

882/42

= 21

(h) (360) ÷ (- 360) = 1

(i) 365 ÷ (- 5) = – 73

Question no – (3)

Solution :

(a) Given statements is – True

(b) Given statements is – False

(c) Given statements is – True

(d) Given statements is – False

(e) Given statements is – False

(f) Given statements is – False

(g) Given statements is – True

(h) Given statements is – True

Integers Exercise 3.6 Solution :

Question no – (1)

Solution :

8 ÷ (14 – 7 – 3) + 4

= 2 ÷ 4 + 4

= 2 + 4

= 6 ….(Simplified)

Question no – (3)

Solution :

5 ÷ (2 of 3 – 6 + 5)+ 8

= 5 ÷ (6 – 6 + 5) + 8

= 5 ÷ 5 + 8

= 1 + 8

= 9 ….(Simplified)

Question no – (4)

Solution :

12 – {16 – (6 + 2 – 6 – 3)}

= 12 – {16 – (6 + 2 – 2)}

= 12 – {16 – 6}

= 12 – 10

= 2 ….(Simplified)

Question no – (4)

Solution :

4 – {3 – 2 + (5 – 4 + 1)}

= 4 – {1 + 2}

= 4 – 3

= 1  ….(Simplified)

Question no – (5)

Solution :

7 – [13 – {52 – (81 – 72 – 35)}]

= 7 – [13 – {52 – 9- 26)}

= 7 – [13 – 78]

= 7 – [- 65]

= 7 + 65

= 72  ….(Simplified)

Question no – (6)

Solution :

7 – [6 {5 + (2 – 3 + 5)

= 7 – [6 – {5 + 4}

= 7 – [6 – 9]

= 7 – (- 3)

= 7 + 3

= 10  ….(Simplified)

Question no – (7)

Solution :

20 + ({10 – 5 (7 – 3 × 2)}

= 20 + {10 – 5 + 97 – 6)

= 20 + {10 – 5 + 13

= 20 + {6}

= 26  ….(Simplified)

Question no – (8)

Solution :

3 –[5 – {2 – (2 + 5 ÷ 7 × 3)}]

= 3 – [5 –{2 – (7 ÷ 7 × 3)}]

= 3 – [5 – {2 – 3}]

= 3 – [5 + 1]

= 3 – 6

= – 3 ….(Simplified)

Question no – (9)

Solution :

2 × [29 – {5 + (12 – 3 + 5)}]

= 2 × [29 – {5 + (12 – 8)}]

= 2 × [29 – ]

= 2 × 20

= 40 ….(Simplified)

Question no – (10)

Solution :

(15 – 10) × [15 – {3 + (3 – 4 + 7)}]

= (15 – 10) × [15 – {3 + 93 – 11)}

= (15 – 10) × [{15 – {3 – 8}]

= 5 × [15 + 5]

= 5 × 20

= 100 ….(Simplified)

Next Chapter Solution :

👉 Chapter 4 👈

Updated: June 22, 2023 — 3:46 pm