# Maths Ace Class 7 Solutions Chapter 1

## Maths Ace Class 7 Solutions Chapter 1 Integers

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Maths Ace Prime Class 7 Math Book, Chapter 1, Integers. Here students can easily find step by step solutions of all the problems for Integers, Exercise 1.1, 1.2, 1.3, 1.4, 1.5 and 1.6 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 1 solutions.

Integers Exercise 1.1 Solution :

Question no – (1)

Solution :

(a) – 8, 11, 14, 0, – 7, – 3 – 1

= – 8, – 7, – 3, – 1, 17, 14

(b) 11, – 11, – 8, – 13, 0, 2, 9

= – 13, – 11, – 8, 0, 2, 9, 11

Question no – (2)

Solution :

(a) |- (- 3)

= |- (- 3) = 3

(b) |8 – 2|

= |8 – 2| = 6

(c) |16 + 5|

= |11| = 11

(d) |(- 20) – (- 20)|

= |- 20 + 20|

= 0

Question no – (3)

Solution :

(a) Given, Additive invers of 42 ____ – 15 – (- 3)

= – 15 + 3 = – 12

– 42 < – 12

(b) Given, Smallest positive integer _____ largest negative integer.

= Smallest positive integer = 1

= Largest negative integer = – 1

(c) Given, – 2 + (- 20) ____ (- 20) – (- 2)

= – 2 – 20 ___ – 20 + 2

= – 22 < – 18

(d) Given, Sum of 16 and (- 30) ____ sum of (- 16) and 30

= 16 + (- 30) __ 16 + 30

= 16 – 30 __ – 16 + 30

= – 4 < 14

Question no – (4)

Solution :

(a) (- 14) + (- 31)

= – 14 – 31

= – 45

(b) 124 + (- 136)

= 124 – 136

= – 12

(c) (- 510) + 300

= – 510 + 300

= – 210

(d) {3 + (- 7)} + (- 6)

= – 4 – 6

= – 10

Question no – (5)

Solution :

(a) (- 2) from 15

= – 17

(b) (- 74) from (- 21)

= – 95

(c) 101 from (- 12)

= 101 + 12

= 113

(d) (- 38) from (- 102)

= – 38 – 102

= – 140

Integers Exercise 1.2 Solution :

Question no – (2)

Solution :

(a) Given, (- 2) × (- 5) × 27

= 270

(b) Given, 8 × (- 10) × 12

= 960

(c) Given, (- 4) × 5 × (- 6) × (- 2)

= – 240

(d) Given, (- 5) × (- 2) × (- 6) × (- 8)

= 480

Question no – (3)

Solution :

(a) 0 ÷ (- 8)

= 0

(b) 18 ÷ (- 6)

= – 3

(c) (- 81) ÷ (- 3)

= 27

(d) 18 ÷ (- 6)

= – 9

(e) (- 99) ÷ 33

= – 3

(f) 95 ÷ (- 19)

= – 5

Question no – (4)

Solution :

(a) (- 105) ÷ 21

= – 5

(b) (- 90) ÷ (- 15)

= 4

(c) 1728 ÷ (- 12)

= – 144

(d) (- 243) ÷ 9

= – 27

(e) (- 810) ÷ (- 9)

= – 90

(f) (- 126) ÷ 18

= – 7

Question no – (5)

Solution :

(a) (-9) × 0 × 13 = – 117

(b) (- 1) × (- 1) × 1 = 1

(c) 26 ÷ 26 = 1

(d) (- 15) ÷ 15 = – 1

(e) 13 ÷ (- 13) =- 1

(f) (- 35) ÷ (- 1) = 35

Question no – (6)

Solution :

(a) 6 × (- 12)

= – 72

(b) (- 9) × (19)

= – 171

(c) (- 81) ÷ 9

= – 9

(d) (- 169) ÷ (- 13)

= 13

Question no – (7)

Solution :

= (- 6) × 12 = – 72

The product of 6 negative and 12 positive integers is = – 72

Integers Exercise 1.3 Solution :

Question no – (1)

Solution :

(a) (- 5) + (- 8) = (- 8) + ____

= – 5

(b)  – 53 + ____ = – 53

= 0

(c) 17 + ___ = 0

= – 17

(d) {13 + (- 12)} + ______ = 13 + {(- 12) + (- 7)}

= – 7

(e) (- 4) + {15 + (- 3)} = {(- 4) + 15} + ____

= – 3

(f) {(- 8) + (- 3)} + (- 12)

= – 12

= (- 8) + {____ + (- 3)}

= – 12

Question no – (2)

Solution :

(a) (18 – 3) + 5 = 18 – (3 + 5) → True

(b) (76 + 4) + 20 = 76 (20 + 4) → True

(c) 346 – 124 = 124 – 346 → False

(d) 56 + {(- 90) + 7}

= {56 + (- 90)} + 7 → True

(e) (234 + 162) – 123

= 234 – (123 + 162) → True

(f) 890 – 0 = 889 → False

Question no – (3)

Solution :

(a) (- 6) + (- 17) + (- 4) + (- 3)

Now,

= (- 6) + (- 17) + (- 4) + (- 3)

= – (6 + 17 + 4 + 3)

= 30

(b) (- 79) + 56 + (- 21) + 4

Now,

(- 79) + 56 + (- 21) + 4

= 60 + (79 – 21) = 60 – 100

= – 40

(c) 87 + (- 7) + 13 (- 3)

Now,

87 + (- 7) + 13 (- 3)

= 100 + (- 10)

= 90

(d) 64 + (- 176) + (- 24) + 36

Now,

= 64 + (- 176) + (- 24) + 36

= 100 + (- 176 – 24)

= 100 – 299

= – 100

Question no – (4)

Solution :

 Round A B C 1st 34 15 x 2nd 12 5 x 3rd 3 – 32 x Total 49 – 12 x

A was the winner of quiz

Question no – (5)

Solution :

According to the questions,

[(- 16) + 5 = (- 16) + (6 + 5)

L.H.S.

= 916 + 6) + 5

= – 19 + 5 = – 5

R.H.S.

= (- 16) + (6 + 5)

= – 16 + 11 = – 5

L.H.S = R.H.S …….[Proved]

Integers Exercise 1.4 Solution :

Question no – (1)

Solution :

(a) (- 60) × (- 4) × 5 (- 25)

= – 30,000

(b) 125 × 5 × (- 8) × (- 20)

= 100,000

(c) 30 × 12 × (- 5) × 40

= – 72,000

(d) 82 × 20 × (- 5)

= – 8, 200

Question no – (2)

Solution :

According to the question,

(a) 27 × [6 + 9- 4)] = [27 × 6] + [27 × (- 4)]

L.H.S

= 27 × [6 + (- 4)]

= 27 × (- 2)

= – 54

R.H.S

= [27 × 6] × [27 × (- 4)]

= 162 × 108

= 17,496

Question no – (3)

Solution :

(a) (- 3) × ____ = 36

= – 12

(b) 15 × ____ = 0

= 0

(c) ____ × (- 7) = (- 7)

= 1

(d) (- 75) ÷ (- 12) = ____

= – 8

(e) (- 75) ÷ ____  = – 1

= – 75

(f) ____ ÷ (- 245) = 0

= 0

(g) (- 14) ÷ ____ not defined

= 0

Question no – (4)

Solution :

(a) Given, x = – 2, y = 3 and z = – 4

L.H.S

= (x × y) × z

= (- 2 × 3) × (- 4)

= (- 6) × (- 4)

= 24

R.H.S

= x × y (y × z)

= – 2 × (3 × 4)

= – 2 × (- 12)

= 24

(b) x = – 5, y = – 12 and z = 8

L.H.S

= (x × y) × z

= (- 5 × – 12) × 8

= 60 × 8

= 480

R.H.S

= x × (y × z)

= – 5 × (- 12 × 8)

= – 5 × (- 96)

= 480

Question no – (5)

Solution :

(a) Given, (- 876) × 9 + (- 876)

= – 876 (9 + 1)

= – 876 × 10

= 8760

(b) Given, (- 2315) × 98 + (- 2315) × 2

= – 2315 (98 + 2)

= – 2315 × 100

= – 231500

(c) Given, (- 678) × 8 + 576 × (- 92)

= – 678 (49 + 1)

= – 678 × 50

= – 33,900

(d) Given, (- 576) × 8 + 576 × (92)

= – 576 (8 + 92)

= – 576 + 100

= – 57600

(e) Given, 1100 × (- 102) – (- 1100) × 2

= 100 (102 – 2) = 1100 × 100

= 110000

(f) Given, (- 891) × 93 – (- 891) × 3

= – 891 × (93 – 3)

= – 891 × 90

Question no – (6)

Solution :

(a) (3 + 2) + 4 = 3 + (2 + 4)

= Associative property of addition integer

(b) 210 × 0 = 0

= Property of zero

(c) 968 × 1 = 968

= Multiplicative identity

(d) 81 × (50 – 15) = 81 × 50 – 81 × 15

= Distributive property of multiplication of integers over subtraction.

(e) 325 + 800 + 275 = 800 + 600

= Associative property of addition of integers.

(f) 195 × (10 – 6) = 195 × 10 – 195 × 6

= Distributive property of multiplication of integers over subtraction.

Integers Exercise 1.5 Solution :

Question no – (1)

Solution :

(a) 83 – [29 – {6 ÷ 3 – (6 – 9 ÷ 3) ÷ 3 }]

= 83 – [29 – {2 – (6 – 3) ÷ 3}]

= 83 – [29 – {2 – 3 ÷ 3}]

= 83 – [29 – {2 – 1}

= 83 – [29 + 1]

= 83 – 30

= 53

(b) [87 – 12 ÷ 3 of 4] + (37 – 29) × 4

= (87 – 4 × 4) + (8 × 4)

= (87 – 16) + 12

= 71 + 12

= 83

(c) 500 – [80 + {20 – (60 – 50)}]

= 500 – [180 + (20 – 10)

= 500 – [180 + 10]

= 500 – 170

= 330

(d) (- 21) ÷ [16 + (- 13)] + (- 5)

= – 21 ÷ 3 – 5

= – 7 – 5

= – 12

(e) (- 20) + (- 4) ÷ (- 1) ÷ (- 8)

= 80 ÷ 8

= 10

(f) (- 7) × (- 15) ÷ 3 + (- 2) × 6

= 105 ÷ 3 – 12

= 35 – 12

= 23

(g) 100 × (- 10) + [300 ÷ {100 – (100 – 50)}]

= – 100 + [300 ÷ {100 – 50}]

= – 1000 + [300 ÷ {1– – 50}]

= – 100 + [300 ÷ 50]

= – 1000 + 6

= – 994

Integers Exercise 1.6 Solution :

Question no – (1)

Solution :

= 250 – 600

= – 300

So, Its new position is – 300 feet.

Question no – (2)

Solution :

As per the question,

Winter day temperature = 5°C

Midnight temperature dropped = 12°C

Now,

= 5°C – 12°C

= – 7°C

So, the temperature at midnight was – 7°C

Question no – (3)

Solution :

The sum of integers is,

= – 250 – 120

= – 370

So, the other integer is – 370.

Question no – (4)

Solution :

(a) Mark for 12 correct answers

= 12 × 4

= 48

= Ruchi scored = 20 marks

Ruchi incorrect narks

= 48 – 20

= 28

No of Ruchi questions

= 28/2

= 14

(b) Rohit’s correct mark

= 7 × 4

= 28

Rohit’s incorrect mark

= 28 – (- 6)

= 28 + 6

= 3

No of incorrect work = 34/x

= 17

Question no – (5)

Solution :

As per the question,

1st day deposit = 5000

2nd day withdraw = 2400

Now, bank balance,

= 500 – 2.400

= 2600

3rd again deposit = 1800

Now, his bank balance

= 2600 + 1800

= 4400

Therefore, his balance at the end of the third day was 4400 Rs.

Question no – (6)

Solution :

The product of two negative integers is,

420/- 5

= – 84

So, the other integer is – 84

Next Chapter Solution :

Updated: June 16, 2023 — 3:15 pm