**Rd Sharma Solutions Class 7 Chapter 1 Integers**

Welcome to NCTB Solution. Here with this post we are going to help 7th class students for the Solutions of Rd Sharma Class 7 Mathematics, Chapter 1, Integers. Here students can easily find Exercise wise solution for chapter 1, Integers. Students will find proper solutions for Exercise 1.1, 1.2, 1.3 and 1.4. Our teachers solved every problem with easily understandable methods so that every students can understand easily. Here all solutions are based on the CBSE latest curriculum.

**Integers Exercise 1.1 Solution**

**Question no – (1) **

**Solution : **

**(i) 12 × 7**

= 84

Thus, the product is 84

**(ii) (- 15) × 8**

= – 120

Hence, the product is -120

**(iii) (- 25) × (- 9)**

= 225

So, the product is 225

**(iv) 125 × (- 8)**

= -1000

Therefore, the product is 1000

**Question no – (2) **

**Solution :**

**(i) Given 3 × (- 8) × 5**

= 3 × (- 8) × 5

= (- 24) × 5

= – 120

So, the product is -120.

**(ii) Given, 9 × (- 3) × (- 6)**

= 9 × (- 3) × (- 6)

= (- 27) × (- 6)

= 162

Thus, the product is 162.

**(iii) Given, (-2) × 36 × (-5)**

= (-2) × 36 × (-5)

= (-72) × (-5)

= 360

Hence, the product is 360.

**(iv) Given, (-2) × (-4) × (-6) × (-8)**

= (+8) × (-6) × (-8)

= (-48) × (-8)

= 384

Therefore, the product is 384.

**Question no – (3) **

**Solution : **

**(i)** From the given question,

= (-2) × (-4) × (-6) × (-8)

= (+8) × (-6) × (-8)

= (-48) × (-8)

= 38

Therefore, the product will be 384.

**(ii)** As per the question,

= 28945 × 99 – (- 28945)

= 28945 (99 + 1)

= 28945 × 100

= 2894500

Thus, the value will be 2894500.

**Question no – (4)**

**Solution : **

× | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |

– 4 | + 16 | + 12 | + 8 | + 4 | 0 | – 4 | – 8 | – 12 | – 16 |

– 3 | + 12 | + 9 | + 6 | + 3 | 0 | – 3 | – 6 | – 9 | – 12 |

– 2 | + 8 | + 6 | 4 | 2 | 0 | – 2 | – 4 | – 6 | – 8 |

– 1 | + 4 | + 3 | 2 | 1 | 0 | – 1 | – 2 | – 3 | – 4 |

0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

1 | – 4 | – 3 | – 2 | – 1 | 0 | 1 | 2 | 3 | 4 |

2 | – 8 | – 6 | – 4 | – 2 | 0 | 2 | 4 | 6 | 8 |

3 | – 12 | – 9 | – 6 | – 3 | 0 | 3 | 6 | 9 | 12 |

4 | – 16 | – 12 | – 8 | – 4 | 0 | 4 | 8 | 12 | 16 |

Yes, the multiplication table symmetrical about the diagonal joining the upper left corner to the lower right corner.

**Question no – (5) **

**Solution :**

**(i) 58**

= 58 × (- 1)

= – 58

**(ii) 0**

= 0 × (- 1)

= 0

**(iii) -225**

= (- 225) × (- 1)

= 225

**Question no – (6) **

**Solution : **

**(i)** 8 negative integers and 1 positive integer?

= 8 negative integers × 1 positive integers

= positive

**(ii)** 21 negative integers and 3 positive integers?

= 21 negative integers × 3 positive integers

= Negative.

**(iii)** 199 negative integers and 10 positive integers?

= 199 negative integers × 10 positive integers

= Negative.

**Question no – (7) **

**Solution : **

**(i)** Given, (8 + 9) × 10 and 8 + 9 × 10

**∴** (8 + 9) × 10

= 17 × 10

= 170

**∴** 8 + 9 × 10

= 8 + 90

= 98

Hence, first one is greater.

**(ii)** Given, (8 – 9) × 10 and 8 – 9 × 10

**∴** (8 – 9) × 10

= – 1 × 10

= – 10

**∴** 8 – 9 × 10

= 8 – 90

= – 72

Thus, First one is grater.

**(iii)** Given, {(- 2) – 5} × (- 6) and (- 2) – 5 × (- 6)

**∴** {(- 2) – 5} × (-6)

= (- 2 – 5) × – 6

= 42

**∴** (-2) – 5 × (-6)

= -2 + 30

= + 28

Therefore, First one is greater.

**Question no – (8)**

**Solution : **

**(i)** Given, a × (-1) = -30

The integer is positive.

**(ii)** Given, a × (-1) = 30

The integer is negative.

**Question no – (9) **

**Solution : **

**(i)** In the given question,

= 19 × {7 + (- 3)} = 19 × 7 + 19 × (- 3)

∴ L.H.S, = 19 × {7 + (- 3)}

= 19 × 4

= 76

**∴** R.H.S, = 19 × 7 + 19 × (- 3)

= 133 – 57

= 76

**∴** L.H.S = R.H.S [verified]

**(ii)** In the given question,

= (-23) {(-5) + (+ 19)} = (-23) × (-5) + (-23) × (+19)

L.H.S = (-23) {(-5) + (+ 19)}

= (- 23) × 14

= -322

R.H.S = (-23) × (-5) + (-23) × (+19)

= -23 × (- 5) + (- 23) × (19)

= 115 – 437

= -322

**∴** L.H.S = R.H.S [Verified]

**Question no – (10)**

**Solution :**

**(i)** Given statement is **True.**

**(ii)** Given statement is **True.**

**(iii)** Given statement is **False.**

**(iv)** Given statement is **False.**

**(v)** Given statement is **True.**

**Integers Exercise 1.2 Solution**

**Question no – (1) **

**Solution : **

**(i) 102 by 17**

= 102 ÷ 17

= 6

**(ii) -85 by 5**

= -85 ÷ 5

= -17

**(iii) -161 by – 23**

= -161 ÷ -23

= 7

**(iv) Given, 76 by -19**

= 76 ÷ -19

= -4

**(v) Given, 17654 by -17654**

= 17654 ÷ -17654

= -1

**(vi) (-729) by (-27)**

= -729 ÷ -27

= 27

**(vii) 21590 by -10**

= 21590 ÷ -10

= – 2159

**(viii) 0 by -135**

= 0 ÷ -135

= 0

**Question no – (2) **

**Solution :**

**(i)** 296 ÷ -2 = -148

**(ii)** -88 ÷ -8 = 11

**(iii)** 84 ÷ 7 = 12

**(iv)** -125 ÷ -5 = 25

**(v)** -312 ÷ 156 = -2

**(vi)** -567 ÷ 677 = -1

**Question no – (3) **

**Solution :**

**(i)** 0 ÷ 4 = 0

This statement is **(True).**

**(ii)** 0 ÷ (- 7) = 0

This statement is **(True).**

**(iii)** – 15 ÷ 0 = 0 =

This statement is **(False).**

**(iv)** 0 ÷ 0 = 0

This statement is **(False).**

**(v)** 9- 8) ÷ (- 1) = – 8

This statement is **(False).**

**(vi)** – 8 ÷ (- 2) = 4

This statement is **(True).**

**Integers Exercise 1.3 Solution**

**Question no – (1)**

**Solution : **

In the question,

= 36 ÷ 6 + 3

= (36 ÷ 6) + 3

= 6 + 3

= 9

Therefore, the value will be 9.

**Question no – (2)**

**Solution : **

In the given question,

= 24 + 15 ÷ 3

= 24 + (15 ÷ 3)

= 24 + 5

= 29

Hence, the value will be 29.

**Question no – (3)**

**Solution : **

Given in the question,

= 120 – 20 ÷ 4

= 120 – (20 ÷ 4)

= 120 – 5

= 115

Hence, the value is 115.

**Question no – (4)**

**Solution : **

Given in the question,

= 32 – (3 × 5) + 4

= 32 – 15 + 4

= 21

Thus, the value will be 21.

**Question no – (5)**

**Solution : **

In the given question,

= 5 – (5 – 6 ÷ 3)

= 5 – (5 – 2)

= 5 – 3

= 2

Therefore, the value will be 2.

**Question no – (6)**

**Solution : **

Given in the question,

= 21 – 12 ÷ 3 × 2

= 21 – (12 ÷ 3) × 2

= 21 – 4 × 2

= 21 – 8

= 13

Hence, the value will be 13.

**Question no – (7)**

**Solution : **

As per the question,

= 16 + 8 ÷ 4 – 2 × 3

= 16 + (8 ÷ 4) – 2 × 3

= 16 + 2 – 6

= 18 – 6

= 12

Thus, the value will be 12.

**Question no – (8)**

**Solution : **

In the given question,

= 28 – 5 × 6 + 2

= 28 – 30 – 2

= 28 – 28

= 0

Therefore, the value will be 0.

**Question no – (9)**

**Solution : **

As per the question,

= (-20) ×(-1) + (-28) ÷ 7

= 20 – 4

= 16

Hence, the value will be 16

**Question no – (10)**

**Solution : **

Given in the question,

= (-2) + (-8) ÷ (-4)

= -2 + 2

= 0

Thus, the value will be 0

**Question no – (11)**

**Solution : **

In the question,

= (-15) + 4 ÷ (5 – 3)

= -15 + 4 ÷ 2

= -15 + 2

= -13

Hence, the value will be -13

**Question no – (13)**

**Solution : **

In the given question,

= (-40) × (- 1) + (- 28) ÷ 7

= 40 + (- 4)

= 36

Therefore, the value will be 36.

**Question no – (13)**

**Solution : **

Given in question,

= (- 3) + (- 8) ÷ (- 4) – 2 × (- 2)

= -3 + 2 + 4

= 3

Thus, the value will be 3

**Question no – (14)**

**Solution : **

Given in the question,

= (-3) × (-4) ÷ (-2) + (-1)

= -3 × 2 – 1

= -6 – 1

= -7

Hence, the value is -7.

**Integers Exercise 1.4 Solution **

**Question no – (1) **

**Solution :**

In the given question, 3 – (5 – 6 ÷ 3)

= 3 – (5 – 2)

= 3 – 3

= 0…(Simplified)

**Question no – (2) **

**Solution :**

From the given question, -25 + 14 ÷ (5 – 3)

= – 25 + 4 ÷ 2

= – 25 + 7

= – 18…(Simplified)

**Question no – (3) **

**Solution :**

In the given question, 25 – 1/2 {5 + 4 – (3 + 2 – 1 + 3)}

= 15 – 1/2 {5 + 4 – (3 + 2 – 4)}

= 25 – 1/2 {(5 + 4 – 1)}

= 25 -1/2 × 8

= 25 – 4

= 21…(Simplified)

**Question no – (4) **

**Solution :**

In the given question, 27 – [38 – {46 – (15 – 13 – 2)}]

= 27 – [38 – {46 – (15 – 11)}]

= 27 – [38 – {46 – 4}]

= 27 – [38 – 42]

= 27 + 4

= 31…(Simplified)

**Question no – (5) **

**Solution :**

Given in the question, 36 – [18 – {14 – (15 – 4 ÷ 2 × 2)}]

= 36 – [18 – {14 – (15 – 4 ÷ 2 × 2)}]

= 36 – [18 – 3]

= 36 – 15

= 21…(Simplified)

**Question no – (6) **

**Solution :**

In the given question, 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]

= 45- [38 – {20 – (6 – 3) ÷ 3}]

= 45 – [38 – {20 – 1}]

= 45 – {38 – 19}

= 45 – 19

= 26…(Simplified)

**Question no – (7) **

**Solution :**

Given in the question, 23 – [23 – {23 – (23 – 23 – 23)}]

= 23 – [23 – {23 – (23- 0)}]

=23 – [23 – {23 – 23}]

= 23 – [23 – 0]

= 23 – 23

= 0…(Simplified)

**Question no – (8) **

**Solution :**

As per the question, 2550 – [510 – {270 – (90 – 80 + 70)}]

= 2550 – [510 – {270 – (90 – 150)}]

= 2550 – [510 – {270 + 60}]

= 25550 – [510 – 230]

= 2550 – 280

= 2370…(Simplified)

**Question no – (9) **

**Solution :**

In the given question, 4 + 1/5 [{-10 × (25 – 13 – 3)} ÷ (-5)]

= 4 + 1/5 [{-10 × (25 – 10)} ÷ (-5)}]

= 4 + 1/5 [{(-10 × 15) ÷ (-5)}]

= 4 + 1/5 × 30

= 4 + 6

= 10…(Simplified)

**Question no – (10) **

**Solution :**

In the given question, 22 -1/4 {-5 -(-48) ÷ (-16)}

= 22 -1/4 {-5 – 3}

= 22 -1/4 × (-8)

= 22 + 2

= 24…(Simplified)

**Question no – (11) **

**Solution :**

In the question, 63 – [(-3) {-2 – 8 – 3}] ÷ [3{5 + (-2) (-1)}]

= 63 – [(-3)} – 2 – 5}] ÷ [3 {5 + 2}]

= 63 – [(-3) × (-7)] ÷ 3 × 7

= 63 – 21 ÷ 21

= 63 – 1

= 62…(Simplified)

**Question no – (12) **

**Solution :**

In the given question, [29 – (-2) {6 – (7 -3)}] ÷ [3 × {5 + (-3) × (-2)}]

= [29 – (-2) {6 – 4}] ÷ [3 × {5 + 6}]

= [29 – (-2) × 2] ÷ [3 × 11]

= [29 + 4] ÷ 33

= 33 ÷ 33

= 1…(Simplified)

**Question no – (13) **

**Solution :**

**(i)** Nine multiplied by the sum of two and five.

= 9 (2 + 5)

**(ii)** Twelve divided by the sum of one and three.

= 12 ÷ (1 + 3)

**(iii)** Twenty divided by the difference of seven and two.

= 20 ÷ (7 – 2)

**(iv)** Eight subtracted from the product of two and three.

= (2 × 3) – 8

**(v)** Forty divided by one more than the sum of nine and ten.

= 40 ÷ (9 + 10+ 1)

**(vi)** Two multiplied by one less than the difference of nineteen and six.

= 2 × [(19 – 6) – 1]

**Next Chapter Solution : **

👉 Chapter 2 👈