# Selina Concise Solutions for Chapter 1 Integers Class 7 ICSE Mathematics

## ### Exercise 1(A)

1. Evaluate:

(a) 427 × 8 + 2 × 427

(b) 394 × 12 + 394 × (-2)

(c) 558 × 27 + 3 × 558

(a) 427 × 8 + 2 × 427

= 427 × (8 + 2) (Distributive property)

= 427 × 10

= 4270

(b) 394 × 12 + 394 × (-2)

= 394 × (12-2) (Distributive property)

= 394 × 10

= 3940

(c) 558 × 27 + 3 × 558

= 558 × (27 + 3) (Distributive property)

= 558× 30

= 16740

2. Evaluate:

(a) 673 × 9 + 673

(b) 1925 × 101 – 1925

(a) 673 × 9 + 673

= 673 × (9 + 1) (Distributive property)

= 673 × 10

= 6730

(b) 1925 × 101 – 1925

= 1925 × (101 – 1) (Distributive property)

= 1925 × 100

= 19250

3. Verify:

(a) 37 × {8 +(-3)} = 37 × 8 + 37 × – (3)

(b) (-82) × {(-4) + 19} = (-82) × (-4) + (-82) × 19

(c) {7 – (-7)} × 7 = 7× 7 – (-7) × 7

(d) {(-15) – 8} × -6 = (-15) × (-6) – 8 × (-6)

(a) 37 × {8 + (-3)} = 37 × 8 + 37 × – (3)

L.H.S. = 37 × {8 + (-3)}

= 37 × {8-3}

= 37 × {5}

= 37 × 5

= 185

R.H.S. = 37 × 8 + 37 – 3

= 37 × (8 – 3)

= 37 × 5

= 185

Hence, L.H.S. = R.H.S.

(b) (-82) x {(-4) + 19} = (-82) × (-4) + (-82) × 19

L.H.S. = (-82) × {(_4) + 19}

= (-82) × {-4 + 19}

= (-82) × {15}

= -82 × 15

=-1230

R.H.S. = (-82) × (-4) + (-82) × 19

= -82 × (-4 + 19)

= -82 × 15

=-1230

Hence, L.H.S. = R.H.S.

(c) {7 – (-7)}. × 7 = 7 × 7 – (-1) × 7

L.H.S. = {7 – (-7)} × 7

= {7 + 7} × 7

= {14}× 7

= 14 × 7

= 98

R.H.S. = 7 × 7 – (-7) × 7

=7 × 7+7 × 7 =

× (7 + 7)

= 7 × (14)

= 98

Hence, L.H.S. = R.H.S.

(d) {(-15) – 8} × -6 = (-15) × (-6) – 8 × (-6)

L.H.S. = {(-15)-8} × -6

= {-15-8} × -6

= {-23} × -6

= -23 × - 6

= 138

R.H.S. = (-15) × (-6) – 8 × (-6)

= -6 × (-15-8)

= -6 × -23

= 138

Hence, L.H.S. = R.H.S.

4. Evaluate:

(a) 15 × 8

(b) 15 × (-8)

(c) (-15) × 8

(d) (-15) × -8

(a) 15 × 8= 120

(b) 15 × (-8) = -120

(c) (-15) × 8 = -120

(d) (-15) × -8 = 120

(Since the number of negative integers in the product is even)

5. Evaluate:

(a) 4 × 6 × 8

(b) 4 × 6 × (-8)

(c) 4 × (-6) × 8

(d) (-4) × 6 × 8

(e) 4 × (-6) × (-8)

(f) (-4) × (-6) × 8

(g) (-4) × 6 × (- 8)

(h) (-4) × (-6) × (-8)

(a) 4 × 6 × 8 = 192

(b) 4 × 6 × (-8) = -192

It have one negative factor.

(c) 4 × (-6) × 8 = -192

(It have one negative factor)

(d) (-4 )× 6 x 8 = -192

It have one negative factor.

(e) 4 × (-6) × (-8) = 192

It have two negative factors.

(f) (-4) × (-6) × 8 = 192

It have two negative factors.

(g) (-4) × 6 × (-8) = 192

It have two negative factors.

(h) (-4) × (-6) × (-8) = -192

It have three negative factors.

6. Evaluate:

(i) 2 × 4 × 6 × 8

(ii) 2 × (-4) × 6 × 8

(iii) (-2) × 4 × (-6) × 8

(iv) (-2) × (-4) × 6× (-8)

(v) (-2) × (-4) × (-6) × (-8)

(i) 2 × 4 × 6 × 8 = 384

(ii). 2 × (-4) × 6 × 8 = -384

(Number of negative integer in the product is odd)

(iii) (-2) × 4 × (-6) × 8 = 384

(Number of negative integer in the product is even)

(iv) (-2) × (-4) × 6 × (-8) = -384

(Number of negative integer in the product is odd)

(v) (-2) × (-4) × (-6) × (-8) = 384

(Number of negative integer in the product is even)

7. Determine the integer whose product with ‘-1’ is:

(i) -47

(ii) 63

(iii) -1

(iv) 0

(i) -1 × 47 = -47

Hence, integer is 47

(ii) -1 × -63 = 63

Hence, integer is -63

(iii) -1 × 1 = -1

Hence, integer is 1

(iv) -1 × 0 = 0

Hence, integer is 0

8. Eighteen integers are multiplied together. What will be the sign of their product, if:

(i) 15 of them are negative and 3 are positive?

(ii) 12 of them are negative and 6 are positive?

(iii) 9 of them are positive and the remaining are negative?

(iv) all are negative?

(i) Since out of eighteen integers, 15 of them are negative, which is odd number. Hence, sign of product will be negative (-).

(ii) Since out of eighteen integers 12 of them are negative, which is even number. Hence sign of product will be positive (+).

(iii) Since out of eighteen integers 9 of them are negative, which is odd number. Hence, sign of product will be negative (-).

(iv) Since all are negative, which is even number. Hence sign of product will be positive (+).

9. Find which is greater?

(i) (8 + 10) × 15 or 8 + 10 × 15

(ii) 12 × (6 – 8) or 12 × 6 – 8

(iii) {(-3) – 4} × (-5) or (-3) – 4 × (-5)

(i) (8 + 10) × 15 or 8 + 10 × 15

⇒ (8 + 10) × 15 = 18 × 15 = 270

⇒ 8 + 10 × 15 = 8 + 150 = 158

∴ (8 + 10) × 15 > 8 + 10 × 15

(ii) 12 × (6 – 8) or 12 × 6 – 8

12 × (6 – 8) = 12 (-2) = -24

12 × 6 – 8 = 72 – 8 = 64

∴12 × 6 – 8 > 12 × (6-8)

(iii) {(-3) – 4} × (-5) or (-3) – 4 × (-5)

{(-3) – 4} × (-5) = {-3 – 4} × (-5) = -7 × -5 = 35

(-3) – 4 × (-5) = -7 × (-5) = 35

∴{(-3) – 4} × (-5) = (-3) – 4 × (-5)

10. State, true or false :

(i) product of two integers can be zero.

(ii) product of 120 negative integers and 121 positive integers is negative.

(iii) a x (b + c) = a × b + c

(iv) (b – c) × a=b – c × a

(i) False.

(ii) False.
Correct : Since 120 integers are even numbers, hence product will be positive and for 121 integers are positive in numbers, hence product will be positive.

(iii) False.
Correct :a x (b + c) ≠ a x b + c
ab + ac ≠ ab + c

(iv) False.
Correct: (b – c) x a ≠ b – c x a
ab – ac ≠ b – ca

### Exercise 1 (B)

1. Divide:

(i) 117 by 9

(ii) (-117) by 9

(iii) 117 by (-9)

(iv) (-117) by (-9)

(v) 225 by (-15)

(vi) (-552) ÷ 24

(vii) (-798) by (-21)

(viii) (-910) ÷  (– 26)

2. Evaluate:

(i) (-234) ÷ 13

(ii) 234 ÷ (-13)

(iii) (-234) ÷ (-13)

(iv) 374 ÷ (-17)

(v) (-374) ÷ 17

(vi) (-374) ÷ (-17)

(vii) (-728) ÷ 14

(viii) 272 ÷ (-17)

3. Find the quotient in each of the following divisions:

(i) 299 ÷ 23

(ii) 299 ÷ (-23)

(iii) (-384) ÷ 16

(iv) (-572) ÷ (-22)

(v) 408 ÷ (-17)

4. Divide:

(i) 204 by 17

(ii) 152 by-19

(iii) 0 by 35

(iv) 0 by (-82)

(v) 5490 by 10

(vi) 762800 by 100

5. State, true or false :

(i) 0 ÷ 32 = 0

(ii) 0 ÷ (-9) = 0

(iii) (-37) ÷ 0 = 0

(iv) 0 ÷ 0 = 0

(i) True.

(ii) True.

(iii) False.

Correct: It is not meaningful (defined)

(iv) False.

Correct: It is not defined.

6. Evaluate:

(i) 42 ÷ 7 + 4

(ii) 12+18 ÷ 3

(iii) 19 – 20 ÷ 4

(iv) 16 – 5 × 3+4

(v) 6 – 8 – (-6) ÷ 2

(vi) 13 -12 ÷ 4 × 2

(vii) 16 + 8 ÷ 4- 2 × 3

(viii) 16 ÷ 8 + 4 – 2 × 3

(ix) 16 – 8 + 4 ÷ 2 × 3

(x) (-4) + (-12) ÷ (-6)

(xi) (-18) + 6 ÷ 3 + 5

(xii) (-20) × (-1) + 14 – 7

(i) 42 ÷ 7 + 4
= 42/7  + 4
= 6+ 4
= 10

(ii) 12 + 18 ÷ 3
= 12 + 18/3
= 12 +6
= 18

(iii) 19 - 20 ÷ 4
= 19 - 20/4
= 19 - 5
= 14

(iv) 16 - 5×3 + 4
= 16 - 15 + 4
= 20 - 15
= 5

(v) 6 - 8 - (-6) ÷ 2
= 6 - 8 - (- 6/2)
= 6 - 8 - (-3)
= 6 - 8 + 3
= 9 - 8
= 1

(vi) 13 - 12 ÷ 4×2
= 13 - 12/4  ×2
= 13 -3×2
= 13 -6
= 7

(vii) 16 + 8 ÷ 4 -2×3
= 16 + 8/4 - 6
= 16 + 2 - 6
= 18 - 6
= 12

(viii) 16 ÷ 8 + 4 - 2×3
= 16/8 + 4 -6
= 2 + 4 -6
= 6 - 6
= 0

(ix) 16 - 8 + 4 ÷ 2×3
= 16 - 8 + 4/2 ×3
= 16 - 8 + 2 × 3
= 16 - 8 + 6
= 22 - 8
= 14

(x) (-4) + (-12) ÷ (-6)
= (-4) + (-12/-6)
= -4 + 2
= -2

(xi) (-18) + 6 ÷ 3 + 5
= (-18) + 6/3 + 5
= -18 + 2 + 5
= -18+ 7
= -11

(x) (-20) × (-1) + 14 ÷ 7
= -20 × (-1) + 14/7
= 20 + 2
= 22

### Exercise 1 (C)

1. Evaluate:

18 -(20 - 15 ÷ 3)

18 -(20 - 15 ÷ 3)
= 18 – (20 - 15/3)
= 18 – (20 – 5)
= 18 – 20 + 5
= 18 + 5 – 20
= 23– 20
= 3

2. -15+ 24÷ (15-13)

-15+ 24 ÷ (15- 13)
= -15 + 24 ÷ 2
= -15 + 12
= -3

3. 35 – [15 + {14-(13 + 2-1+3)}]

35- [15 + {14-(13 + 2-1+3)}]

= 35-[15+ 14 - (13+4)]
= 35 — [15 + 14 – (13 + 4}]
= 35-{15 + 14-17]
= 35-15-14+ 17
= 35 + 17-15-14
= 52 – 29
= 23

4. 27- [13 + {4-(8 + 4 – 1+3)}]

27- [13 + {4-(8 + 4 – 1+3)}]

= 27-[13 +{4-(8+ 4-4)}]
= 27-[13 + {4-8}]
= 27 – [13 + (-4)]
= 21 – 
= 27-9
= 18

5. 32 – [43-{51 -(20 – 18-7)}]

32 – [43 – {51 – (20 – 18-7)}]
= 32-[43 – {51 -(20- 11)}]
= 32-[43-{51 -9}]
= 32-[43 -42]
= 32-1
=31

6. 46-[26-{14-(15-4÷ 2×2)}]

46 – [26 – {14 – (15 – 4 ÷ 2×2)}]
= 46-[26- {14-(15- 2×2)}]
= 46-[26- {14-(15 -4)}]
= 46-[26- {14- 11}]
= 46 – [26 – 3]
= 46 – 23
= 23

7. 45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]

45 – [38 – {60 ÷ 3 – (6 – 9 ÷ 3) ÷ 3}]
= 45-[38- {60 ÷ 3-(6-3)÷ 3}]
= 45-[38 -{20-3 ÷ 3}]
= 45-[38- {20-1}]
= 45-[38- 19]
= 45-19
= 26

8. 17- [17 - {17 - (17 – 17-17)}]

17- [17-{17-(17 – 17-17)}]

= 17-[17-{17-(17-0)}]
= 17 - [17 – {17 - 17}]
= 17 - [17 - 0]
= 17-17
= 0

9. 2550 – [510 – {270 – (90 – 80+7)}]

2550- [510-{270-(90- 80+7)}]

= 2550 – [510 – {270 – (90 – 87)}]
= 2550 -[510- {270 -3}]
= 2550-[510-267]
= 2550 – 243
= 2307

10. 30+ [{-2× (25- 13+3)}]

30+ [{-2 × (25-13+3 )}]

= 30 + [{-2 × (25 – 10)}]
= 30 + [{-2 × 15}]
= 30 + [-30]
= 30-30
= 0

11. 88-{5-(-48)+ (-16)}

88- {5-(-48)+ (-16)}
=88 – { 5 + 48 - 16 }
= 88 – {53-16}
= 88 – 37
= 51

12. 9× (8- 3+2) - 2(2+3+3)

9× (8- 3+2) - 2(2+3+3)
= 9× (8 – 5) – 2(2 + 6)
= 9× 3 – 2×8
= 27- 16
= 11

13. 2 – [3 – {6 – (5 – 4-3)}]

2 – [3 – {6 – (5 –4-3 )}]
= 2 – [3 – {6 – (5 – 1)}]
= 2 – [3 – {6 – 4}]
= 2 – (3 – 2)
= 2-1 = 1

### Exercise 1 (D)

1. The sum of two integers is -15. If one of them is 9, find the other.

Sum of two integers = -15
One integer = 9
∴ Second integer = -15 – 9
= -(15 + 9)
= -24

2. The difference between an integer and -6 is -5. Find the values of x.

The difference between an integer
= x-(-6) = -5
∴ Value of
⇒ x – (-6) = -5
⇒ x + 6 = -5
⇒ x = -5 – 6
⇒ x = -11

3. The sum of two integers is 28. If one integer is -45, find the other.

Sum of two integers = 28
One integer = -45
∴ Second integer = 28 – (-45)
= 28 + 45
= 73

4. The sum of two integers is -56. If one integer is -42, find the other.

Sum of two integers = -56
One integer = -42
∴Second integer = -56 - (-42)
= -56+ 42
=-14

5. The difference between an integer x and (-9) is 6. Find all possible values of x.

The difference between an integer x - (-9) = 6 or -9 – x = 6
∴ Value of x
⇒ x – (-9) = 6 or ⇒ -9 – x = 6
⇒ x + 9 = 6 or -x = 6 + 9
⇒ x = 6 – 9 or -x = 15
⇒ x = -3 or  x = -15
Hence, possible values of x are -3 and -15.

6. Evaluate:

(i). (-1) ×(-1)×(-1) × ....60 times.

(ii). (-1)× (-1) ×(-1) ×(-1) × .... 75 times.

(i) 1 (because -1 is multiplied even times.)

(ii) -1 (because -1 is multiplied odd times.)

7. Evaluate:

(i) (-2) × (-3) × (-4) × (-5) × (-6)

(ii) (-3) × (-6) × (-9) × (-12)

(iii) (-11) × (-15) + (-11) × (-25)

(iv) 10× (-12) + 5× (-12)

(i) (-2) × (-3)× (-4)× (-5) ×(-6)

= 6 ×20 ×(-6)

= 120 ×(-6)

= -720

(ii) (-3)×(-6)× (-9)× (-12)

= 18 ×108

= 1944

(iii) (-11)× (-15) + (-11)×(-25)

= 165 + 275

= 440

(iv) 10×(-12) + 5×(-12)

= -120-60

= -180

8. (i). If x ×(-1) = -36, is x positive or negative?

(ii). If x×(-1) = 36, is x positive or negative?

(i) x× (-1) = -36

⇒ -lx = -36

⇒ x = -36/-1

⇒ x = 36

∵ x = 36

∴ It is a positive integer.

(ii) x× (-1) = 36

⇒ -1x = 36

⇒ x = 36/ -1

⇒ x = -36

∵ x = -36

∴ It is a negative integer.

9. Write all the integers between -15 and 15, which are divisible by 2 and 3.

The integers between -15 and 15 are :
-12, -6, 0, 6 and 12
That are divisible by 2 and 3.

10. Write all the integers between -5 and 5, which are divisible by 2 or 3.

The integers between -5 and 5 are :
-4, -3, -2, 0, 0, 2, 3 and 4
That are divisible by 2 or 3.

11. Evaluate:

(i) (-20) + (-8) ÷ (-2)×3

(ii) (-5) – (-48) ÷ (-16) + (-2)×6

(iii) 16 + 8 ÷ 4- 2×3

(iv) 16 ÷ 8×4 – 2×3

(v) 27 – [5 + {28 – (29 – 7)}]

(vi) 48 – [18 – {16 – (5 – )}]

(vii) -8 – {-6 (9 – 11) + 18 = -3}

(viii) (24 ÷ –12) – (3×8 ÷ 4 + 1)

We know that, if these type of expressions that has more than one fundamental operations, we use the rule of DMAS i.e., First of all we perform D (division), then M (multiplication), then A (addition) and in the last S (subtraction).

(i) (-20) + (-8) ÷ (-2)×3
= -20 + 4×3
= -20+ 12
= -8

(ii) (-5) - (-48) ÷ (-16) + (-2)×6
= (-5) – 3 + (-2)× 6
= -5 - 3 - 12
= -8- 12
= -20

(iii) 16 + 8 ÷ 4 – 2×3
= 16 + 2 – 2×3
=16 + 2 – 6
= 18-6
= 12

(iv) 16 ÷ 8×4 – 2×3
= 2×4 – 2×3
= 8 - 6
= 2

(v) 27 - [5 + {28 – (29 – 7)}]
⇒ 27 - [5 + {28 – 22}]
⇒ 27 - [5 + 6]
⇒ 27 - 11
= 16

(v) 48-[18-{16-(5 – )}]
= 48-[18-{16-(5-5)}]
= 48-[18- {16-0)}]
= 48-[18- 16]
= 48 – 2
= 46

(vii) -8 – {-6 (9 – 11) + 18 ÷ -3}
= -8 – {-6 (-2) – 6}
= -8- {12-6}
= -8 – {6}
= -8-6
= -14

(viii) (24 ÷ – 12) – (3×8 = 4 + 1)
⇒ (24 ÷ 3-12)-(3×2 + 1)
⇒ (8- 12)-(6+ 1)
⇒ -4 - 7
= -11

12. Find the result of subtracting the sum of all integers between 20 and 30 from the sum of all integers from 20 to 30.

Required number = (Sum of all integers between 20 and 30 – Integers between 20 and 30)
(20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30) – (21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 )
⇒ 20 + 30 = 50
∴ Required number = 50

13. Add the product of (-13) and (-17) to the quotient of (-187) and 11.

(-13)×(-17)+ (-187- 11)
⇒ (-13)×(-17) + (-17)
⇒ 221 – 17 = 204

14. The product of two integers is-180. If one of them is 12, find the other.

The product of two integers = -180
One integer = 12
∴ Second integer = -180 – 12 = -15

15. (i) A number changes from -20 to 30. What is the increase or decrease in the number?

(ii) A number changes from 40 to -30. What is the increase or decrease in the number?