Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers

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Integers Exercise 1A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:

  1. 427 x 8 + 2 x 427
  2. 394 x 12 + 394 x (-2)
  3. 558 x 27 + 3 x 558

Solution:

  1. 427 x 8 + 2 x 427 = 427 x (8 + 2) (Distributive property)
    = 427 x 10
    = 4270
  2. 394 x 12 + 394 x (-2) = 394 x (12-2) (Distributive property)
    = 394 x 10
    = 3940
  3. 558 x 27 + 3 x 558 = 558 x (27 + 3) (Distributive property)
    = 558 x 30
    = 16740

Question 2.
Evaluate:

  1. 673 x 9 + 673
  2. 1925 x 101 – 1925

Solution:

  1. 673 x 9 + 673 = 673 x (9 + 1) (Distributive property) = 673 x 10 = 6730
  2. 1925 x 101 – 1925 = 1925 x (101 – 1) (Distributive property) = 1925 x 100 = 192500

Question 3.
Verify:

  1. 37 x {8 +(-3)} = 37 x 8 + 37 x – (3)
  2. (-82) x {(-4) + 19} = (-82) x (-4) + (-82) x 19
  3. {7 – (-7)} x 7 = 7 x 7 – (-7) x 7
  4. {(-15) – 8} x -6 = (-15) x (-6) – 8 x (-6)

Solution:

  1. 37 x {8 + (-3)} = 37 x 8 + 37 x – (3)
    L.H.S. = 37 x {8 + (-3)}
    = 37 x {8-3}
    = 37 x {5}
    = 37 x 5
    = 185
    R.H.S. = 37 x 8 + 37 – 3
    = 37 x (8 – 3)
    = 37 x 5
    = 185
    Hence, L.H.S. = R.H.S.
  2. (-82) x {(-4) + 19} = (-82) x (-4) + (-82) x 19
    L.H.S. = (-82) x {(_4) + 19}
    = (-82) x {-4 + 19}
    = (-82)x {15}
    = -82 x 15
    =-1230
    R.H.S. = (-82) x (-4) + (-82) x 19
    = -82 x (-4 + 19)
    = -82 x 15
    =-1230
    Hence, L.H.S. = R.H.S.
  3. {7 – (-7)}. x 7 = 7 x 7 – (-1) x 7
    L.H.S. = {7 – (-7)} x 7
    = {7 + 7} x 7
    = {14} x 7
    = 14 x 7
    = 98
    R.H.S. = 7 x 7 – (-7) x 7
    =7 x 7+7 x 7 =
    7 x (7 + 7)
    = 7 x (14)
    = 98
    Hence, L.H.S. = R.H.S.
  4. {(-15) – 8} x -6 = (-15) x (-6) – 8 x (-6)
    L.H.S. = {(-15)-8} x-6
    = {-15-8} x-6
    = {-23} x-6
    = -23 x- 6
    = 138
    R.H.S. = (-15) x (-6) – 8 x (-6)
    = -6 x (-15-8)
    = -6 x -23
    = 138
    Hence, L.H.S. = R.H.S.

Question 4.
Evaluate:

  1. 15 x 8
  2. 15 x (-8)
  3. (-15) x 8
  4. (-15) x -8

Solution:

  1. 15 x 8= 120
  2. 15 x (-8) = -120
  3. (-15) x 8 = -120
  4. (-15) x -8 = 120
    (Since the number of negative integers in the product is even)

Question 5.
Evaluate:

  1. 4 x 6 x 8
  2. 4 x 6 x (-8)
  3. 4 x (-6) x 8
  4. (-4) x 6 x 8
  5. 4 x (-6) x (-8)
  6. (-4) x (-6) x 8
  7. (-4) x 6 x (- 8)
  8. (-4) x (-6) x (-8)

Solution:

  1. 4 x 6 x 8 = 192
  2. 4 x 6 x (-8) = -192
    (It have one negative factor)
  3. 4 x (-6) x 8 = -192
    (It have one negative factor)
  4. (-4 )x 6 x 8 = -192
    (It have one negative factor)
  5. 4 x (-6) x (-8) = 192
    (It have two negative factors)
  6. (-4) x (-6) x 8 = 192
    (It have two negative factors)
  7. (-4) x 6 x (-8) = 192
    (It have two negative factors)
  8. (-4) x (-6) x (-8) = -192
    (It have three negative factors)

Question 6.
Evaluate:

  1. 2 x 4 x 6 x 8
  2. 2 x (-4) x 6 x 8
  3. (-2) x 4 x (-6) x 8
  4. (-2) x (-4) X 6 x (-8)
  5. (-2) x (-4) x (-6) x (-8)

Solution:

  1. 2 x 4 x 6 x 8 = 384
  2. 2 x (-4) x 6 x 8 = -384
    (Number of negative integer in the product is odd)
  3. (-2) x 4 x (-6) x 8 = 384
    (Number of negative integer in the product is even)
  4. (-2) x (-4) x 6 x (-8) = -384
    (Number of negative integer in the product is odd)
  5. (-2) x (-4) x (-6) x (-8) = 384
    (Number of negative integer in the product is even)

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

  1. -47
  2. 63
  3. -1
  4. 0

Solution:

  1. -1 x 47 = -47
    Hence, integer is 47
  2. -1 x -63 = 63
    Hence, integer is -63
  3. -1 x 1 = -1
    Hence, integer is 1
  4. -1 x 0 = 0
    Hence, integer is 0

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

  1. 15 of them are negative and 3 are positive?
  2. 12 of them are negative and 6 are positive?
  3. 9 of them are positive and the remaining are negative?
  4. all are negative?

Solution:

  1. Since out of eighteen integers, 15 of them are negative, which is odd number. Hence, sign of product will be negative (-).
  2. Since out of eighteen integers 12 of them are negative, which is even number. Hence sign of product will be positive (+).
  3. Since out of eighteen integers 9 of them are negative, which is odd number. Hence, sign of product will be negative (-).
  4. Since all are negative, which is even number. Hence sign of product will be positive (+).

Question 9.
Find which is greater?

  1. (8 + 10) x 15 or 8 + 10 x 15
  2. 12 x (6 – 8) or 12 x 6 – 8
  3. {(-3) – 4} x (-5) or (-3) – 4 x (-5)

Solution:

  1. (8 + 10) x 15 or 8 + 10 x 15
    (8 + 10) x 15 = 18 x 15 = 270
    8 + 10 x 15 = 8 + 150 = 158
    ∴(8 + 10) x 15 > 8 + 10 x 15
  2. 12 x (6 – 8) or 12 x 6 – 8
    12 x (6 – 8) = 12 (-2) = -24
    12 x 6 – 8 = 72 – 8 = 64
    ∴12 x 6 – 8 > 12 x (6-8)
  3. {(-3) – 4} x (-5) or (-3) – 4 x (-5)
    {(-3) – 4} x (-5) = {-3 – 4} x (-5) = -7 x -5 = 35
    (-3) – 4 x (-5) = -7 x (-5) = 35
    ∴{(-3) – 4} x (-5) = (-3) – 4 x (-5)

Question 10.
State, true or false :

  1. product of two integers can be zero.
  2. product of 120 negative integers and 121 positive integers is negative.
  3. a x (b + c) = a x b + c
  4. (b – c) x a=b – c x a

Solution:

  1. False.
  2. 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.
  3. False.
    Correct :a x (b + c) ≠ a x b + c
    ab + ac ≠ ab + c
  4. False.
    Correct: (b – c) x a ≠ b – c x a
    ab – ac ≠ b – ca

Integers Exercise 1B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 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

Solution :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 3

Question 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)

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 4
Question 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)

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 5
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 6

Question 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

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 7

Question 5.
State, true or false :

  1. 0 ÷ 32 = 0
  2. 0 ÷ (-9) = 0
  3. (-37) ÷ 0 = 0
  4. 0 ÷ 0 = 0

Solution:

  1. True.
  2. True.
  3. False.
    Correct: It is not meaningful (defined)
  4. False.
    Correct: It is not defined.

Question 6.
Evaluate:
(i) 42 ÷ 7 + 4
(ii) 12+18 ÷ 3
(iii) 19 – 20 ÷ 4
(iv) 16 – 5 x 3+4
(v) 6 – 8 – (-6) ÷ 2
(vi) 13 -12 ÷ 4 x 2
(vii) 16 + 8 ÷ 4- 2 x 3
(viii) 16 ÷ 8 + 4 – 2 x 3
(ix) 16 – 8 + 4 ÷ 2 x 3
(x) (-4) + (-12) ÷ (-6)
(xi) (-18) + 6 ÷ 3 + 5
(xii) (-20) x (-1) + 14 – 7

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 1 Integers image - 2

 

Integers Exercise 1C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Evaluate:
18-(20- 15 ÷ 3)
Solution:
18-(20- 15 ÷ 3)
= 18 – \(\left( 20\quad -\frac { 15 }{ 5 } \right)\)
= 18 – (20 – 5)
= 18 – 20 + 5
= 18 + 5 – 20
= 23 – 20
= 3

Question 2.
-15+ 24÷ (15-13)
Solution:
-15+ 24÷ (15- 13)
= -15 + 24 ÷ 2
= -15 + 12
= -3

Question 3.
35 – [15 + {14-(13 + \(\overline { 2-1+3 }\))}]
Solution:
35- [15 + {14-(13 + \(\overline { 2-1+3 }\))}]
= 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

Question 4.
27- [13 + {4-(8 + 4 – \(\overline { 1+3 }\))}]
Solution:
27- [13 + {4-(8 + 4 – \(\overline { 1+3 }\))}]
= 27-[13 +{4-(8+ 4-4)}]
= 27-[13 + {4-8}]
= 27 – [13 + (-4)]
= 21 – [9]
= 27-9
= 18

Question 5.
32 – [43-{51 -(20 – \(\overline { 18 -7 }\))}]
Solution:
32 – [43 – {51 – (20 – \(\overline { 18 -7 }\))}]
= 32-[43 – {51 -(20- 11)}]
= 32-[43-{51 -9}]
= 32-[43 -42]
= 32-1
=31

Question 6.
46-[26-{14-(15-4÷ 2 x 2)}]
Solution:
46 – [26 – {14 – (15 – 4 ÷ 2 x 2)}]
= 46-[26- {14-(15-2 x 2)}]
= 46-[26- {14-(15 -4)}]
= 46-[26- {14- 11}]
= 46 – [26 – 3]
= 46 – 23
= 23

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

Question 8.
17- [17 — {17 — (17 – \(\overline { 17 -17 }\))}]
Solution:
17- [17-{17-(17 –\(\overline { 17 -17 }\))}]
= 17-[17-{17-(17-0)}]
= 17 – [17 – {17 — 17}]
= 17 — [17 — 0]
= 17-17
= 0

Question 9.
2550 – [510 – {270 – (90 – \(\overline { 80 + 7 }\))}]
Solution:
2550- [510-{270-(90-\(\overline { 80 + 7 }\))}]
= 2550 – [510 – {270 – (90 – 87)}]
= 2550 -[510- {270 -3}]
= 2550-[510-267]
= 2550 – 243
= 2307

Question 10.
30+ [{-2 x (25-\(\overline { 13 -3 }\))}]
Solution:
30+ [{-2 x (25-\(\overline { 13 -3 }\))}]
= 30 + [{-2 x (25 – 10)}]
= 30 + [{-2 x 15}]
= 30 + [-30]
= 30-30
= 0

Question 11.
88-{5-(-48)+ (-16)}
Solution:
88- {5-(-48)+ (-16)}
=88 – \(\left\{ 5-\frac { (-48) }{ -16 } \right\}\)
= 88 – {5-3}
= 88 – 2
= 86

Question 12.
9 x (8-\(\overline { 3 +2 }\)) – 2 (2 + \(\overline { 3 +3 }\))
Solution:
9 x (8-\(\overline { 3 +2 }\)) -2(2 + \(\overline { 3 +3 }\))
= 9 x (8 – 5) – 2(2 + 6)
= 9 x 3 – 2 x 8
= 27- 16
= 11

Question 13.
2 – [3 – {6 – (5 – \(\overline { 4 -3 }\))}]
Solution:
2 – [3 – {6 – (5 – \(\overline { 4 -3 }\))}]
⇒ 2 – [3 – {6 – (5 – 1)}]
⇒ 2 – [3 – {6 – 4}]
⇒2 – (3 – 2)
⇒2-1 = 1

Integers Exercise 1D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
The sum of two integers is -15. If one of them is 9, find the other.
Solution:
Sum of two integers = -15
One integer = 9
∴ Second integer = -15 – 9
= -(15 + 9)
= -24

Question 2.
The difference between an integer and -6 is -5. Find the values of x.
Solution:
The difference between an integer
= x-(-6) = -5
∴ Value of
⇒ x – (-6) = -5
⇒ x + 6 = -5
x = -5 – 6
x = -11

Question 3.
The sum of two integers is 28. If one integer is -45, find the other.
Solution:
Sum of two integers = 28
One integer = -45
∴ Second integer = 28 – (-45)
= 28 + 45
= 73

Question 4.
The sum of two integers is -56. If one integer is -42, find the other.
Solution:
Sum of two integers = -56
One integer = -42
∴Second integer = -56 – (-42)
= -56+ 42
=-14

Question 5.
The difference between an integer x and (-9) is 6. Find all possible values ofx.
Solution:
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 Answer-x = 6 + 9
⇒ x = 6 – 9 or ⇒ -x = 15
⇒x = -3 or ⇒ x = -15
Hence, possible values ofx are -3 and -15.

Question 6.
Evaluate:

  1. (-1) x (-1) x (-1) x  ….60 times.
  2. (-1) x (-1) x (-1) x (-1) x …. 75 times.

Solution:

  1. 1 (because (-1) is multiplied even times.)
  2. -1 (because (-1) is multiplied odd times.)

Question 7.
Evaluate:

  1. (-2) x (-3) x (-4) x (-5) X (-6)
  2. (-3) x (-6) x (-9) x (-12)
  3. (-11) x (-15) + (-11) x (-25)
  4. 10 x (-12) + 5 x (-12)

Solution:

  1. (-2) x (-3) x (-4) x (-5) x (-6)
    ⇒ 6 x 20 x (-6) = 120 x (-6)
    = -720
  2. (-3) x (-6) x (-9) x (-12)
    ⇒ 18 x 108
    = 1944
  3. (-11) x (-15) + (-11) x (-25)
    ⇒ 165 + 275
    = 440
  4. 10 x (-12) + 5 x (-12)
    ⇒ -120-60
    = -180

Question 8.

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

Solution:

  1. x x (-1) = -36
    -lx = -36
    x = \(\frac { -36 }{ -1 }\)
    x = 36
    ∵ x = 36
    ∴ It is a positive integer.
  2. x x (-1) = 36
    -1x = 36
    x = \(\frac { 36 }{ -1 }\)
    x = -36
    ∵x = -36
    ∴It is a negative integer.

Question 9.
Write all the integers between -15 and 15, which are divisible by 2 and 3.
Solution:
The integers between -15 and 15 are :
-12, -6, 0, 6 and 12
That are divisible by 2 and 3.

Question 10.
Write all the integers between -5 and 5, which are divisible by 2 or 3.
Solution:
The integers between -5 and 5 are :
-4, -3, -2, 0, 0, 2, 3 and 4
That are divisible by 2 or 3.

Question 11.
Evaluate:

  1. (-20) + (-8) ÷ (-2) x 3
  2. (-5) – (-48) ÷ (-16) + (-2) x 6
  3. 16 + 8 ÷ 4- 2 x 3
  4. 16 ÷ 8 x 4 – 2 x 3
  5. 27 – [5 + {28 – (29 – 7)}]
  6. 48 – [18 – {16 – (5 – \(\overline { 4 +1 }\))}]
  7. -8 – {-6 (9 – 11) + 18 = -3}
  8. (24 ÷ \(\overline { 12 -9 }\) – 12) – (3 x 8 ÷ 4 + 1)

Solution:
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).

  1. (-20) + (-8) ÷ (-2) x 3
    ⇒ -20 + 4 x 3
    ⇒ -20+ 12
    =-8
  2. (-5) – (-48) ÷ (-16) + (-2) x 6
    ⇒ (-5) – 3 + (-2) x 6
    ⇒ -5 – 3 – 12
    ⇒ -8- 12
    = -20
  3. 16 + 8 ÷ 4 – 2 x 3
    ⇒ 16 + 2 – 2 x 3
    ⇒16 + 2 – 6
    ⇒ 18-6
    = 12
  4. 16 ÷ 8 x 4 – 2 x 3
    ⇒ 2 x 4 – 2 x 3
    ⇒ 8 – 6
    = 2
  5. 27 – [5 + {28 – (29 – 7)}]
    ⇒ 27 – [5 + {28 – 22}]
    ⇒ 27 – [5 + 6]
    ⇒ 27 — 11
    = 16
  6. 48-[18-{16-(5 – \(\overline { 4 +1 }\))}]
    ⇒ 48-[18-{16-(5-5)}]
    ⇒ 48-[18- {16-0)}]
    ⇒ 48-[18- 16]
    ⇒ 48 – 2
    = 46
  7. -8 – {-6 (9 – 11) + 18 ÷ -3}
    ⇒ -8 – {-6 (-2) – 6}
    ⇒ -8- {12-6}
    ⇒ -8 – {6}
    ⇒ -8-6
    = -14
  8. (24 ÷ \(\overline { 12 -9 }\) – 12) – (3 x 8 = 4 + 1)
    ⇒ (24 ÷ 3-12)-(3 x 2 + 1)
    ⇒ (8- 12)-(6+ 1)
    ⇒ —4 — 7
    = —11

Question 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.
Solution:
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

Question 13.
Add the product of (-13) and (-17) to the quotient of (-187) and 11.
Solution:
(-13) x (-17)+ (-187- 11)
⇒ (-13) x (-17) + (-17)
⇒ 221 – 17 = 204

Question 14.
The product of two integers is-180. If one of them is 12, find the other.
Solution:
The product of two integers = -180 One integer = 12
∴ Second integer = -180 – 12 = -15

Question 15.

  1. A number changes from -20 to 30. What is the increase or decrease in the number?
  2. A number changes from 40 to -30. What is the increase or decrease in the number?

Solution:

  1. ∵A number changes from = -20 to 30
    ⇒ -20 – 30 = -50
    ∴-50, it will be increases.
  2. ∵A number changes from = 40 to -30
    ⇒ 40 – (-30)
    40 + 30 = 70
    ∴70, it will be decreases

 

 

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