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Integers – Maharashtra Board Class 6 Solutions for Mathematics

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Integers – Maharashtra Board Class 6 Solutions for Mathematics (English Medium)

MathematicsGeneral ScienceMaharashtra Board Solutions

Exercise-42

Solution 1:

  1. +2
  2. – 6
  3. – 10
  4. 0
  5. +18
  6. – 23

Solution 2:

  1. 9 = Negative nine
  2. + 5 = Positive five
  3. -28 = Negative twenty-eight
  4. -100 = Negative hundred
  5. +81 = Positive eighty-one
  6. -4 = Negative nine
  7. -1 = Negative one
  8. +1 = Positive one
  9. +72 = Positive seventy-two
  10. -48 = Negative forty-eight
  11. +65 = Positive sixty-five
  12. -95 = Negative ninety-five

Solution 3:
Numbers to the left of zero: -9, -28, -100, -4, -1, -48, -95.
Numbers to the right of zero: +5, +81, +1, +72, +65.

Solution 4:

  1. 0
  2. +1
  3. G
  4. J
  5. -2
  6. +2

Solution 5:
integers-maharashtra-board-class-6-solutions-for-mathematics-ex(42)-5

Exercise-43

Solution 1:

  1. +1 < +6
  2. – 8 < – 5
  3. – 5 > – 8
  4. – 2 < +3
  5. +3 > – 2
  6. – 1 < +1
  7. 0 > – 7
  8. – 4 < +4
  9. +2 > – 6
  10.  – 3 < 0
  11.  – 6 < +5
  12.  0 < +7

Solution 2:

  1. +5, +6, +7
  2. -4, -5, -6, -7, -8
  3. -3, -2, -1, 0, +1
  4. -8
  5. +7

Solution 3:

There are unlimited number of integers both to the left and the right of zero, hence we cannot determine the biggest or the smallest integer.

Exercise-44

Solution 1:

  1. 38
  2. 23
  3. 0
  4. 5
  5. 14

Solution 2(1):
Magnitude of the numbers = 8, 6
Bigger magnitude = 8
Difference between the magnitudes = 8 – 6 = 2

Solution 2(2):
Magnitude of the numbers = 8, 6
Bigger magnitude = 8
Difference between the magnitudes = 8 – 6 = 2

Solution 2(3):
Magnitude of the numbers = 2, 11
Bigger magnitude = 11
Difference between the magnitudes = 11 – 2 = 9

Solution 2(4):
Magnitude of the numbers = 15, 20
Bigger magnitude = 20
Difference between the magnitudes = 20 – 15 = 5

Solution 2(5):
Magnitude of the numbers = 45, 35
Bigger magnitude = 45
Difference between the magnitudes = 45 – 35 = 10

Solution 2(6):
Magnitude of the numbers = 32, 45
Bigger magnitude = 45
Difference between the magnitudes = 45 – 32 = 13

Solution 2(7):
Magnitude of the numbers = 16, 16
Bigger magnitude = equal magnitudes
Difference between the magnitudes = 16 – 16 = 0

Solution 2(8):
Magnitude of the numbers = 0, 4
Bigger magnitude = 4
Difference between the magnitudes =4 – 0 = 4

Solution 3(1):
The magnitudes of -12 is 12 and that of +10 is 10.
The difference between them is 12 – 10 = 2
The magnitude 12 is bigger than 10. So, we give 2 the sign of -12 i.e. the negative sign.
∴ (-12) + (+10) = -2

Solution 3(2):
The magnitude of +12 is 12 and that of -10 is 10.
The difference between them is 12 – 10 = 2
The magnitude 12 is bigger than 10. So, we give 2 the sign of +12 i.e. the positive sign.
∴ (+12) + (-10) = +2

Solution 3(3):
The magnitude of +12 is 12 and that of +10 is 10.
Their sum is 12 + 10 = 22
The magnitude 12 is bigger than 10. So, we give 22 the sign of +12 i.e. the negative sign.
∴ (12) + (+10) = +22

Solution 3(4):
The magnitude of -12 is 12 and that of -10 is 10.
Their sum is 12 + 10 = 22
The magnitude 12 is bigger than 10. So, we give 22 the sign of -12 i.e. the negative sign.
∴ (-12) + (-10) = -22

Solution 3(5):
The magnitude of +37 is 37 and that of -22 is 22.
The difference between them is 37 – 22 = 15
The magnitude 37 is bigger than 22. So, we give 15 the sign of +37 i.e. the positive sign.
∴ (+37) + (-22) = 15

Solution 3(6):
The magnitude of -37 is 37 and that of +22 is 22.
The difference between them is 37 – 22 = 15
The magnitude 37 is bigger than 22. So, we give 15 the sign of -37 i.e. the negative sign.
∴ (-37) + (22) = -15

Solution 3(7):
The magnitude of -37 is 37 and that of -22 is 22.
Their sum is 37 + 22 = 59
The magnitude 37 is bigger than 22. So, we give 59 the sign of -37 i.e. the negative sign.
∴ (-37) + (-22) = -59

Solution 3(8):
The magnitude of +37 is 37 and that of +22 is 22.
Their sum is 37 + 22 = 59
The magnitude 37 is bigger than 22. So, we give 59 the sign of -37 i.e. the positive sign.
∴ (+37) + (+22) = +59

Solution 3(9):
The magnitude of -23 is 23 and that of -27 is 27.
Their sum is 23 + 27 = 50
The magnitude 27 is bigger than 23. So, we give 50 the sign of -27 i.e. the negative sign.
∴ (-23) + (-27) = -50

Solution 3(10):
The magnitude of +23 is 23 and that of -27 is 27.
The difference between them is 27 – 23 = 4
The magnitude 27 is bigger than 23. So, we give 4 the sign of -27 i.e. the negative sign.
∴ (+23) + (-27) = -4

Solution 3(11):
The magnitude of +27 is 27 and that of +23 is 23.
Their sum is 27 + 23 = 50
The magnitude 27 is bigger than 23. So, we give 50 the sign of +27 i.e. the positive sign.
∴ (+27) + (23) = 50

Solution 3(12):
The magnitude of -23 is 23 and that of +27 is 27.
The difference between them is 27 – 23 = 4
The magnitude 27 is bigger than 23. So, we give 4 the sign of +27 i.e. the positive sign.
∴ (-23) + (+27) = +4

Solution 3(13):
The sum of any integer and zero is equal to the integer itself.
∴ -8 + 0 = -8

Solution 3(14):
The magnitude of -5 is 5 and that of -15 is 15.
Their sum is 15 + 5 = 20
The magnitude 15 is bigger than 5. So, we give 20 the sign of -15 i.e. the negative sign.
∴ (-5) + (-15) = -20

Solution 3(15):
The magnitude of -15 is 15 and that of -5 is 5.
Their sum is 15 + 5 = 20
The magnitude 15 is bigger than 5. So, we give 20 the sign of -15 i.e. the negative sign.
∴ (-15) + (-5) = -20

Solution 3(16):
The magnitude of +11 is 11 and that of +9 is 9.
Their sum is 11 + 9 = 20
The magnitude 11 is bigger than 9. So, we give 20 the sign of 11 i.e. the positive sign.
∴ (+11) + (+9) = +20

Solution 3(17):
The magnitude of +9 is 9 and that of +11 is 11.
Their sum is 11 + 9 = 20
The magnitude 11 is bigger than 9. So, we give 20 the sign of 11 i.e. the positive sign.
∴ (+9) + (+11) = +20

Solution 3(18):
The magnitude of +20 is 20 and that of -1 is 1.
The difference between them is 20 – 1 = 19
The magnitude 20 is bigger than 1. So, we give 19 the sign of +20 i.e. the positive sign.
∴ (+20) + (-1) = +19

Solution 3(19):
The magnitude of -1 is 1 and that of +20 is 20.
The difference between them is 20 – 1 = 19
The magnitude 20 is bigger than 1. So, we give 19 the sign of +20 i.e. the positive sign.
∴ (-1) + (+20) = +19

Solution 3(20):
0 does not have a positive or negative sign.
Hence, the magnitude of 0 is 0 itself.
∴ 0 + 0 = 0

Solution 3(21):
The magnitude of -10 is 10 and that of +10 is 10.
The difference between them is 10 – 10 = 0
∴ (-10) + (+10) = 0 (The number 0 has no sign)

Solution 3(22):
The magnitude of +11 is 11 and that of -11 is 11.
The difference between them is 11 – 11 = 0
∴ (+11) + (-10) = 0 (The number 0 has no sign)

Solution 3(23):
The magnitude of -165 is 165 and that of +165 is 165.
The difference between them is 165 – 165 = 0
∴ (-165) + (+165) = 0 (The number 0 has no sign)

Solution 3(24):
The magnitude of +92 is 92 and that of -92 is 92.
The difference between them is 92 – 92 = 0
∴ (+92) + (-92) = 0 (The number 0 has no sign)

Exercise-45

Solution 1:
Opposite numbers:

  1. -5
  2. +2
  3. +15
  4. -27
  5. -10

Exercise-46

Solution 1:

  1. Subtracting (-8) from 13 means adding the opposite of (-8) to 13.
  2. Subtracting (-11) from -4 means adding the opposite of (-11) to -4.
  3. Subtracting (-6) from 6 means adding the opposite of (-6) to 6.
  4. Subtracting 9 from 9 means adding the opposite of 9 to 9.
  5. Subtracting (-5) from -5 means adding the opposite of (-5) to 5.
  6. Subtracting 0 from 14 means adding 0 to 14. (Since 0 is neither positive nor negative, so the opposite of 0 is 0 itself.)
  7. Subtracting 14 from 0 means adding the opposite of 14 to 0.
  8. Subtracting -14 from 0 means adding the opposite of -14 to 0.
  9. Subtracting 12 from 20 means adding the opposite of 12 to 20.

Solution 2:

1. 8 – 5
= 8 + (-5)
= 3		 11. 5 – 5
= 5 – (+5)
= 5 + (-5)
= 0
2. (-8) – (-5)
= (-8) + 5
= -3		 12.  -5 – (-5)
= -5 + 5
= 0
3. 8 – (-5)
= 8 + 5
= 13		 13.  -28 – (-35)
= -28 + 35
= 7
4. -8 – 5
= (-8) – (+5)
= -8 + (-5)
= -13		 14.  41 – (-33)
= 41 + 33
= 74
5. -16 – (-9)
= -16 + 9
= 7		 15.  -19 – 15
= -19 – (+15)
= -19 + (-15)
= -34
6. 16 – 9
= 16 + (-9)
= 7		 16. 12 – (-2)
= 12 + 2
= 14
7. -16 – 9
= -16 – (+9)
= -16 + (-9)
= -25		 17. 55 – (-30)
= 55 + 30
= 85
8. 16 – (-9)
= 16 + 9
= 25		 18.  49 – 14
=49 – (+14)
=49 + (-14)
= 35
9. 5 – (-5)
= 5 + 5
= 10		 19. -27 – (-127)
= -27 + 127
= 100
10.  -5 – 5
= -5 + (-5)
= -10		 20. -19 – 35
= -19 – (+35)
= -19 + (-35)
= -54

Exercise-47

Solution 1:

  1. The magnitude of 12 and -3 are 12 and 3 respectively.
    Their product, 12 × 3 = 36
    ∴ 12 × (-3) = -36
    As one number is negative and the other positive, the product is negative.
  2. The magnitude of -6 and 4 are 6 and 4 respectively.
    Their product, 6 × 4 = 24
    ∴ (-6) × 4 = -24
    As one number is negative and the other positive, the product is negative.
  3. The magnitude of -15 and -5 are 15 and 5 respectively.
    Their product , 15 × 5 = 75
    ∴ (-15) × (-5) = 75
    The product of two negative numbers is positive.
  4. The magnitude of 35 and 8 are 35 and 8 respectively.
    Their product , 35 × 8 = 280
    ∴ 35 × 8 = 280
    The product of two positive numbers is positive.
  5. The magnitude of -38 and -2 are 38 and 2 respectively.
    Their product , 38 × 2 = 76
    ∴ (-38) × (-2) = 76
    The product of two negative numbers is positive.
  6. The magnitude of 15 and -61 are 15 and 61 respectively.
    Their product , 15 × 61 = 915
    ∴ 15 × (-61) = -915
    As one number is negative and the other positive, the product is negative.

Solution 2:
integers-maharashtra-board-class-6-solutions-for-mathematics-ex(47)-2
integers-maharashtra-board-class-6-solutions-for-mathematics-ex(47)-2.1

Exercise-48

Solution 1(1):
-5 + [(9) × (-3) + (6 × 11)] ÷ 13
= -5 + [(-27) + 66] ÷ 13 (multiplication)
= -5 + 39 ÷ 13 (subtraction in brackets)
= -5 + 3 (division)
= -2 (subtraction)

Solution 1(2):
[180 + (-15) + 20] – [(-2) × (-11) – (4 + 3)]
= [(180 -15)+ 20] – [(-2) × (-11) – (4 + 3)]
= (165 + 20) – (22 – 7) (addition, multiplication)
= 185 – 15 (addition, subtraction)
= 170

Solution 1(3):
(210 – 150) + [9 × 10 + (-5 × 2)] – 100
= 60 + [90 + (-10)] – 100 (subtraction, multiplication)
= 60 + (90 – 10) – 100
= 60 + 80 – 100 (subtraction)
= 140 – 100 (addition)
= 40 (subtraction)

Solution 1(4):
-10 + [(-3) × (-5) ÷ 3]
= -10 + [15 ÷ 3] (multiplication)
= -10 + 5 (division)
= -5 (subtraction)

Solution 1(5):
(12 × 4) ÷ 2 – 24
= 48 ÷ 2 – 24 (multiplication)
= 24 – 24 (division)
= 0 (subtraction)

Solution 1(6):
[(15) × (2) + (-4) × (5)] ÷ (-5)
= [(30 + (-20)] ÷ (-5) (multiplication)
= (30 – 20) ÷ (-5)
= 10 ÷ (-5) (subtraction)
= -2 (division)

Exercise-49

Solution 1:

  1. (-8) + (-3)
    = -11
  2. 13 – 15
    = -2
  3. 6 – (-19)
    = 6 + 19
    = 25
  4. 10 + (-7)
    = 10 – 7
    = 3

Solution 2:

  1. 16 + (-5)
    = 11
  2. (-5) + 16
    = 11
  3. (-7) + (-11)
    = -18
  4. (-11) + (-7)
    = -18
  5. 16 × (-5)
    = -80
  6. (-5) × 16
    = -80
  7. (-7) × (-11)
    = 77
  8. 52 × 1
    =52
  9. (-25) × 1
    = -25

Solution 3:

  1. [5 × (-3)] × 6
    = (-15) × 6
    = -90
  2. 5 × [(-3) × 6]
    = 5 × (-18)
    = -90
  3. (-16) × [4 × 3]
    = (-16) × 12
    = -192
  4. (-16 × 4) × 3
    = (-64) × 3
    = -192
  5. [5 + (-3)] + 6
    = 2 + 6
    = 8
  6. 5 + [(-3) +6]
    = 5 + 3
    = 8
  7. -16 + [4 + 3]
    = -16 + 7
    = -9
  8. [-16 + 4] + 3
    = -12 + 3
    = -9

Solution 4:

  1. 4 × [10 + (-12)]
    = 4 × (-2)
    = -8
  2. 4 × 10 + 4 × (-12)
    = 40 + (-48)
    = -8
  3. (-5) × [-13 + 10]
    = (-5) × (-3)
    = 15
  4. (-5) × (-13) + (-5) × (10)
    = 65 + (-50)
    = 15