Contents

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

MathematicsGeneral ScienceMaharashtra Board Solutions

### Exercise-42

**Solution 1:**

- +2
- – 6
- – 10
- 0
- +18
- – 23

**Solution 2:**

- 9 = Negative nine
- + 5 = Positive five
- -28 = Negative twenty-eight
- -100 = Negative hundred
- +81 = Positive eighty-one
- -4 = Negative nine
- -1 = Negative one
- +1 = Positive one
- +72 = Positive seventy-two
- -48 = Negative forty-eight
- +65 = Positive sixty-five
- -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:**

- 0
- +1
- G
- J
- -2
- +2

**Solution 5:**

### Exercise-43

**Solution 1:**

- +1
+6**<** - – 8
– 5**<** - – 5
– 8**>** - – 2
+3**<** - +3
– 2**>** - – 1
+1**<** - 0
– 7**>** - – 4
+4**<** - +2
– 6**>** - – 3
0**<** - – 6
+5**<** - 0
+7**<**

**Solution 2:**

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

- 38
- 23
- 0
- 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:

- -5
- +2
- +15
- -27
- -10

### Exercise-46

**Solution 1:**

- Subtracting (-8) from 13 means adding the opposite of (-8) to 13.
- Subtracting (-11) from -4 means adding the opposite of (-11) to -4.
- Subtracting (-6) from 6 means adding the opposite of (-6) to 6.
- Subtracting 9 from 9 means adding the opposite of 9 to 9.
- Subtracting (-5) from -5 means adding the opposite of (-5) to 5.
- Subtracting 0 from 14 means adding 0 to 14. (Since 0 is neither positive nor negative, so the opposite of 0 is 0 itself.)
- Subtracting 14 from 0 means adding the opposite of 14 to 0.
- Subtracting -14 from 0 means adding the opposite of -14 to 0.
- 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:**

- 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. - 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. - 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. - 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. - 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. - 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:**

### 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:**

- (-8) + (-3)

= -11 - 13 – 15

= -2 - 6 – (-19)

= 6 + 19

= 25 - 10 + (-7)

= 10 – 7

= 3

**Solution 2:**

- 16 + (-5)

= 11 - (-5) + 16

= 11 - (-7) + (-11)

= -18 - (-11) + (-7)

= -18 - 16 × (-5)

= -80 - (-5) × 16

= -80 - (-7) × (-11)

= 77 - 52 × 1

=52 - (-25) × 1

= -25

**Solution 3:**

- [5 × (-3)] × 6

= (-15) × 6

= -90 - 5 × [(-3) × 6]

= 5 × (-18)

= -90 - (-16) × [4 × 3]

= (-16) × 12

= -192 - (-16 × 4) × 3

= (-64) × 3

= -192 - [5 + (-3)] + 6

= 2 + 6

= 8 - 5 + [(-3) +6]

= 5 + 3

= 8 - -16 + [4 + 3]

= -16 + 7

= -9 - [-16 + 4] + 3

= -12 + 3

= -9

**Solution 4:**

- 4 × [10 + (-12)]

= 4 × (-2)

= -8 - 4 × 10 + 4 × (-12)

= 40 + (-48)

= -8 - (-5) × [-13 + 10]

= (-5) × (-3)

= 15 - (-5) × (-13) + (-5) × (10)

= 65 + (-50)

= 15