WBBSE Solutions For Class 6 Maths Chapter 16 Concept Of Directed Numbers And Number Line

Class 6 Math Solutions WBBSE Chapter 16 Concept Of Directed Numbers And Number Line  Exercise 16

Question 1. Let us draw a number line put the following numbers on the line and name them.

1. Name + 5;- 2, + 3;- 6, + 2,- 5 respectively as A, B, C, D, E, and F.
Solution: + 5;-2; + 3;-6; + 2;-5,

name as A, B, C, D, E, F respectively.

2. Let’s measure how many units E is from B.
Solution: Measure of E from B is units.

3. How many units is A from B towards right?
Solution: Measure of A from B towards the right is 7 units.

4. How many units is D from E towards left?
Solution: Measure of D from E towards the left is 8 units.

5. How many units is D from F towards left ?
Solution: Measure of D from F towards left is 1 unit.

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6. What is the relation between the numbers which are at A and F?
Solution: Relation between the numbers which are at A and F – Mutually opposite numbers.

7. What are the absolute values of the numbers of B and E?
Solution: Absotute values of the numbers of B and E = 2.

Class 6 Math Solutions WBBSE

Question 2. What do the following mean?

1. Profit of -10 rupees
Solution: Profit of -10 rupees = Loss of Rs. 10.

2. -15 m above
Solution: -15 m above = 15 m down

3. -36 g less
Solution: -36 gm less = 36 gm more.

4. -18 meter towards East
Solution: -18 meter towards East = 18 meter toward West.

5. Saved -23 rupees
Solution: Saved -23 rupees = Spent Rs. 23.

6. -5 km towards South.
Solution: -5 km towards south = 5 km towards North.

Question 3. Let’s write the absolute values of the following numbers

1. -12
2. + 13
3. – 22
4. – 61
5. + 17

Solution: Absolute value of the following

1. -12 → 12
2. +13 → 13
3. -22 → 22
4. -61 → 61
5. +17 → 17

Class 6 Math Solutions WBBSE

Question 4. Let’s find the opposite of the following:

1. Spent Rs.-10
Solution: Spent Rs. -10 Rs. 10 saved

2. Climbed up -15 m.
Solution: Climbed up -15m 15m going up

3. Profit of 81
Solution: Profit of 81 :- Loss of Rs. – 81

4. move – 35m down
Solution: move – 35 m down: and 35 m up

5. – 24 kg increase in weight.
Solution: – 24 kg increase in weight = 24 kg weight decreased

6. 28 m towards the right
Solution: 28 m towards right = 28 m towards right

7. 9 kg decrease of weight.
Solution: 9 kg decrease of weight = 9 kg decrease of weight.

Question 5. Using a number line, put < or > in the blank spaces.

Class 6 Math Solutions WBBSE

1. 0 ______ 5
Solution: 0 < 5

2. 0 ________ -6
Solution: 0 > -6

3. 6 ________ -6
Solution: 6 > -6

4. – 8
Solution: -8 > -10

5. -1 ______ -11
Solution: -1 > -11

6. ______ 15
Solution: 11 < 15

7. —10 _____ 12
Solution: -10 < 2

8. -100 _____ -50
Solution: -100 < -50

Question 6. (1) Let’s write 4 negative whole numbers less than -12.
Solution: —15; —18; — 20; – 25;

(2) Let’s write 4 negative whole numbers greater than – 8.
Solution: -6; -4; -3; -1

Class 6 WBBSE Math Solutions Chapter 16 Concept Of Directed Numbers And Number Line  Exercise 16.1

Question 1. Let us add on a number line

1. (+7) – (+2)
Solution: (+7) – (+2)

∴ (+7) + (+2) = +9.

2. (+2)- (-4)
Solution: (+2)- (-4)

∴ (+2) + (—4) = -2

3. (+6) + (-11)
Solution: (+6) + (-11)

∴ (+6) + (-11) = -5

Class 6 WBBSE Math Solutions

4. (-5), (-7)
Solution: (-5), (-7)

∴ (-5), (-7) = -12

5. (+8) + (-8)
Solution: (+ 8), (-8)

∴ (+8) + (-8) = 0

6. (+7), (-7)
Solution: (+7), (-7)

∴ (+ 7) + (-7) = 0

7. (+9), (-17)
Solution: (+9), (-17)

∴ + 9 +(-17)=-8.

Class 6 Maths Solutions WBBSE

8. (-11), (-9)
Solution: (-11), (-9)

∴ (-11) +(-9) = -20

Question 2. Let’s add the following

1. (+9) + (+2)
Solution:

(+9) + (+2) = + 11

2. (+11) – (+ 5)
Solution: (+11) +(+5) = +16

3. (+27) + (-11)
Solution: (+27)+ (-11) = +16

4. (-25) + (+6)
Solution: (-25) + (+6) = -19;

5. (-5) + (+9)
Solution: (—5) + (+9) = +4

6. (+13)+ (-13)
Solution: (+13) + (-13) = 0

Question 3. Let us simplify

1. (+13) + (+12) + (-10)
Solution: (+13) + (+12) + (-10) = +25 – 10 = (+15)

2. (+31) + (+13) + (-16)
Solution: (+31)+ (+13)+ (-16)

= +44 + (-16)

= 44 – 16 = (+28)

Class 6 Maths Solutions WBBSE

3. (+25) + (-16) + (+ 2)
Solution: (+25) +(-16) +(+2)

= (+9) + (+2)

= (+11)

4. (-11) + (+18) + (-16)
Solution: (-11)+ (+18)+ (-16)

= (+7)+ (-16)

= (-9)

Question 4. Let’s add the following

1. (-2), (-10), (+21)
Solution: (-2)+ (-10)+ (+21)

= (-12) + (+21)

= (+9)

2. (-18), (-7), (-2)
Solution: (-18) + (-7) + (-2)

=(-25)+ (-2)

= (-27)

Class 6 Maths Solutions WBBSE

3. (+10), (-8), (-10)
Solution: (+10) + (-8) + (-10)

= (+2) + (-10)

= (-8)

4. (-8), (-10), (+2)
Solution: (-8) + (-10) + (+2)

= (-18) + (+2)

= (-16)

5. (-19),(-9),(+5)
Solution: (-19) + (-9) + (+5)

= (-28) + (+5)

= (-23)

6. (+20), (-9), (-6)
Solution: (+ 20) + (-9) + (-6)

= (+11) + (-6)

= (+5)

7. (-14), (-12), (+ 21)
Solution: (-14) + (-12) + (+21)

= (-26) + (+21)

= (-5)

8. (-13), (+7), (-2)
Solution: (-13) + (+7) + (-2)

= (-6) + (-2)

= (-8)

9. (+15), (-9), (-5)
Solution: (+15) + (-9) + (-6)

= (+6) + (-6)

= 0

WBBSE Math Solutions Class 6 Chapter 16 Concept Of Directed Numbers And Number Line  Exercise 16.2

Question 1. Let’s do it

1. (- 6) – (+2) = _____
Solution: (-6) – (+2)

= -6-2 = —8

2. (-12) — (+12) = ______
Solution: (-12) – (+12)

= -12-12 = -24

3. (+11)-(+3) = ______
Solution: (+11)-(+3)

= 11-3 = +8

4. (-7) – (+8) = _____
Solution: (-7) – (+8)

= -7-8 = -15

5. (+20) – (-7) = ______
Solution: (+20) – (-7)

= 20 + 7 = 27

6. (-18)-(-8) = _________
Solution: (-18)-(-8)

= -18 + 8

= -10

7. (- 9) – (-9) = _______
Solution: (- 9) – (- 9)

= -9+9

= 0

WBBSE Math Solutions Class 6

8. (+ 13)- (-7) = ________
Solution: (+ 13)-(-7)

= 13 + 7 = 20

Question 2. Let’s complete the table given below

Solution:

Question 3. Let us mark (√) for the correct statement and (x) for wrong statement:

1. There are definite numbers of positive whole numbers.
Solution: There are definite numbers of positive whole numbers. [√]

2. 5.3 is a natural number.
Solution: 5.3 is a natural number. [X]

3. – 2.1 is a negative whole number.
Solution: -2.1 is a negative whole number. [x]

4. There is no existence of biggest whole number.
Solution: There is no existence of biggest whole number. [√]

WBBSE Math Solutions Class 6

Question 4. 1. (+14) — (+16)
Solution: (+14)-(+16)

= (+14)+ (-16)

= 14-16 = – 2

2. (+25) – (+21)
Solution: (+ 25)-(+21)

= (+ 25) + (-21)

= 25-21 = 4

3. (+ 34) – (-19)
Solution: (+ 34) – (-19)

= (+34)+ (+19)

= 34 + 19

= +53

4. (-15)-(-27)
Solution: (-15)-(-27)

=(-15)+(+27)

= -15 + 27

= +12

5. (-25) -(+13)
Solution: (-25) -(+13)

= (-25) + (-13)

= -25-13

= -38

6. (-16)-(-10)
Solution: (-16)-(-10)

= (-16)+ (+10)

= -16 + 10

= – 6

7. (+ 31) — (— 12)
Solution: (+31)-(-12)

= (+31)+ (+12)

= +31+12 = +43

8. (—31) — (—45)
Solution: (-31)-(-45)

= (-31)+ (+45)

= – 31 + 45 = +14

9. (-21)-(+21)
Solution: (-21)-(+21)

= (-21)+ (-21)

= -21-21

= -42

WBBSE Math Solutions Class 6

Question 5. Let’s put >, < or = in respective blank spaces:

1. (+13) + (- 8) _______ (+3) – (-2)
Solution: L.H.S. = (+13) + (-8)

= 13-8 = 5

⇒ R.H.S. = (+ 3) – (-2)

= 3 + 2 = 5

∴ (+13) + (-8) [ = ] (+3) – (-2)

2. (-12)-(-10) _______ (-9) +(+3)
Solution: L.H.S. = (-12)-(-10)

= -12 + 10 = – 2

⇒ R.H.S. = (-9) + (+3)

= -9 + 3

= -6

∴ (-12) – (-10) [ > ] (-9) + (+3)

3. (+35) – (-5) _____ (- 24) – (-64)
Solution: L.H.S. = (+ 35) – (-5)

= 35 + 5 = 40

⇒ R.H.S. = (-24)-(-64)

= – 24 + 64 = 40

∴ (+35) – ( -5) [ = ] (-24) – (-64)

Class 6 Math WBBSE Solutions

4. (-18) – (+6) ______ (-18) – (-6)
Solution: L.H.S. = (-18) – (+6)

= -18-6 = -24

⇒ R.H.S. = (-18) -(-6)

= -18 + 6 = -12

∴ (-18) (+ 6) [ < ] (—18) — (—6)

5. (-45) – (-52) _______ (-52) – (-45)
Solution: L.H.S. = (-45) – (-52)

= -45 + 52 = + 7

⇒ R.H.S. = (-52)-(- 45)

= – 52 + 45 = —7

∴ (-45) – (—52) [ > ] (-52) – (-45)

6. (+25) -(-19) _______ (-25) -(+19)
Solution: L.H.S. = (+25)-(-19)

= +25 + 19 = + 44

⇒ R.H.S. = (-25)-(+19)

= -25-19 = -44

∴ (+25) — (—19) [ > ] (—25) – (+19)

Question 6. Let’s put number in blank spaces:

1. (-3) + ________ = 0
Solution: (—3) + [+3] = 0

2. (+16) + ________ = 0
Solution: (+16) + [-16] = 0

3. (-9) + _______ = (-15)
Solution: (-9) + [-6] = – 15

4. _____ + (-7) = (-10)
Solution: [-3] +(-7) = (-10)

Question 7. Let’s simplify:

1. (-5) + (opposite number of -7) – (-5)
Solution: (-5) + (+7) + (5)

= + 7

2. 12 – (-3) + (opposite number of +6)
Solution: 12 + 3 + (-6)

= 15-6 = 9

3. 15 – (+4) + (opposite number of +9)
Solution: 15 – 4 + (-9)

= 15-4-9 = 15-13 = 2

4. (opposite number of +20) – (opposite number of -7) – (-8)
Solution: (-20) – (+7) + 8

= -20 – 7 + 8 = – 27 + 8

= -19

Question 8. Let’s find what must be added to the first to get the second:

1. -7,-12
Solution: -12-(-7)

= -12 + 7 = – 5

2. 24, – 32
Solution: -32 – (+24)

= – 32 – 24

= -56

3. -17,12
Solution: 12-(-17)

= 12+17

= 29

Class 6 Math WBBSE Solutions

4. 16, 0
Solution: 0 – (+ 16)

= 0-16

= -16

5. 25,-42
Solution: -42 – (+25)

= -42 -25 = -67

Question 9. Let’s find what must be added to the first to get the second:

1. (+7), (+2)
Solution: (+2) – (+7)

= 2-7 = -5

.2. (+7), (-2)
Solution: (-2)-(+7)

= -2-7 = —9

3. (-7), (+2)
Solution: (+2)-(-7)

= 2 + 7 = 9

4. (-7), (-2)
Solution: (-2)-(-7)

= -2 + 7

= + 5

Question 10. Let’s verify the commutative property of addition for the following:

1. (+5), (+3)
Solution: (+5) + (+3) = +8,

⇒ Again, (+3) + (+5) = +8 (+5) + (+3) = (+3) + (+5)

2. (+ 5), (-3)
Solution: (+5) + (-3) = +2,

⇒ Again, (-3) + (+5) = + 2 (+5) + (-3) = (-3) + (+5)

3. (-5), (+3)
Solution: (-5) + (+3) = -2,

⇒ Again, (+3) + (-5) = – 2 (-5) + (+3) = (+3) + (-5)

4. (-5), (-3)
Solution:

⇒ (-5) + (-3) = -8,

⇒ Again (-3) + (-5) = -8

⇒ (-5) + (-3) = (-3) + (-5)

Question 11. Let’s verify the associative property of addition for the following:

1. (+5), (+3), (+2)
Solution: (+5), (+3), (+2)

= {(+5) + (+3)} + (+2)

= (+8) + (+2)

= (+10)

⇒ and, = (+5) + {(+3) + (+2)}

= +5 + 5 = (+10)

{(+5) + (+3)} + (+2)

= (+5) + {(+3) + (+2)}

(+5), (+3), (+2) = (+5) + {(+3) + (+2)}

2. (+5), (-3), (+2)
Solution: (+5), (-3), (+2)

= {(+5) + (-3)) + (+2)

= (+2) + (+2) = (+4)

⇒ and, (+5) + {(-3) + (+2)}

= (+5) + (-1) = (+4)

= {(+ 5) + (-3)} + (+2)

= (+5) + {(-3) + (+2)}

(+5), (-3), (+2) = (+5) + {(-3) + (+2)}

Class 6 Math WBBSE Solutions

3. (-5), (-3), (+2)
Solution: (-5), (-3), (+2)

⇒ {(-5) + (-3)} + (+2)

= (-8) + (+2) = -6 and, (—5) + {(—3) + (+2)}

= (—5) + (—1) = -6

⇒ {(-5) + (-3)} + (+2)

= -5 + {(-3) + (+2)}

{(-5) + (-3)} + (+2) = -5 + {(-3) + (+2)}

4. (—5), (—3), (-2)
Solution: (-5), (-3), (-2)

⇒ {(- 5) + (-3)} + (-2)

= (-8) + (-2) = (-10)

⇒ and, (-5) + {(-3) + (-2)}

= (- 5) + (- 5) = (-10)

⇒ {(-5) + (-3)} + (-2)

= (-5) + {(-3) + (-2)}

(-5), (-3), (-2) = (-5) + {(-3) + (-2)}