WBBSE Solutions For Class 6 Maths Algebra Chapter 2 Concept Of Directed numbers And Numbers Line
Question 1. What do the following quantities mean:
1. Profit of Rs. (- 7)
Solution:
A profit of ₹ (- 7) means a Loss of Rs. 7
2. – 5m. above
Solution:
– 5 metres above means 5 metres below or down
3. – 26 gm less
Solution:
– 26 gm less means 26 gm more
WBBSE Solutions For Class 6 Maths
4. – 18 meters towards the east
Solution:
– 18 metres towards east means 18 metres towards West
5. savings of ₹ (- 23).
Solution:
Savings of ₹ (- 23) means the expenditure of ₹ 23
WBBSE Class 6 Directed Numbers Notes
Question 2. Write the opposite of the following quantities:
1. Expenditure of Rs. 15
Solution:
The opposite quantity of “Expenditure of ₹ 15” is “Income of ₹ 15” or “Expenditure of ₹ (- 15)”.
Class 6 Math Solution WBBSE
2. Climbing – 12 metres up
Solution:
The opposite quantity of “climbing (- 12) metres up” is “Descing (- 12) metres down” or “climbing 12 metres up”.
3. Profit of ₹ 80
Solution:
The opposite of “Profit of ₹ 80” is “Loss of ? 80” or “Profit of ₹ (- 80)”.
4. Descending – 35 m down
Solution:
The opposite of “Descending (- 35) metres down” is “climbing (- 35) metres up” or “Descending 35 metres down”.
5. – 24 kg increase in weight
Solution:
The opposite quantity of “- 24 kg increase in weight” is 24 kg decrease in weight” or “24 kg increase in weight”.
6. 28 metres towards the right
Solution:
The opposite of “28 metres towards the right” is “28 metres towards left” or “- 28 metres towards the right”.
Class 6 Math Solution WBBSE
7. 9 kg decrease in weight
Solution:
The opposite of “9 kg decrease of weight” is “9 kg increase in weight” or “(- 9) kg decrease of weight”.
8. Loss of ₹ (- 5).
Solution:
The opposite of “Loss of ₹ (- 5)” is “Profit of ₹ (- 5)” or “Loss of ₹ 5”.
Question 3. Write the synonyms of the following quantities:
1. 10 km towards the north
Solution:
The synonym of “10 km towards the north” is “-10 km towards the south”.
Understanding Number Line
2. – 3 kg decrease in weight
Solution:
The synonym of “-3 kg decrease of weight” is “3 kg increase in weight”.
3. climbing 11 metres up
Solution:
The synonym of “climbing 11 metres up” is “descending – 11 metres down”.
4. Profit of ₹ (- 18).
Solution:
The synonym of “Profit of ₹ (- 18)” is “Loss of ₹ 18”.
Class 6 Math Solutions WBBSE English Medium
Question 4. Write the opposite numbers of the following
1. – 17,
Solution :
The opposite number of – 17 is + 17.
2. 0
Solution :
The opposite number of 0 is 0.
3. 1
Solution :
The opposite number of 1 is – 1.
4. 00
Solution :
The opposite number of 100 is – 100.
Short Questions on Directed Numbers
Question 5. Write the absolute values of the following numbers :
1. – 12,
Solution:
|- 12| = – (- 12) = + 12 = 12 (v – 12 < 0)
2. + 13.
Solution:
|+ 13| = + (+ 13) = + 13 = 13 (v + 13 > 0)
Question 6.
1. Write 4 negative integers less than (- 8).
Solution:
4 negative integers less than – 8, are – 9, – 10, – 11, – 12.
Common Questions About Number Line Operations
2. Write 4 negative integers greater than (- 12).
Solution:
4 negative integers greater than (- 12) are – 11, – 10, – 9, – 8.
Question 7. Using the concept of opposite numbers, subtract the following :
1. (+ 14) – (+ 16)
Solution :
(+ 14) – (+ 16) = (+ 14) + (- 16)
[∵ The opposite number of (+ 16) is – 16]
= [- (16 – 14)]
= (- 2)
= – 2.
(+ 14) – (+ 16) = – 2.
2. (+ 25) – (+ 21)
Solution :
(+ 25) – (+ 21) = (+ 25) + (- 21)
[∵ the opposite number of (- 21) is + 21]
= [+ (25 – 21)]
= (+ 4)
= 4.
(+ 25) – (+ 21) = 4.
3. (+ 34) – (- 19)
Solution :
(+ 34) – (- 19) = (+ 34) + (+ 19)
[∵ the opposite number of (- 19) is (+ 19)]
= [+ (34 + 19)] (+ 53)
= 53.
(+ 34) – (- 19) = 53.
4. (- 15) – (- 27).
Solution :
(- 15) – (- 27) = (- 15) +- (+ 27)
[∵ the opposite number of (- 27)) is (+27)]
= [+ (27 – 15)]
= (+ 12)
= 12.
(- 15) – (- 27) = 12.
Practice Problems on Directed Numbers
5. (- 25) – (+ 13)
Solution :
(- 25) – (+ 13) = (- 25) + (- 13)
[∵ the opposite number of (+13) is (- 13)]
= [- (25 + 13)]
= (- 38)
= – 38.
(- 25) – (+ 13) = – 38.
Question 8. Put the numbers in blank spaces:
1. (- 3) + □ = 0
Solution:
We know that the sum of two opposite numbers is always zero.
Now, the opposite number of (- 3) is (+ 3).
∴ (- 3) + (+3) = 0
2. (+ 16) + □ = 0
Since the sum of two opposite numbers is always zero
Now, the opposite number of (+ 16) is (- 16), we have
∴ (+ 16) + (- 16) = 0
3. (- 7) + □ = (- 10).
Let (- 7) + m= (- 10)
∴ x = (- 10) -(-7)
= (- 10) + (+ 7)
[∵ The opposite number of (- 1) is (+ 7)]
= h (10 – 7) = [(- 3)]
∴ x = (- 3)
So, (-7) +03= (- 10)
Important Definitions Related to Directed Numbers
Question 9. Simplify :
1. (+ 12) – (- 3) + [opposite number of (+ 6)]
Solution: (i) (+ 12) – (- 3) + (opposite number of + 6)
= (+ 12) + (+ 3) + (- 6)
= [+ (12 + 3)] + (- 6)
= (+ 15) + (- 6)
= [+ (15 – 6)]
= (+ 9)
= 9.
(+ 12) – (- 3) + [opposite number of (+ 6)] = 9.
2. (Opposite number of + 20) – (opposite number of – 7) – (- 8).
Solution:
(opposite number of + 20) – (opposite number of – 7) – (- 8)
= (- 20) – (+ 7) + (+ 8)
= (- 20) + (- 7) + (+ 8)
= [- (20 + 7)] + (+ 8)
= (- 27) + (+ 8)
= [- (27 – 8)]
= (- 19)
= – 19.
(Opposite number of + 20) – (opposite number of – 7) – (- 8) = – 19.
3. 15 – (+ 14) + (opposite number of + 9)
Solution:
15 – (+ 4) + (opposite number of + 9)
= 15 + (- 4) + (- 9)
= 15 + [- (4 + 9)]
= 15 + (- 13)
= (15 – 13)
= 2.
15 – (+ 14) + (opposite number of + 9) = 2.
4. (- 5) + (opposite number of – 7) – (- 5).
Solution:
(- 5) + (opposite number of – 7) – (- 5)
= (- 5) + (+ 7) + (+ 5)
= (- 5) + [+ (7 + 5)] ‘ ’
= (- 5) + ( + 12)
= [+ (12 – 5)]
= (+7)
= 7.
(- 5) + (opposite number of – 7) – (- 5) = 7.
Examples of Real-Life Applications of Directed Numbers
Question 10. What must be added to the first to get the second in the following:
1. – 7, – 12
Solution:
The required number = – 12 – (- 7)
= – 12 + (+ 7)
= – (12 – 7) = – 5
2. 24, – 32
Solution:
The required number = – 32 – (+ 24)
= – 32 + (- 24)
= – (32 + 24)
= – 56.
24, – 32 = – 56.
3. – 12, 17
Solution:
The required number = 17 – (- 12)
= 17 + (+ 12)
= 17 + 12
= 29
– 12, 17 = 29
4. 25, – 42.
Solution:
The required number = – 42 – ( + 25)
= – 42 + ( – 25)
= – (42 + 25)
= – 67
25, – 42 = – 67
Question 11. Put <, > or = sign properly in the appropriate blank spaces of the following :
1. (+ 13) + (- 8) □ (+ 3) – (- 2)
Solution : (i) (+ 13) + (- 8) = [+ (13 – 8)] = (+ 5) = 5
(+ 3) – (- 2) = (+ 3) + (+ 2) = [+ (3 + 2)] = (+ 5) = 5
But 5 = 5
(+ 13) + (- 8) C=] (+ 13) – (- 2)
2. (- 18) – (+ 6) □ (- 18) – (- 6)
Solution:
(- 18) – (+ 6) = (- 18) + (- 6) = [- (18 + 6)] = (- 24) = – 24
(- 18) – (- 6) = (- 18) + (+ 6) = [- (18 – 6)] = (- 12) = – 12
But – 24 < – 12
∴ (18) – (+ 6) < (- 18) – (- 6)
Verify the commutative property of addition for the following :
(+ 5) + (- 3) ;
Solution : (i) (+ 5) + (- 3)
= [+ (5 – 3)] = (+ 2)
= 2 (- 3) + (+ 5)
= [+ (- 3 + 5)]
= (+ 2)
= 2
∴ (+5) +(-3) = (-3) +(+5)
So commutative law of addition is verified.
Conceptual Questions on Positive and Negative Numbers
2. (- 5) + (+ 3).
Solution:
(- 5) + (+ 3) = [- (5 – 3)]
= (- 2)
= – 2
(- 5) + (+ 3) = – 2
(+ 3) + (- 5) = [- (5 – 3)]
= (- 2)
= – 2
∴ (-5) + (+ 3) = (+ 3) + (- 5)
So commutative law of addition is verified.