Ncert Class 6 Mathematics Solutions Chapter 6 Integers
Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of NCERT Class 6 Mathematics Book, Chapter 6, Integers. Here students can easily find step by step solutions of all the problems for Integers, Exercise 6.1, 6.2 and 6.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 6 solutions. Here all the solutions are based on NCERT latest syllabus.
Integers Exercise 6.1 Solution :
(1) Write opposites of the following :
(a) Increase in weight
(b) 30 km north
(c) 80 m east
(d) Loss of Rs 700
(e) 100 m above sea level
Solution :
(a) opposites of Increase in weight is Decrease in weight
(b) opposite of 30 km north is 30 km south
(c) opposite of 30 km north is 80 m west
(d) opposite of Loss of 700 is Gain of 700
(e) opposite of 100 m above sea level is 100 m below sea level.
(2) Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
(c) A deposit of rupees two hundred.
(d) Withdrawal of rupees seven hundred.
Solution :
(a) + 2000 m.
(b) 800 m.
(c) + 200
(d) -700
(4) Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points :
(a) If point D is + 8, then which point is – 8?
(b) Is point G a negative integer or a positive integer?
(c) Write integers for points B and E.
(d) Which point marked on this number line has the least value?
(e) Arrange all the points in decreasing order of value.
Solution :
(a) point D is + 8, then which point is – 8 is F.
(b) point G a negative integer
(c) point B is 4 and point E is -10.
(d) point E has the least value.
(e) D, C, B, A, O, H, G, F, E are points in decreasing order of value.
(6) In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9; (b) -3, -8
(c) 0, -1; (d) -11, 10
(e) -6, 6; (f) 1, -100
Solution :
(a) 9 is to the right of the other on the number line.
(b) -3 is to the right of the other on the number line.
(c) 0 is to the right of the other on the number line.
(d) 10 is to the right of the other on the number line.
(e) 6 is to the right of the other on the number line.
(f) 1 is to the right of the other on the number line.
(7) Write all the integers between the given pairs (write them in the increasing order.)
(a) 0 and -7
(b) -4 and 4
(c) -8 and -15
(d) -30 and -23
Solution :
(a) 6, – 5, – 4, – 3, – 2, – 1 are integers between the 0 and – 7.
(b) -3, -2, -1, 0, 1, 2, 3 are integers between the – 4 and 4.
(c) -14, -13, -12, -11, -10, -9 are integers between the -8 and – 15.
(d) -29, -28, -27, -26, -25, -24 are integers between the – 30 and – 23.
(8) – (a) Write four negative integers greater than – 20.
Solution :
= – 19, – 18, – 17, – 16 are negative integers greater than – 20
(8) – (b) Write four integers less than – 10.
Solution :
= – 11, – 12, – 13, – 14 are integers less than – 10.
(9) For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) -8 is to the right of -10 on a number line.
(b) -100 is to the right of -50 on a number line.
(c) Smallest negative integer is -1.
(d) -26 is greater than -25.
Solution :
(a) Statement is – True
(b) Statement is – False
Reason : -100 is to the left of -50 on a number line.
(c) Statement is – False
Because, Largest negative integer is -1.
(d) Statement is – False
Integers Exercise 6.2 Solution :
(3) Add without using number line :
(a) 11 + (– 7)
(b) (– 13) + (+ 18)
(c) (– 10) + (+ 19)
(d) (– 250) + (+ 150)
(e) (– 380) + (– 270)
(f) (– 217) + (– 100)
Solution :
(a) 11 + (– 7)
= 11 – 7
= 4
(b) (– 13) + (+ 18)
= (– 13) + 18
= 5
(c) (– 10) + (+ 19)
= (– 10) + 19
= 9
(d) (– 250) + (+ 150)
= (– 250) + 150
= 100
(e) (– 380) + (– 270)
= – 380 – 270
= – 550
(f) (– 217) + (– 100)
= -217 – 100
= -317
(4) Find the sum of :
(a) 137 and -354
(b) -52 and 52
(c) -312, 39 and 192
(d) -50, -200 and 300
Solution :
(a) 137 and -354
= 137 + (- 354)
= – 217
(b) -52 and 52
= – 52 + 52
= 0
(c) -312, 39 and 192
= – 312 + 39 + 192
= – 312 + 231
= – 81
(d) -50, -200 and 300
= (- 50)+ (- 200) + 300
–250 + 300
= 50
(5) Find the sum :
(a) (- 7) + (- 9) + 4 + 16
(b) (37) + (- 2) + (- 65) + (- 8)
Solution :
(a) (- 7) + (- 9) + 4 + 16
= – 7 – 9 + 4 + 16
= -16 + 20
= 4
(b) (37) + (- 2) + (- 65) + (- 8)
= 37 – 2 – 65 – 8
= 37 – 75
= -38
Integers Exercise 6.3 Solution :
(1) Find
(a) 35 – (20); (b) 72 – (90)
(c) (- 15) – (- 18); (d) (- 20) – (13)
(e) 23 – (- 12); (f) (- 32) – (- 40)
Solution :
(a) 35 – (20)
= 35 -20
= 15
(b) 72 – (90)
= 72 – 90
= -18
(c) (– 15) – (– 18)
= (– 15) + 18
= 3
(d) (–20) – (13)
= –20 –13
= -33
(e) 23 – (– 12)
= 23 + 12
= 35
(f) (–32) – (– 40)
= (–32) + 40
= 8
(2) Fill in the blanks with >, < or = sign.
(a) (– 3) + (– 6) __ (– 3) – (– 6)
(b) (– 21) – (– 10) __ (– 31) + (– 11)
(c) 45 – (– 11) __ 57 + (– 4)
(d) (– 25) – (– 42) __ (– 42) – (– 25)
Solution :
(a) (- 3) + (- 6) ___ (- 3) – (- 6)
= (- 3) – 6 (- 3) + 6)
= -9 < 3
= (- 3) + (- 6) -41
∴ (- 21) – (- 10) > (- 31) + (- 11)
(c) 45 – (- 11) ___ 57 + (- 4)
= 45 + 11 57 – 4
= 56 > 53
∴ 45 – (- 11) > 57 + (- 4)
(d) (- 25) – (- 42) ___ (- 42) – (- 25)
= (- 25) + 42 (- 42) + 25
= 17 > – 17
∴ (- 25) – (- 42) > (- 42) – (- 25)
(3) Fill in the blanks :
(a) (– 8) + __ = 0
(b) 13 + __ = 0
(c) 12 + (– 12) = __
(d) (– 4) + __ = – 12
(e) __ – 15 = – 10
Solution :
(a) (– 8) + 8 = 0
(b) 13 + (-13) = 0
(c) 12 + (– 12) = 12 – 12 = 0
(d) – 12 + 4 = –8
(e) – 10 + 15 = 5
(4) Find
(a) (– 7) – 8 – (– 25)
(b) (– 13) + 32 – 8 – 1
(c) (– 7) + (– 8) + (– 90)
(d) 50 – (– 40) – (– 2)
Solution :
(a) (- 7) – 8 – (- 25)
= (- 7) – 8 – (- 25)
= (- 7) – 8 + 25
= – 15 + 25
= 10
(b) (- 13) + 32 – 8 – 1
= (- 13) + 32 – 8 – 1
= (- 13) + 32 – 9
= 32 – 22
= 10
(c) (- 7) + (- 8) + (- 90)
= (- 7) + (- 8) + (- 90)
= – 7 – 8 – 90
= (- 7) + (- 8) + (- 90)
= – 105
(d) 50 – (- 40) – (- 2)
= 50 – (- 40) – (- 2)
= 50 + 40 + 2
= 50 – (- 40) – (- 2)
= 92.
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