NCERT Solutions Class 6 Maths
Chapter – 6 (Integers)
The NCERT Solutions in English Language for Class 6 Mathematics Chapter – 6 Integers Exercise 6.2 has been provided here to help the students in solving the questions from this exercise.
Chapter 6: Integers
Exercise – 6.2
1. Using the number line write the integer which is:
(a) 3 more than 5
(b) 5 more than –5
(c) 6 less than 2
(d) 3 less than –2
Solutions:
(a) We want to obtain integer 3 more than 5. So, we start from 5 and proceed 3 units to the right to obtain 8 as shown in the figure.
Hence, 3 more than 5 is 8.
(b) We want to obtain integer 5 more than -5. So, we start from -5 and proceed 5 units to the right to obtain 0 as shown in the figure.
Hence, 5 more than -5 is 0.
(c) We want to obtain an integer 6 less than 2. So, we start from 2 and proceed 6 units to the left of it to obtain -4 as shown in the figure.
Hence, 6 less than 2 is -4.
(d) We want to obtain an integer 3 less than -2. So, we start from -2 and proceed 3 units to the left of it to obtain -5 as shown in the figure.
Hence, 3 less than -2 is -5.
2. Use number line and add the following integers:
(a) 9 + (–6)
(b) 5 + (–11)
(c) (–1) + (–7)
(d) (–5) + 10
(e) (–1) + (–2) + (–3)
(f) (–2) + 8 + (–4)
Solutions:
(a) First we move to the right of 0 by 9 steps reaching 9. Then we move 6 steps to the left of 9 reaching 3 as shown in the figure.
Thus, 9 + (-6) = 3.
(b) First we move to the right of 0 by 5 steps reaching 5. Then, we move 11 steps to the left of 5 reaching -6 as shown in the figure.
Thus, 5 + (-11) = -6.
(c) First we move to the left of 0 by 1 step reaching -1. Then we move 7 steps to* the left of -1 reaching -8 as shown in the figure.
Thus, (-1) + (-7) = -8.
(d) First we move to the left of 0 by 5 steps reaching -5. Then we move 10 steps to the right of -5 reaching 5 as shown in the figure.
Thus, (-5) + 10 = 5.
(e) First we move to the left of 0 by 1 step reaching -1. Then we move 2 steps to the left of -1 reaching -3. Again, we move 3 steps to the left of -3 reaching -6 as shown in the figure.
Thus, (-1) + (-2) + (-3) = -6.
(f) First we move to the left of 0 by 2 steps reaching -2. Then we move 8 steps to the right of -2 reaching 6. Again, we move 4 steps to the left of 6 reaching -2 as shown in the figure.
Thus, (-2) + 8 + (-4) = 2.
3. Add without using number line:
(a) 11 + (–7)
(b) (–13) + (+18)
(c) (–10) + (+19)
(d) (–250) + (+150)
(e) (–380) + (–270)
(f) (–217) + (–100)
Solutions:
(a) 11 + (-7) = 4
(b) (-13) + (+18) = 5
(c) (-10) + (+19) = 9
(d) (-250) + (+150) = -100
(e) (-380) + (-270) = -650
(f) (-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
Solutions:
(a) 137 and -354
(137) + (-354)
= (137) + (-137) + (-217)
= 0 + (-217) [(137) + (-137) = 0]
= (-217)
= -217
(b) -52 and 52
(-52) + (+52)
= 0 [(-a) + (+a) = 0]
(c) -312, 39 and 192
(-312) + (+39) + (+192)
= (-231) + (-81) + (+39) + (+192)
= (-231) + (-81) + (+231)
= (-231) + (+231) + (-81)
= 0 + (-81) [(-a) + (+a) = 0]
= -81
(d) -50, -200 and 300
(-50) + (-200) + (+300)
= (-50) + (-200) + (+200) + (+100)
= (-50) + 0 + (+100) [(-a) + (+a) = 0]
= (-50) + (+100)
= (-50) + (+50) + (+50)
= 0 + (+50) [(-a) + (+a) = 0]
= 50
5. Find the sum:
(a) (–7) + (–9) + 4 + 16
(b) (37) + (–2) + (–65) + (–8)
Solutions:
(a) (-7) + (-9) + 4 + 16
= (-7) + (-9) + 4 + (+7) + (+9)
= (-7) + (+7) + (-9) + (+9) + 4
= 0 + 0 + 4 [(-a) + (+a) = 0]
= 4
(b) (37) + (-2) + (-65) + (-8)
= (+37) + (-75)
= (+37) + (-37) + (-38)
= 0 + (-38) [(-a) + (+a) = 0]
= -38
