Haryana State Board HBSE 7th Class Maths Solutions Chapter 1 Integers InText Questions and Answers.
Haryana Board 7th Class Maths Solutions Chapter 1 Integers InText Questions
Try These (Page 2) :
Question 1.
Number line representing integers is given below :
– 3 and – 2 are marked by E and F respectively. Which integers are marked by alphabets B, D, H, J, M, O ?
Solution:
Question 2.
Arrange 7, – 5, 4, 0, and – 4 in ascending order and then mark them on a number line to check your answer.
Solution:
Try These (Page 3) :
Question 1.
We have done various patterns with numbers in our previous class.
Can you find a pattern for each of the following ? If yes, complate them :
(a) 7,3, -1, 5, ………… , ………… , …………
(b) -2,-4,-6,-8, ………… , ………… , …………
(c) 15, 10, 5, 0, ………… , ………… , …………
id) – 11, -8,-5,-2, ………… , ………… , …………
Solution:
(a) 7, 3, -1, 5, -9 . -13 . -14
(b) -2,-4, – 6, – 8, -10 , – 12, -14
(c) 15, 10, 5, 0, -5 . -10 . – 15
(d) – 11, – 8, – 5, – 2, 1, 4, 7
Try These (Page 8) :
Question 1.
Write pair of integers whose sum gives:
(a) A negative integer.
(b) Zero.
(c) An integer smaller than both the integers.
(d) An integer smaller than only one of the integers.
(e) An integer greater than both the integers.
Solution:
(a) – 3 + (- 3) = – 3 – 3 = – 6
(b) 3 + (-3) = 3 -3 = 0
(c) 3 + (- 2) = 3 – 2 = 1
(d) – 3 + (- 1) = – 3 – 1 = – 4
(e) 4 + 5 = 9
Question 2.
Write a pair of integers whose diffeences gives:
(a) A negative integer.
(b) Zero.
(c) An integer smaller than both the integers.
(d) An integer greater than only one of the integers.
(e) An integer greater than both the integers.
Solution:
(a) – 3 – (+ 3) = – 3 – 3 = – 6
(b) – 3 – (+ 3) = – 3 + 3 = – 0
(c) – 3 – (+ 2) = – 3 – 2 = – 5
(d) – 2 – (- 1) = – 2 + 1 = – 0
(e) – 3 – (- 4) = – 3 + 4 = 1
I. Try These (Page 10) :
Question 1.
Find 4 x (- 8), 8 x (- 2), 3 x (- 7), 10 x (¬1), using number line.
Solution:
(- 8) + (— 8) + (— 8) + (— 8) = -32
4 x (-8) = -32
(- 2) + (- 2) + (- 2) + (- 2) + (- 2) + (- 2) + (- 2) + (- 2) = – 16
8 x (- 2) = – 16
(- 7) + (- 7) + (- 7) = -21
3 x (- 7) = – 21
(— 1) + (— 1) + (— 1) + (— 1) + (— 1) + (— 1) + (— 1) + (- 1) + (- 1) + (- 1) = – 10
10 x (- 1) = – 10
Try These (Page 10) :
Question 1.
Find:
(i) 6 x (- 19)
(ii) 12 x (- 32)
(iii) 1 x (-22)
Solution:
(i) 6 x (- 19) = – (6 x 19) = – 114
(ii) 12 x(- 32) = -(12×32) = -384
(iii) 7 x (- 22) = – (7 x 22) = – 154
Try These (Page 11) :
Question 1.
Find (a) 15 x (- 16)
(b) 21 x (- 32)
(c) (- 42) x 12
(d) – 55 x 15
Solution:
(a) 15 x (-16) = -240 = -(15 x 16)
(b) 21 x(- 32) = -672 = -(21 x 32)
(c) (-42) x (12) = -504 = -(42 x 12)
(d) – 55 x 15 = – 825 = – (55 x 15)
Question 2.
Check if: (a) 25 x (-21) = (-25) x 21 (6) (-23) x 20 = 23 x (-20)
Write five more such examples.
Solution:
(a) 25 x (- 21) = (- 25) x 21
-(25 x 21) = -(25 x 21)
-525 = -525
(- 23) x 20 = 23 x (- 20)
-(23 x 20) = -(23 x 20)
-460 = -460
1. 12 x (-11) = (— 11) x 12
2. 13 x (-12) = 0-13) x 12
3. 20 x (-19) = (— 20) x 19
4. (-21) x(20) = 21 x (- 20)
5. (- 24) x (23) = 24 x (— 23)
Try These (Page 12) :
Question 1.
(i) Starting from (- 5) x 4, find (- 5) x (- 6)
(ii) Starting from (- 6) x 3, find (- 6) x (- 7)
Solution:
(i) -5 x 4 = -20
-5 x 3 = -15
-5 x 2 = -10
-5 x 1 = -5
-5 x 0 = 0
– 5 x – 1 = + 5
– 5 x – 2 = + 10
– 5 x – 3 = + 15
– 5 x – 4 = + 20
– 5 x – 5 = + 25
– 5 x – 6 = + 30
(ii) -6 x 3 = -18
-6 x 2 = -12
-6 x 1 = -6
-6 x 0 = 0
-6 x – 1 = + 6
– 6 x – 2 = + 12
– 6 x – 3 = + 18
– 6 x – 4 = + 24
– 6 x – 5 – + 30
– 6 x – 6 = + 36
– 6 x – 7 = + 42
Try These (Page 12) :
Question 1.
Find (- 31) x (-100), (- 25) x (- 72), (- 83) x (- 28)
Solution:
(- 31) x (-100) = 3100
(-25) x (-72) = 1800
(-83) x (-28) = 2324
I. Try These (Page 18) :
Question 1.
(i) Is 10 x [6 + (-2)] = 10 x 6 + 10 x (-2) ?
(ii) Is (-15) x [(- 7) + (-1)] = (-15) x (- 7) + (- 5) x (- 1) ?
Solution:
(i) 10 x [6 + (- 2)] = 10 x 6 +10 x (-2) 10 x 4 = 60-20 40 = 40
(ii)(- 15) x [(- 7) + (- 1)] = (- 15) x (- 7) + (- 5) x (- 1)
— 15 x (— 8) = 105 + 5
120 = 120
I. Try These (Page 18) :
Question 1.
(i) Is 10 x [6- (-2)] = 10 x 6 – 10 x (- 2) ?
(ii) Is (- 15) x [(- 7) – (- 1)1 = (- 15) x (-7) – (- 15) x (- 1) ?
Solution:
(i) 10 x [6 + 2] = 60 + 20
10 x 8 = 80
80 = 80
(ii) – 15 x [- 7 + 1] = 105-15
15 x (- 6) = 90
=> 90 = 90
Try These (Page 18) :
Question 1.
Find (- 49) x 18; (- 25) x (- 31); 70 x (-19) + (- 1) x 70 using distributivity peroperly.
Solution:
(- 49) x 18 = (- 49) x [10 + 8]
= (- 49) x 10 + (- 49) x 8
= -490 – 392 = -882
(- 25) x (- 31) = (- 25) x [(- 30) + (- 1)]
= (- 25) x (- 30) + (- 25) x(- 1)
= 750 + 25 = 775
70 x (- 19) + (- 1) x 70
= 70 [(- 19) + (-1)]
= 70 [-19-1]
= 70 x (-20) = – 1400
Try These (Page 22) :
Question 1.
Find (a) (-100) ÷ 5, (b) (-81) ÷ 9, (c) (-75) ÷ 25, (d) (- 32) ÷ 2
Solution:
(a) (-100) ÷ 5 = -20
(b) (- 81) ÷ 9 = – 9
(c) (- 75) ÷ 25 = – 3
(d) (-32) ÷ 2 = -16
Try These (Page 23) :
Question 1.
Find (a) 125 ÷ (- 25), (b) 88 ÷ (- 5), (c) (64) ÷ (-16)
Solution:
(a) 125 ÷ (- 25) = – 5
(b) 80 ÷ (- 5) = -16
(c) 64 ÷ (- 16) = – 4
Try These (Page 23) :
Question 1.
Find (a) (- 36) ÷ (- 4), (b) (- 201) ÷ (- 3), (c) (-325) ÷ (-13)
Solution:
(a) (-36) ÷ (-4) =9
(6) (-201) ÷ (-3) = 67
(c) (-325) ÷ (-13) = 25.
Try These (Page 24) :
Question 1.
Is (i) Is 1 ÷ a = 1 ?
(ii) a ÷ (-1) = – a ? For any integer. Take different values of a and check.
Solution:
(i) 1 ÷ a = \(\frac{1}{a}=\frac{1}{a}\)
hence \(\frac{1}{a}\) ≠ 1 L.H.S ≠ R.H.S
Check, a = 1 then, 1 ÷ 1 = 1.
a = 2 then, 1 ÷ 2 = \(\frac{1}{2}\)
i.e. 1 ≠ \(\frac{1}{2}\) , hence, verified
(ii) a ÷ (- 1) = a x \(\frac{1}{-1}\) = -a
hence, L.H.S = R.H.S
i.e. – a = – a
Check, a = 1 then, 1 ÷ (- 1) = -1
– 1= – 1
a = 2
then, 2 ÷ (-1) = -2 => -2 = -2