Class 7 Maths NCERT Chapter 1 Integers Try These Solutions. Here I will be providing you the solution of all the try these or inText questions of class 7 Maths NCERT Chapter 1 Integers for CBSE as well as other state boards like Gujarat Board
Class 7 Maths NCERT Chapter 1 Integers Try These Solutions
Class
7 Maths NCERT Try
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1. A number line representing integers is given below
–3 and –2 are marked by E and F respectively. Which integers are marked by B, D, H, J, M and O?
Ans: Integers are marked
by B is -6
Integers are marked by D is -4
Integers are marked by H is 0
Integers are marked by J is 2
Integers are marked by M is 5
Integers are marked by O is 7
2. Arrange 7, –5, 4, 0 and – 4 in ascending order and then
mark them on a number line to check your answer.
Ans: -5,-4,0,4,7
(Explanation:
integer occurring to the right on a number line is
greater than that on the left)
Class
7 Maths NCERT Try
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We have done various patterns with numbers in our previous
class.
Can you find a pattern for each of the following?
If yes, complete them:
(a) 7, 3, – 1, – 5, -9, -13, -17
(b) – 2, – 4, – 6, – 8, -10, -12,
-14
(c) 15, 10, 5, 0, -5, -10, -15
(d) – 11, – 8, – 5, – 2, 1, 4, 7
Make some more such patterns and ask your friends to complete
them.
Class
7 Maths NCERT Try
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1. Write a pair of integers whose sum gives
(a) a negative integer
Ans: -10
& 6
(Explanation: -10 + 6 = -4)
(b) zero
Ans: -8 & 8
(Explanation: -8 + 8 = 0)
(c) an integer smaller than both the integers.
Ans: -5 & -3
(Explanation: -5 + (-3) = -8)
(d) an integer smaller than only one of the integers.
Ans: -8
& 2
(Explanation: -8 + 2 = -6)
(e) an integer greater
than both the integers.
Ans: 5
& 3
(Explanation: 5 + 3 = 8)
2. Write a pair of integers whose difference gives
(a) a negative integer.
Ans: -5
& 3
(Explanation: (-5) – 3 = -8)
(b) zero.
Ans: 7 & 7
(Explanation: 7 - 7 = 0)
(c) an integer smaller
than both the integers.
Ans: 10
& 7
(Explanation: 10 - 7 = 3)
(d) an integer greater
than only one of the integers.
Ans: 10 & 3
(Explanation: 10 - 3 = 7)
(e) an integer greater
than both the integers.
Ans: 5
& -3
(Explanation: 5 – (-3) = 8 here 8 > 5 & -3 )
Class
7 Maths NCERT Try
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Find: 4 × (– 8),
8 × (–2),
3 × (–7),
10 × (–1) using number line
Solution:
·
4 × (– 8)
Ans:
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4 × (– 8) = -32
·
8 × (–2)
Ans:
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8 × (–2) = -16
·
3 × (–7)
Ans:
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3 × (–7) = -21
·
10 × (–1)
Ans:
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10 × (–1) = -10
Class
7 Maths NCERT Try
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Find: (i) 6 × (–19)
Ans: 6 × (–19)
= - (6 × 19)
= -114
(ii) 12 × (–32)
Ans: 12 × (–32)
= - (12 × 32)
= -384
(iii) 7 × (–22)
Ans: 7 ×
(–22)
= - (7 × 22)
= - 154
Class
7 Maths NCERT Try
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1. Find:
(a) 15 × (–16)
Ans: 15 × (–16) = - (15 ×
16) = -240
(b) 21 × (–32)
Ans: 21 × (–32) = – (21 ×
32) = – 672
(c) (– 42) × 12
Ans: (– 42) × 12 = – (42 ×
12) = – 504
(d) –55 × 15
Ans: –55 × 15 = – (55 ×
15) = – 825
2. Check if
(a) 25 × (–21) = (–25) × 21
Ans: Solving L.H.S
25 × (–21) = – (25 × 21) = – 525
Solving R.H.S
(–25) × 21 = – (25 × 21) = – 525
Because L.H.S = R.H.S
Therefore 25 × (–21) = (–25) × 21
(b) (–23) × 20 = 23 ×
(–20)
Ans: Solving L.H.S
(–23) × 20 = – (23 × 20) = – 460
Solving R.H.S
23 × (–20) = – (23 × 20) = – 460
Because L.H.S = R.H.S
Therefore (–23) × 20 = 23 × (–20)
Write five more such examples.
14 × (–18) = (–14) × 18
Class 7 Maths NCERT Try these page-12 (top)
(i) Starting
from (–5) × 4, find (–5) × (– 6)
Ans:
–5 × 4 = –
20
–5
× 3 = –15 = –20 + 5
–5
× 2 = – 10 = –15 + 5
–5
× 1 = – 5 = – 10 + 5
–5
× 0 = 0 = – 5 + 5
–5
× (–1) = 0 + 5 = 5
–5
× (–2) = 5 + 5 = 10
–5
× (–3) = 10 + 5 = 15
–5
× (–4) = 15 + 5 = 20
–5
× (–5) = 20 + 5 = 25
Thus,
–5 × (–6) = 25 + 5 = 30
(ii)
Starting from (– 6) × 3, find (– 6) × (–7)
Ans: – 6 x 3 = – 18
– 6 x 2 = – 12 = – 18 + 6
– 6 x 1 = – 6 = – 12 + 6
– 6 x 0 = 0 = – 6 + 6
– 6 x (- 1) = 0 + 6 = 6
– 6 x (- 2) = 6 + 6 = 12
– 6 x (- 3) = 12 + 6 = 18
– 6 x (- 4) = 18 + 6 = 24
– 6 x (- 5) = 24 + 6 = 30
– 6 x (- 6) = 30 + 6 = 36
– 6 x (- 7) = 36 + 6 = 42
Thus, (- 6) x (- 7) = 42
Class
7 Maths NCERT Try
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Basic
Knowledge: for any two positive integers a and
b,
(– a) × (– b) = a × b
Find: (–31) × (–100)
Ans: (–31)
× (–100) = + 3100 = 3100
(–25) × (–72)
Ans: (–25) × (–72) = +
1800 = 1800
(–83) × (–28)
Ans: (–83) × (–28) = +
2324 = 2324
Class
7 Maths NCERT Try
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(i) Is 10 ×
[(6 + (–2)] = 10 × 6 + 10 × (–2)?
Ans:
Solving
L.H.S
10
× [6 + (–2)]
=
10 × (6 – 2)
=
10 × 4
=
40
Solving
R.H.S
10
× 6 + 10 × (–2)
=
60 + (– 20)
=
60 – 20
=
40
Since
L.H.S = R.H.S
Hence
Yes, 10 × [(6 + (–2)] = 10 × 6 + 10 × (–2)
(ii) Is
(–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)?
Ans: Solving L.H.S
(–15)
× [(–7) + (–1)]
=
(–15) × (–8)
=
120
Solving
R.H.S
(–15)
× (–7) + (–15) × (–1)
=
105 + 15
=
120
Since
L.H.S = R.H.S
Hence
Yes, (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)
Class 7 Maths NCERT Try these page-18 (bottom)
(i) Is 10 ×
[6 – (–2)] = 10 × 6 – 10 × (–2)?
Ans:
Solving
L.H.S
10
× [6 – (–2)]
=
10 × (6 + 2)
=
10 × 8
=
80
Solving
R.H.S
10
× 6 – 10 × (–2)
=
60 – (–20)
=
60 + 20
=
80
Since
L.H.S = R.H.S
Hence
Yes, 10 × [6 – (–2)] = 10 × 6 – 10 × (–2)
(ii) Is (–15) × [(–7) – (–1)] = (–15)
× (–7) – (–15) × (–1)?
Ans: Solving L.H.S
(–15)
× [(–7) – (–1)]
=
(–15) × [–7 + 1]
=
(–15) × (–6)
=
90
Solving
R.H.S
(–15)
× (–7) – (–15) × (–1)
=
105 – 15
=
90
Since
L.H.S = R.H.S
Hence
Yes, (–15) × [(–7) – (–1)] = (–15) × (–7) – (–15) × (–1)
Class
7 Maths NCERT Try
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Basic
Knowledge: In general, for any three integers a, b and c,
a × (b – c) = a × b – a
× c
Find (– 49) × 18;
(–25) × (–31);
70 × (–19) + (–1) × 70 using distributive property.
(– 49) × 18
Ans: (– 49) × 18
= (– 49) × (20 – 2)
= (– 49 × 20) – (–49 × 2) [using distributive property]
= –980 + 98
= –882
(–25) × (–31)
Ans: (–25)
× (–31)
= (–25) × [(–30) + (–1)]
= (–25) × (–30) + (–25) × (–1) [using distributive property]
= 750 + 25
= 775
70 × (–19) + (–1) × 70
Ans: 70 ×
(–19) + (–1) × 70
= 70 × [(–19) + (–1)] [using distributive property]
= 70 × (–20)
= –1400
Class
7 Maths NCERT Try
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Basic
Knowledge: Rule for Sign in division
(+) ÷ (+) = (+)
(+) ÷ (-) = (-)
(-) ÷ (+) = (-)
(-) ÷ (-) = (+)
Find: (a) (–100) ÷ 5
Ans: ∵ 100 ÷ 5 = 20
∴ (– 100) ÷ 5 = –20
(b) (–81) ÷ 9
Ans: ∵ 81 ÷ 9 = 9
∴ (- 81) ÷ 9 = – 9
(c) (–75) ÷ 5
Ans: ∵ 75 ÷ 5 = 15
∴ (– 75) ÷ 5 = – 15
(d) (–32) ÷ 2
Ans: ∵ 32 ÷ 2 = 16
∴ (– 32) + 2 = – 16
Class
7 Maths NCERT Try
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Find: (a) 125 ÷ (–25)
Ans: ∵ 125 ÷ 25 = 5
∴ 125 ÷ (- 25) = – 5
(b) 80 ÷ (–5)
Ans: ∵ 80 ÷ 5 = 16
∴ 80 ÷ (- 5) = – 16
(c) 64 ÷ (–16)
Ans: ∵ 64 ÷ 16 = 4
∴ 64 ÷ (- 16) = – 4
Class
7 Maths NCERT Try
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Find: (a) (–36) ÷ (– 4)
Ans: ∵ 36 ÷ 4 = 9
∴ (- 36) ÷ (- 4) = 9
(b) (–201) ÷ (–3)
Ans: ∵ 201 ÷ 3 = 67
∴ (- 201) ÷ (- 3) = 67
(c) (–325) ÷ (–13)
Ans: ∵ 325 ÷ 13 = 25
∴ (- 325) ÷ (- 13) = 25
Class
7 Maths NCERT Try
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Is (i) 1 ÷ a
= 1?
(ii) a ÷
(–1) = – a? for any integer a. Take different values of a and check.
(i) 1 ÷ a =
1?
Ans:
As it is
given in question that a is an integer so,
Let
a=2
1
÷ 2 ≠ 1
Here,
1 ÷ a = 1 is not true
Let
a=7
1
÷ 7 ≠ 1
Here,
1 ÷ a = 1 is not true
Let
a=1
1
÷ 1 = 1
Here,
1 ÷ a = 1 is true
Thus
1 ÷ a = 1 is true only if a=1
(ii) a ÷
(–1) = – a?
Ans: As it is
given in question that a is an integer so,
Let
a=3
3
÷ (–1) = – 3
Here,
a ÷ (–1) = – a is true
Let
a=5
5
÷ (–1) = – 5
Here,
a ÷ (–1) = – a is true
Let
a= – 3
–
3 ÷ (–1) = 3
Here,
a ÷ (–1) = – a is true
Thus,
a ÷ (–1) = – a is true for every integer a
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