RS Aggarwal 2019 2020 Solutions for Class 7 Math Chapter 1 Integers are provided here with simple step-by-step explanations. These solutions for Integers are extremely popular among class 7 students for Math Integers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggarwal 2019 2020 Book of class 7 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s RS Aggarwal 2019 2020 Solutions. All RS Aggarwal 2019 2020 Solutions for class 7 Math are prepared by experts and are 100% accurate.
Page No 4:
Question 1:
Answer:
(i) 15 + (−8) = 7
(ii) (−16) + 9 = −7
(iii) (−7) + (−23) = −30
(iv) (−32) + 47 = 15
(v) 53 + (−26) = 27
(vi) (−48) + (−36) = −84
Page No 4:
Question 2:
(i) 15 + (−8) = 7
(ii) (−16) + 9 = −7
(iii) (−7) + (−23) = −30
(iv) (−32) + 47 = 15
(v) 53 + (−26) = 27
(vi) (−48) + (−36) = −84
Answer:
(i) 153 + (−302) = −149
(ii) 1005 + (−277) = 728
(iii) (−2035) + 297 = −1738
(iv) (−489) + (−324) = −813
(v) (−1000) + 438 = −562
(vi) (−238) + 500 = 262
Page No 4:
Question 3:
(i) 153 + (−302) = −149
(ii) 1005 + (−277) = 728
(iii) (−2035) + 297 = −1738
(iv) (−489) + (−324) = −813
(v) (−1000) + 438 = −562
(vi) (−238) + 500 = 262
Answer:
(i) Additive inverse of −83 = −(−83) = 83
(ii) Additive inverse of 256 = −(256) = −256
(iii) Additive inverse of 0 = −(0) = 0
(iv) Additive inverse of 2001 = −(−2001) = 2001
Page No 5:
Question 4:
(i) Additive inverse of −83 = −(−83) = 83
(ii) Additive inverse of 256 = −(256) = −256
(iii) Additive inverse of 0 = −(0) = 0
(iv) Additive inverse of 2001 = −(−2001) = 2001
Answer:
(i) −42 − 28 = (−42) + (−28) = −70
(ii) 42 −(−36) = 42 + 36 = 78
(iii) -53 - (-37) = (-53) - (-37) = -16
(iv) -34 - (-66) = -34 + 66 = 32
(v) 0 - 318 = -318
(vi) (-240) - (-153) = -87
(vii) 0 - (-64) = 0 + 64 = 64
(viii) 144 - (-56) = 144 + 56 = 200
Page No 5:
Question 5:
(i) −42 − 28 = (−42) + (−28) = −70
(ii) 42 −(−36) = 42 + 36 = 78
(iii) -53 - (-37) = (-53) - (-37) = -16
(iv) -34 - (-66) = -34 + 66 = 32
(v) 0 - 318 = -318
(vi) (-240) - (-153) = -87
(vii) 0 - (-64) = 0 + 64 = 64
(viii) 144 - (-56) = 144 + 56 = 200
Answer:
Sum of −1032 and 878 = −1032 + 878
= -154
Subtracting the sum from −34, we get
−34 − (−154)
= (−34)+ 154
= 120
Page No 5:
Question 6:
Sum of −1032 and 878 = −1032 + 878
= -154
Subtracting the sum from −34, we get
−34 − (−154)
= (−34)+ 154
= 120
Answer:
First, we will calculate the sum of 38 and −87.
38 + (−87) = −49
Now, subtracting −134 from the sum, we get:
−49 − (−134)
=(−49) + 134
= 85
Page No 5:
Question 7:
First, we will calculate the sum of 38 and −87.
38 + (−87) = −49
Now, subtracting −134 from the sum, we get:
−49 − (−134)
=(−49) + 134
= 85
Answer:
(i) −41 (âµ Associative property)
(ii) −83 (âµ Associative property)
(iii) 53 (âµ Commutative property)
(iv) −76 (âµ Commutative property)
(v) 0 (âµ Additive identity)
(vi) 83 (âµ Additive inverse)
(vii) (−60) − (−59) = −1
(viii) (−40) − (−31) = −9
Page No 5:
Question 8:
(i) −41 (âµ Associative property)
(ii) −83 (âµ Associative property)
(iii) 53 (âµ Commutative property)
(iv) −76 (âµ Commutative property)
(v) 0 (âµ Additive identity)
(vi) 83 (âµ Additive inverse)
(vii) (−60) − (−59) = −1
(viii) (−40) − (−31) = −9
Answer:
{−13 − (−27)} + {−25 − (−40)}
= {−13 + 27} + {−25 + 40}
=14 + 15
= 29
Page No 5:
Question 9:
{−13 − (−27)} + {−25 − (−40)}
= {−13 + 27} + {−25 + 40}
=14 + 15
= 29
Answer:
36 − (−64) = 36 + 64 = 100
Now, (−64) − 36 = (−64) + (−36) = −100
Here, 100 −100
Thus, they are not equal.
Page No 5:
Question 10:
36 − (−64) = 36 + 64 = 100
Now, (−64) − 36 = (−64) + (−36) = −100
Here, 100 −100
Thus, they are not equal.
Answer:
(a + b) + c = (−8 + (−7)) + 6 = −15 + 6 = −9
a + (b + c) = −8 + (−7 + 6) = −8 + (−1) = −9
Hence, (a + b) + c = a + (b + c) [i.e., Property of Associativity]
Page No 5:
Question 11:
(a + b) + c = (−8 + (−7)) + 6 = −15 + 6 = −9
a + (b + c) = −8 + (−7 + 6) = −8 + (−1) = −9
Hence, (a + b) + c = a + (b + c) [i.e., Property of Associativity]
Answer:
Here, (a − b) = −9 − (−6) = −3
Similarly, (b − a) = −6 − (−9) = 3
∴ (a−b) ≠ (b−a)
Page No 5:
Question 12:
Here, (a − b) = −9 − (−6) = −3
Similarly, (b − a) = −6 − (−9) = 3
∴ (a−b) ≠ (b−a)
Answer:
Let the other integer be a. Then, we have:
53 + a = −16
⇒ a = −16 − 53 = −69
∴ The other integer is −69.
Page No 5:
Question 13:
Let the other integer be a. Then, we have:
53 + a = −16
⇒ a = −16 − 53 = −69
∴ The other integer is −69.
Answer:
Let the other integer be a.
Then, −31 + a = 65
⇒ a = 65 − (−31) = 96
∴ The other integer is 96.
Page No 5:
Question 14:
Let the other integer be a.
Then, −31 + a = 65
⇒ a = 65 − (−31) = 96
∴ The other integer is 96.
Answer:
We have:
a − (−6) = 4
⇒ a = 4 + (−6) = −2
∴ a = −2
Page No 5:
Question 15:
We have:
a − (−6) = 4
⇒ a = 4 + (−6) = −2
∴ a = −2
Answer:
(i) Consider the integers 8 and −8. Then, we have:
8 + (−8) = 0
(ii) Consider the integers 2 and (−9). Then, we have:
2 + (−9)= −7, which is a negative integer.
(iii) Consider the integers −4 and −5. Then, we have:
(−4) + (−5) = −9, which is smaller than −4 and −5.
(iv) Consider the integers 2 and 6. Then, we have:
2 + 6 = 8, which is greater than both 2 and 6.
(v) Consider the integers 7 and −4. Then, we have:
7 + (−4) = 3, which is smaller than 7 only.
Page No 5:
Question 16:
(i) Consider the integers 8 and −8. Then, we have:
8 + (−8) = 0
(ii) Consider the integers 2 and (−9). Then, we have:
2 + (−9)= −7, which is a negative integer.
(iii) Consider the integers −4 and −5. Then, we have:
(−4) + (−5) = −9, which is smaller than −4 and −5.
(iv) Consider the integers 2 and 6. Then, we have:
2 + 6 = 8, which is greater than both 2 and 6.
(v) Consider the integers 7 and −4. Then, we have:
7 + (−4) = 3, which is smaller than 7 only.
Answer:
(i) F (false). −3, −90 and −100 are also integers. We cannot determine the smallest integer, since they are infinite.
(ii) F (false). −10 is less than −7.
(iii) T (true). All negative integers are less than zero.
(iv) T (true).
(v) F (false). Example: −9 + 2 = −7
Page No 9:
Question 1:
(i) F (false). −3, −90 and −100 are also integers. We cannot determine the smallest integer, since they are infinite.
(ii) F (false). −10 is less than −7.
(iii) T (true). All negative integers are less than zero.
(iv) T (true).
(v) F (false). Example: −9 + 2 = −7
Answer:
(i) 16 9 = 144
(ii) 18 (−6) = −108
(iii) 36 (−11) = −396
(iv) (−28) 14 = −392
(v) (−53) 18 = −954
(vi) (−35) 0 = 0
(vii) 0 (−23) = 0
(viii) (−16) (−12) = 192
(ix) (−105) (−8) = 840
(x) (−36) (−50) = 1800
(xi) (−28) (−1) = 28
(xii) 25 (−11) = −275
Page No 9:
Question 2:
(i) 16 9 = 144
(ii) 18 (−6) = −108
(iii) 36 (−11) = −396
(iv) (−28) 14 = −392
(v) (−53) 18 = −954
(vi) (−35) 0 = 0
(vii) 0 (−23) = 0
(viii) (−16) (−12) = 192
(ix) (−105) (−8) = 840
(x) (−36) (−50) = 1800
(xi) (−28) (−1) = 28
(xii) 25 (−11) = −275
Answer:
(i) 3 × 4 × (−5) = (12) × (−5) = −60
(ii) 2 × (−5) × (−6) = (−10) × (−6) = 60
(iii) (−5) × (−8) × (−3) = (−5) × (24) = −120
(iv) (−6) × 6 × (−10) = 6 × (60) = 360
(v) 7 × (−8) × 3 = 21 × (−8) = −168
(vi) (−7) × (−3) × 4 = 21 × 4 = 84
Page No 9:
Question 3:
(i) 3 × 4 × (−5) = (12) × (−5) = −60
(ii) 2 × (−5) × (−6) = (−10) × (−6) = 60
(iii) (−5) × (−8) × (−3) = (−5) × (24) = −120
(iv) (−6) × 6 × (−10) = 6 × (60) = 360
(v) 7 × (−8) × 3 = 21 × (−8) = −168
(vi) (−7) × (−3) × 4 = 21 × 4 = 84
Answer:
(i) Since the number of negative integers in the product is even, the product will be positive.
(4) × (5) × (8) × (10) = 1600
(ii) Since the number of negative integers in the product is odd, the product will be negative.
−(6) × (5) × (7) × (2) × (3) = −1260
(iii) Since the number of negative integers in the product is even, the product will be positive.
(60) × (10) × (5) × (1) = 3000
(iv) Since the number of negative integers in the product is odd, the product will be negative.
−(30) × (20) × (5) = −3000
(v) Since the number of negative integers in the product is even, the product will be positive.
= 729
(vi) Since the number of negative integers in the product is odd, the product will be negative.
= −3125
(vii) Since the number of negative integers in the product is even, the product will be positive.
= 1
(viii) Since the number of negative integers in the product is odd, the product will be negative.
= −1
Page No 9:
Question 4:
(i) Since the number of negative integers in the product is even, the product will be positive.
(4) × (5) × (8) × (10) = 1600
(ii) Since the number of negative integers in the product is odd, the product will be negative.
−(6) × (5) × (7) × (2) × (3) = −1260
(iii) Since the number of negative integers in the product is even, the product will be positive.
(60) × (10) × (5) × (1) = 3000
(iv) Since the number of negative integers in the product is odd, the product will be negative.
−(30) × (20) × (5) = −3000
(v) Since the number of negative integers in the product is even, the product will be positive.
= 729
(vi) Since the number of negative integers in the product is odd, the product will be negative.
= −3125
(vii) Since the number of negative integers in the product is even, the product will be positive.
= 1
(viii) Since the number of negative integers in the product is odd, the product will be negative.
= −1
Answer:
Multiplying 90 negative integers will yield a positive sign as the number of integers is even.
Multiplying any two or more positive integers always gives a positive integer.
The product of both(the above two cases) the positive and negative integers is also positive.
Therefore, the final product will have a positive sign.
Page No 9:
Question 5:
Multiplying 90 negative integers will yield a positive sign as the number of integers is even.
Multiplying any two or more positive integers always gives a positive integer.
The product of both(the above two cases) the positive and negative integers is also positive.
Therefore, the final product will have a positive sign.
Answer:
Multiplying 103 negative integers will yield a negative integer, whereas 65 positive integers will give a positive integer.
The product of a negative integer and a positive integer is a negative integer.
Page No 9:
Question 6:
Multiplying 103 negative integers will yield a negative integer, whereas 65 positive integers will give a positive integer.
The product of a negative integer and a positive integer is a negative integer.
Answer:
(i) (−8) (9 + 7) [using the distributive law]
= (−8) 16 = −128
(ii) 9 (−13 + (−7)) [using the distributive law]
= 9 (−20) = −180
(iii) 20 (−16 + 14) [using the distributive law]
= 20 (−2) = −40
(iv) (−16) (−15 + (−5)) [using the distributive law]
= (−16) (−20) = 320
(v) (−11) (−15 +(−25)) [using the distributive law]
= (−11) (−40)
= 440
(vi) (−12) (10 + 5) [using the distributive law]
= (−12) 15 = −180
(vii) (−16 + (−4)) (−8) [using the distributive law]
= (−20) (−8) = 160
(viii) (−26) (72 + 28) [using the distributive law]
= (−26) 100 = −2600
Page No 9:
Question 7:
(i) (−8) (9 + 7) [using the distributive law]
= (−8) 16 = −128
(ii) 9 (−13 + (−7)) [using the distributive law]
= 9 (−20) = −180
(iii) 20 (−16 + 14) [using the distributive law]
= 20 (−2) = −40
(iv) (−16) (−15 + (−5)) [using the distributive law]
= (−16) (−20) = 320
(v) (−11) (−15 +(−25)) [using the distributive law]
= (−11) (−40)
= 440
(vi) (−12) (10 + 5) [using the distributive law]
= (−12) 15 = −180
(vii) (−16 + (−4)) (−8) [using the distributive law]
= (−20) (−8) = 160
(viii) (−26) (72 + 28) [using the distributive law]
= (−26) 100 = −2600
Answer:
(i) (−6) × (x) = 6
Thus, x = (−1)
(ii) 1 [âµ Multiplicative identity]
(iii) (−8) [âµ Commutative law]
(iv) 7 [âµ Commutative law]
(v) (−5) [âµ Associative law]
(vi) 0 [âµ Property of zero]
Page No 9:
Question 8:
(i) (−6) × (x) = 6
Thus, x = (−1)
(ii) 1 [âµ Multiplicative identity]
(iii) (−8) [âµ Commutative law]
(iv) 7 [âµ Commutative law]
(v) (−5) [âµ Associative law]
(vi) 0 [âµ Property of zero]
Answer:
We have 5 marks for correct answer and (−2) marks for an incorrect answer.
Now, we have the following:
(i) Ravi's score = 4 5 + 6 (−2)
= 20 + (−12) =8
(ii) Reenu's score = 5 5 + 5 (−2)
= 25 − 10 = 15
(iii) Heena's score = 2 5 + 5 (−2)
= 10 − 10 = 0
Page No 9:
Question 9:
We have 5 marks for correct answer and (−2) marks for an incorrect answer.
Now, we have the following:
(i) Ravi's score = 4 5 + 6 (−2)
= 20 + (−12) =8
(ii) Reenu's score = 5 5 + 5 (−2)
= 25 − 10 = 15
(iii) Heena's score = 2 5 + 5 (−2)
= 10 − 10 = 0
Answer:
(i) True.
(ii) False. Since the number of negative signs is even, the product will be a positive integer.
(iii) True. The number of negative signs is odd.
(iv) False. a (−1) = −a, which is not the multiplicative inverse of a.
(v) True. a b = b a
(vi) True. (a b) c = a (b c)
(vii) False. Every non-zero integer a has a multiplicative inverse , which is not an integer.
Page No 12:
Question 1:
(i) True.
(ii) False. Since the number of negative signs is even, the product will be a positive integer.
(iii) True. The number of negative signs is odd.
(iv) False. a (−1) = −a, which is not the multiplicative inverse of a.
(v) True. a b = b a
(vi) True. (a b) c = a (b c)
(vii) False. Every non-zero integer a has a multiplicative inverse , which is not an integer.
Answer:
(i) 65 (−13) = −5
(ii) (−84) 12 = −7
(iii) (−76) 19 = −4
(iv) (−132) 12 = −11
(v) (−150) 25 = −6
(vi) (−72) (−18) =
(vii) (−105) (−21) = 5
(viii) (−36) (−1) = 36
(ix) 0 (−31) = 0
(x) (−63) 63 = −1
(xi) (−23) (−23) = 1
(xii) (−8) 1 = −8
Page No 12:
Question 2:
(i) 65 (−13) = −5
(ii) (−84) 12 = −7
(iii) (−76) 19 = −4
(iv) (−132) 12 = −11
(v) (−150) 25 = −6
(vi) (−72) (−18) =
(vii) (−105) (−21) = 5
(viii) (−36) (−1) = 36
(ix) 0 (−31) = 0
(x) (−63) 63 = −1
(xi) (−23) (−23) = 1
(xii) (−8) 1 = −8
Answer:
(i)
72 ÷ (x) = −4
(ii)
−36 ÷ (x) = −4
(iii)
(x) ÷ (−4) = 24
(iv)
(x) ÷ 25 = 0
(v)
(x) ÷ (−1) = 36
(vi)
(x) ÷ 1 = −37
(vii)
39 ÷ (x) = −1
(viii)
1 ÷ (x) = −1
(ix)
−1 ÷ (x) = −1
Page No 12:
Question 3:
(i)
72 ÷ (x) = −4
(ii)
−36 ÷ (x) = −4
(iii)
(x) ÷ (−4) = 24
(iv)
(x) ÷ 25 = 0
(v)
(x) ÷ (−1) = 36
(vi)
(x) ÷ 1 = −37
(vii)
39 ÷ (x) = −1
(viii)
1 ÷ (x) = −1
(ix)
−1 ÷ (x) = −1
Answer:
(i) True (T). Dividing zero by any integer gives zero.
(ii) False (F). Division by zero gives an indefinite number.
(iii) False (F).
(iv) True (T).
(v) False (F).
(vi) True (T).
Page No 12:
Question 1:
(i) True (T). Dividing zero by any integer gives zero.
(ii) False (F). Division by zero gives an indefinite number.
(iii) False (F).
(iv) True (T).
(v) False (F).
(vi) True (T).
Answer:
(c) 14
Given:
6 − (−8)
= 6 + 8
= 14
Page No 12:
Question 2:
(c) 14
Given:
6 − (−8)
= 6 + 8
= 14
Answer:
(b) −3
Given:
−9 − (−6)
= −9 + 6
= −3
Page No 13:
Question 3:
(b) −3
Given:
−9 − (−6)
= −9 + 6
= −3
Answer:
(d) 5
We can see that
−3 + 5 = 2
Hence, 2 exceeds −3 by 5.
Page No 13:
Question 4:
(d) 5
We can see that
−3 + 5 = 2
Hence, 2 exceeds −3 by 5.
Answer:
(a) 5
Let the number to be subtracted be x.
To find the number, we have:
−1 − x = −6
∴ x = −1 + 6 = 5
Page No 13:
Question 5:
(a) 5
Let the number to be subtracted be x.
To find the number, we have:
−1 − x = −6
∴ x = −1 + 6 = 5
Answer:
(c) 4
We can see that
(−2) − (−6) = (−2) + 6 = 4
Hence, −6 is four (4) less than −2.
Page No 13:
Question 6:
(c) 4
We can see that
(−2) − (−6) = (−2) + 6 = 4
Hence, −6 is four (4) less than −2.
Answer:
(b) −8
Subtracting 4 from −4, we get:
(−4) − 4 = −8
Page No 13:
Question 7:
(b) −8
Subtracting 4 from −4, we get:
(−4) − 4 = −8
Answer:
(b) 2
Required number = (−3) − (−5) = 5 − 3 = 2
Page No 13:
Question 8:
(b) 2
Required number = (−3) − (−5) = 5 − 3 = 2
Answer:
(c) 6
(−3) − x = −9
∴ x = (−3) + 9 = 6
Hence, 6 must be subtracted from −3 to get −9.
Page No 13:
Question 9:
(c) 6
(−3) − x = −9
∴ x = (−3) + 9 = 6
Hence, 6 must be subtracted from −3 to get −9.
Answer:
(c) −11
Subtracting 6 from −5, we get:
(−5) − 6 = −11
Page No 13:
Question 10:
(c) −11
Subtracting 6 from −5, we get:
(−5) − 6 = −11
Answer:
(c) 5
Subtracting −13 from −8, we get:
(−8) − (−13)
= −8 + 13
= 5
Page No 13:
Question 11:
(c) 5
Subtracting −13 from −8, we get:
(−8) − (−13)
= −8 + 13
= 5
Answer:
(a) 4
(−36) ÷ (−9) = 4
Here, the negative signs in both the numerator and denominator got cancelled with each other.
Page No 13:
Question 12:
(a) 4
(−36) ÷ (−9) = 4
Here, the negative signs in both the numerator and denominator got cancelled with each other.
Answer:
(b) 0
Dividing zero by any integer gives zero as the result.
Page No 13:
Question 13:
(b) 0
Dividing zero by any integer gives zero as the result.
Answer:
(c) not defined
Dividing any integer by zero is not defined.
Page No 13:
Question 14:
(c) not defined
Dividing any integer by zero is not defined.
Answer:
(b) −11 < −8
Negative integers decrease with increasing magnitudes.
Page No 13:
Question 15:
(b) −11 < −8
Negative integers decrease with increasing magnitudes.
Answer:
(b) 9
Let the other integer be a. Then, we have:
−3 + a = 6
∴ a = 6 − (−3) = 9
Page No 13:
Question 16:
(b) 9
Let the other integer be a. Then, we have:
−3 + a = 6
∴ a = 6 − (−3) = 9
Answer:
(a) −10
Let the other integer be a. Then, we have:
6 + a = −4
∴ a = −4 − 6 = −10
Hence, the other integer is −10.
Page No 13:
Question 17:
(a) −10
Let the other integer be a. Then, we have:
6 + a = −4
∴ a = −4 − 6 = −10
Hence, the other integer is −10.
Answer:
(a) 22
Let the other integer be a. Then, we have:
−8 + a = 14
∴ a = 14 + 8 = 22
Hence, the other integer is 22.
Page No 13:
Question 18:
(a) 22
Let the other integer be a. Then, we have:
−8 + a = 14
∴ a = 14 + 8 = 22
Hence, the other integer is 22.
Answer:
(c) 6
The additive inverse of any integer a is −a.
Thus, the additive inverse of −6 is 6.
Page No 14:
Question 19:
(c) 6
The additive inverse of any integer a is −a.
Thus, the additive inverse of −6 is 6.
Answer:
(b) −150
We have (−15) × 8 + (−15) × 2
= (−15) × (8 + 2) [Associative property]
= −150
Page No 14:
Question 20:
(b) −150
We have (−15) × 8 + (−15) × 2
= (−15) × (8 + 2) [Associative property]
= −150
Answer:
(b) −24
We have (−12) × 6 − (−12) × 4
= (−12) × (6 − 4) [Associative property]
= −24
Page No 14:
Question 21:
(b) −24
We have (−12) × 6 − (−12) × 4
= (−12) × (6 − 4) [Associative property]
= −24
Answer:
(b) 810
(−27) × (−16) + (−27) × (−14)
= (−27) × (−16 + (−14)) [Associative property]
=(−27) × (−30)
= 810
Page No 14:
Question 22:
(b) 810
(−27) × (−16) + (−27) × (−14)
= (−27) × (−16 + (−14)) [Associative property]
=(−27) × (−30)
= 810
Answer:
(a) −270
30 × (−23) + 30 × 14
= 30 × (−23 + 14) [Associative property]
= 30 × (−9)
= −270
Page No 14:
Question 23:
(a) −270
30 × (−23) + 30 × 14
= 30 × (−23 + 14) [Associative property]
= 30 × (−9)
= −270
Answer:
(c) 152
Let the other integer be a. Then, we have:
−59 + a = 93
∴ a = 93 + 59 = 152
Page No 14:
Question 24:
(c) 152
Let the other integer be a. Then, we have:
−59 + a = 93
∴ a = 93 + 59 = 152
Answer:
(b) 90
Page No 15:
Question 1:
(b) 90
Answer:
Let the other integer be a. Then, we have:
a + (−12) = 43
⇒ a = 43 − (−12) = 55
Hence, the other integer is 55.
Page No 15:
Question 2:
Let the other integer be a. Then, we have:
a + (−12) = 43
⇒ a = 43 − (−12) = 55
Hence, the other integer is 55.
Answer:
Given:
p − (−8)= 3
⇒ p = 3 + (−8)
⇒ p = −5
Hence, the value of p is −5.
Page No 15:
Question 3:
Given:
p − (−8)= 3
⇒ p = 3 + (−8)
⇒ p = −5
Hence, the value of p is −5.
Answer:
Product of (−16) and (−9) = = 144
Now, gives the quotient −22.
∴ 144 + (−22) = 122
Page No 15:
Question 4:
Product of (−16) and (−9) = = 144
Now, gives the quotient −22.
∴ 144 + (−22) = 122
Answer:
Suppose that a divides −240 to obtain 16. Then, we have:
(−240) a = 16
⇒ a = (−240) 16 = −15
Hence, −15 should divide −240 to obtain 16.
Page No 15:
Question 5:
Suppose that a divides −240 to obtain 16. Then, we have:
(−240) a = 16
⇒ a = (−240) 16 = −15
Hence, −15 should divide −240 to obtain 16.
Answer:
Let a be divided by (−7) to obtain 12. Then, we have:
⇒ a =
Hence, should be divided by −7 to obtain 12.
Page No 15:
Question 6:
Let a be divided by (−7) to obtain 12. Then, we have:
⇒ a =
Hence, should be divided by −7 to obtain 12.
Answer:
(i) −450
(ii) 360
(iii) −1080
(iv) −600
(v)
(vi)
Page No 15:
Question 7:
(i) −450
(ii) 360
(iii) −1080
(iv) −600
(v)
(vi)
Answer:
(i) (−16) × 12 + (−16) × 8
= (−16) × (12 + 8) [Associative property]
= (−16) × 20
= −320
(ii) 25 × (−33) + 25 × (−17)
= 25 × ((−33) + (−17)) [Associative property]
= 25 × (−50) = −1250
(iii) (−19) × (−25) + (−19) × (−15)
= (−19) × ((−25) + (−15)) [Associative property]
= (−19) × (−40) = 760
(iv) (−47) × 68 − (−47) × 38
= (−47) × (68 − 38) [Associative property]
= (−47) × 30 = −1410
(v) (−105) ÷ 21 = −5
(vi) 12
(vii) 0 (zero). Dividing 0 by any integer gives 0.
(vii) Not defined. Dividing any integer by zero is not defined.
Page No 15:
Question 8:
(i) (−16) × 12 + (−16) × 8
= (−16) × (12 + 8) [Associative property]
= (−16) × 20
= −320
(ii) 25 × (−33) + 25 × (−17)
= 25 × ((−33) + (−17)) [Associative property]
= 25 × (−50) = −1250
(iii) (−19) × (−25) + (−19) × (−15)
= (−19) × ((−25) + (−15)) [Associative property]
= (−19) × (−40) = 760
(iv) (−47) × 68 − (−47) × 38
= (−47) × (68 − 38) [Associative property]
= (−47) × 30 = −1410
(v) (−105) ÷ 21 = −5
(vi) 12
(vii) 0 (zero). Dividing 0 by any integer gives 0.
(vii) Not defined. Dividing any integer by zero is not defined.
Answer:
(d) −8
Let the other integer be a. Then, we have:
2 + a = −6
⇒ a = −6 − 2 = −8
∴ The other integer is −8.
Page No 15:
Question 9:
(d) −8
Let the other integer be a. Then, we have:
2 + a = −6
⇒ a = −6 − 2 = −8
∴ The other integer is −8.
Answer:
(b) 8
Suppose that a is subtracted from −7. Then, we have:
−7 − a = −15
a = −7 + 15 = 8
∴ 8 must be subtracted from −7 to obtain −15.
Page No 15:
Question 10:
(b) 8
Suppose that a is subtracted from −7. Then, we have:
−7 − a = −15
a = −7 + 15 = 8
∴ 8 must be subtracted from −7 to obtain −15.
Answer:
(b)108
(108) ÷ (−18) = −6
Page No 15:
Question 11:
(b)108
(108) ÷ (−18) = −6
Answer:
(a) 370
We have:
(−37) × (−7) + (−37) × (−3)
= (−37) × {(−7) + (−3)} [Associative property]
= (−37) × (−10)
= 370
Page No 15:
Question 12:
(a) 370
We have:
(−37) × (−7) + (−37) × (−3)
= (−37) × {(−7) + (−3)} [Associative property]
= (−37) × (−10)
= 370
Answer:
(c) −250
(−25) × 8 + (−25) × 2
= (−25) × (8 + 2) [Associative property]
= −250
Page No 15:
Question 13:
(c) −250
(−25) × 8 + (−25) × 2
= (−25) × (8 + 2) [Associative property]
= −250
Answer:
(b) −3
(−9) − (−6)
= (−9) + 6
= −3
Page No 15:
Question 14:
(b) −3
(−9) − (−6)
= (−9) + 6
= −3
Answer:
(b) −6
−8 − (−6) = 2
Hence, −8 is −6 less than −2.
Page No 15:
Question 15:
(b) −6
−8 − (−6) = 2
Hence, −8 is −6 less than −2.
Answer:
(i) −1
(ii) 1
(iii) (−16) [Commutative property]
(iv) 0 [Property of zero]
(v) −7
(vi) −19
(vii) 0
(viii) 152
Page No 15:
Question 16:
(i) −1
(ii) 1
(iii) (−16) [Commutative property]
(iv) 0 [Property of zero]
(v) −7
(vi) −19
(vii) 0
(viii) 152
Answer:
(i) True (T).
(ii) False (F). Dividing any integer by zero is not defined.
(iii) False (F). (−1) ÷ (−1) = 1
(iv) True (T).
(v) True (T).
(vi) False (T). 68 ÷ (−17) = −4
View NCERT Solutions for all chapters of Class 7