CBSE Class 7 Mathematics Integers Worksheet Set A

Question. The value of 5(10 – 9) is            
(A) 5
(B) 5 × 10 – 5 × 9
(C) (A) and (B)
(D) none of these

Answer:        D

Question. The sum of two integers is also an integer, this property of integers is called         
(A) Closure
(B) Commutative
(C) Associative
(D) None of these

Answer:      A 

Question. Reciprocal of 1/7 is:            
(A) 7
(B) 1
(C) –7
(D) 1/7

Answer:    A

Question. For any integer x what is true:            
(A) x/0 is not defined (B) x/1 = a (where x ≠ a)
(C) option
(A) and
(B) both are wrong
(D) option (A) and (B) both are rigth

Answer:    A

Question. Every integer is also a            
(A) natural number
(B) whole number
(C) (A) and
(B) both
(D) none of these

Answer:          D

Question. When 0 is multiplied by any negative integer, their product will be            
(A) a positive integer
(B) a negative integer
(C) zero
(D) none of these

Answer:           C

Question. Every positive integer is greater than            
(A) zero
(B) every negative integer
(C) both (A) and (B)
(D) none of these

Answer:   C

Question. The product of two integers is 12, if one integer is –3 then the other one is:            
(A) +4
(B) –4
(C) 3
(D) –3

Answer:   B

Question. On subtracting (–6) from 0, we get:            
(A) –6
(B) 6
(C) 7
(D) None of these

Answer:   B

Question. The sum of two integers is always            
(A) a natural number
(B) a whole number
(C) an integer
(D) none of these

Answer:          B

Question. The multiplicative identity of integers is            
(A) 0
(B) +1
(C) –1
(D) none of these

Answer:   C

Question. The additive inverse of –6 is:            
(A) 6
(B) 0
(C) –5
(D) –7

Answer:   A

Question. 30 × (–23) + 30 × 14 = ? 
(A) –270
(B) 270
(C) 1110
(D) –1110

Answer:   A

Question. (–8) / 0 = ?  
(A) –8
(B) 0
(C) 8
(D) Not defined

Answer:     D

Question. How much less than –8 is –3?   
(A) –5
(B) 5
(C) 11
(D) –11

Answer:    A

Question. The sum of two integers is 93. If one of them is –59, the other one is: 
(A) 34
(B) –34
(C) 152
(D) –152

Answer:    C

Question. Resolve the brackets and simplify: (28 / 2) / (56 / 8).
(A) 1
(B) 4
(C) 3
(D) 2

Answer:    D

Question. For integers:            
(A) Addition is associative
(B) Addition is commutative
(C) Integer “0” is the identity under addtion
(D) All of the above

Answer:      D

Question. By how much does –3 exceed –5 ?  
(A) –2
(B) 2
(C) 8
(D) –8

Answer:   B

Question. What must be subtracted from –3 to get –9?   
(A) –6
(B) 12
(C) 6
(D) –12

Answer:     C

Question. The additive identity of integers is            
(a) –1
(B) 1
(C) 0
(D) none of these

Answer:    c

Question. The greatest positive integer is            
(A) 0
(B) 100
(C) 999
(D) none of these

Answer:   D

Question. Write the value of
(i) | +22 |
(ii) | –8 |
(iii) | 18 – 8 |
(iv) | – 5 – 4 |
(v) – | 3 – 2 |

Answer:  (i) 22  (ii) 8  (iii) 10  (iv) 9  (v) –1

Question. Arrange the following integers in ascending order
(i) – 20, 13, 4, 0, –5, +5
(ii) +30, –2, 0, –6, –20, 8

Answer: (i) –20, –5, 0, 4, 5, 13   (ii) –20, –6, –2, 0, 8, 30

Question. The temperature at 12 noon was 10°C above zero. At what time the temperature will be 8°C below 0°C, if it decreases at the rate of 2°C ? If it decreases at the rate of 2°C per hour till midnight, what would be the temperature at mid-night ?

Answer: 9 pm, –14ºC

Question. In a class test (+3) marks are given for every correct answer and (–2) marks are given for every incorrect answer and no marks for not attempting any questions.
(i) Ram scored 20 marks. If he has got 12 correct answers, how many questions has he attempted incorrectly ?
(ii) Mohan scores –5 marks in the test though he has written 7 correct answers. How many questions has he attempted incorrectly ?

Answer: (i) 8    (ii) 13

Question. A water tank has steps inside it. A monkey is sitting on the toppest step (i.e., the first step). The water level is at the ninth step.
(i) He jumps 3 steps down and then jumps 2 steps up. If he continues in this way, in how many jumps will he reach the water level ?
(ii) After drinking water, he wants to go back, for this he jumps 4 steps up and then jumps 2 steps down in every move. In how many jumps will he reach back the top step ?

Answer: (i) 11 times     (ii) 5 times

Question. Which temperature is higher ?
(i) 40°C or –40°C
(ii) –18°C or 12°C
(iii) –2°C or –4°C
(iv) 17°C or 27°C

Answer: (i) 40ºC  (ii) 12ºC  (iii) –2ºC  (iv) 27ºC

Question. Verify and name the property used :
(i) –110 × (–237) = (–237) × (–110)
(ii) (–35 × 4) × (–152) = –35 × [4 × (–152)]

Answer: (i) Commutative property of multiplication.  (ii) Associative property of multiplication

Question. Verify and name the property used :
(i) –117 × 251 + (–117) × 249
(ii) 156 × 273 – 156 × (–73)

Answer: (i) Distributive property of multiplication over addition
              (ii) Distributive property of multiplication over subtraction

Question. A boy has j- 350 in his bank account. He deposits j- 40 everyday for 10 days. What will be the amount in his account at the end of 10 days ?

Answer: j- 750

Question. In a class test containing 10 questions, 5 marks are answered for every correct answer and (–2) marks are awarded for every incorrect answer and 0 for questions not attempted .
(i) Mohan gets four correct and six incorrect answers. What is his score ?
(ii) Reshma gets five correct answer and five incorrect answers. What is her score ?
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score ?

Answer:  (i) 8 marks (ii) 15 marks (iii) 0 mark

Question. Evaluate the following :           
(i) (– 40) ÷ 10
(ii) 60 ÷ (–6)
(iii) (– 49) ÷ (–7) (iv) (–79) ÷ 79
(v) 13 ÷ [(–4) + 3]
(vi) 0 ÷ (–14) (vii) (– 41) ÷ [(– 40) + (–1)]
(viii) [(– 48) ÷ 12] ÷ 4
(ix) Is [(–7) + (6)] = [(–3) + 2] ?

Answer: (i) –4  (ii) –10  (iii) 7  (iv) –1  (v) –13  (vi) 0  (vii) 1  (viii) –1   (ix) yes

Question. Write down a pair of integers whose :
(i) sum is – 7
(ii) difference is –10
(iii) sum is 0

Answer: (i) –1, –6 or –9, 2       (ii) –11, –1 or 35, –45     (iii) –1, 1 or 20, –20

A. Define

i.Natural number:- The natural numbers include the positive integers (also known as non-negative integers) and a fewexamples include 1, 2, 3, 4, 5, 6, .. ∞. In other words,natural numbers are a set of all the whole numbersexcluding 0.

ii.Whole number :- Whole numbers are a set of numbers including the set of natural numbers (1 to infinity) and the integer'0'. Fraction numbers and negative numbers are not counted in whole numbers.

iii. Prime number:- prime numbers are wholenumbers greater than 1, that have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7 and 11 are the first few prime numbers.

Iv. Integers:- An integer is a whole number (not a fractional number) that can be positive, negative, or zero. For example :- 1,2,3,4,0,-1,-2,-3,-4,-5 etc.

B.PROPERTIES OF INTEGERS FOR ADDITION AND SUBTRACTION:-

C. Solve the following:-

1.Evaluate:

(i) 15 + (−8)
Answer. 15 + (−8) = 7 

(ii) (−16) + 9
Answer. (−16) + 9 = −7

(iii) (−7) + (−23)
Answer. (−7) + (−23) = −30

(iv) (−32) + 47
Answer. (−32) + 47 = 15

(v) 53 + (−26)
Answer. 53 + (−26) = 27

(vi) (−48) + (−36)
Answer. (−48) + (−36) = −84

2.Find the sum of:

(i) 153 and − 302
Answer. 153 + (−302) = −149

(ii) 1005 and − 277
Answer. 1005 + (−277) = 728

(iii) − 2035 and 297
Answer. (−2035) + 297 = −1738

(iv) − 489 and − 324
Answer. (−489) + (−324) = −813

(v) − 1000 and 438
Answer. (−1000) + 438 = −562

(vi) − 238 and 500
Answer. (−238) + 500 = 262

3. Find the additive inverse of:

(i) − 83
Answer. Additive inverse of −83 = −(−83) = 83

(ii) 256
Answer. Additive inverse of 256 = −(256) = −256

(iii) 0
Answer. Additive inverse of 0 = −(0) = 0

(iv) – 2001
Answer. Additive inverse of 2001 = −(−2001) = 2001

4. Subtract:

(i) 28 from − 42
Answer. −42 − 28 = (−42) + (−28) = −70

(ii) − 36 from 42
Answer. 42 −(−36) = 42 + 36 = 78

(iii) − 37 from − 53
Answer. -53 - (-37) = (-53) - (-37) = -16

(iv) − 66 from − 34
Answer. -34 - (-66) = -34 + 66 = 32

(v) 318 from 0
Answer. 0 - 318 = -318

(vi) − 153 from − 240
Answer. (-240) - (-153) = -87

(vii) − 64 from 0
Answer. 0 - (-64) = 0 + 64 = 64

(viii) − 56 from 144
Answer. 144 - (-56) = 144 + 56 = 200

5.Subtract the sum of 

- 1032 and 878 from -34.
Answer. Sum of -1032 and 878 = -1032 + 87 = -154
Subtracting the sum from -34, we get -34 - (-154)
= (−34)+ 154 = 120

6. Subtract 

−134 from the sum of 38 and −87
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

7.Fill in the blanks:

(i) {(−13) + 27} + (−41) = (−13) + {27 + (......)}
Answer. −41 (∵ Associative property)

(ii) (−26) + {(−49) + (−83)} = {(−26) + (−49)} + (......)
Answer. −83 (∵ Associative property)

(iii) 53 + (−37) = (−37) + (......)
Answer. 53 (∵ Commutative property)

(iv) (−68) + (−76) = (......) + (−68)
Answer.−76 (∵ Commutative property)

(v) (−72) + (......) = −72
Answer. 0 (∵ Additive identity)

(vi) − (−83) = ......   
Answer. 83 (∵ Additive inverse)

(vii) (−60) − (......) = − 59
Answer. (−60) − (−59) = −1

(viii) (−31) + (......) = − 40
Answer. (−40) − (−31) = −9

8.Simplify:

{−13−(−27)} + {−25−(−40)}.
Answer.{−13 − (−27)} + {−25 − (−40)}
= {−13 + 27} + {−25 + 40}
=14 + 15 = 29

Q1 What is the value of (−23) –[(−25) – {(−17) –(−19) }
(a) 38
(b) 24
(c) −14
(d) −34

Q2 What should be subtracted from −1963 to obtain −9512?
(a) −11475
(b) −7549
(c) 7549
(d) 11475

Q3 What is the missing value in the expression
{(−267) – (−276) – 15= □ +(−2) + (−1) } ?
(a) −18
(b) −3
(c) 3
(d) 8

Q4 What is the additive inverse of the result obtained by subtraction of −8 from the additive inverse of −13?
(a) −21
(b) −5
(c) 5
(d) 21 

Q5 The temperature of a city is 2°C.Next day the temperature falls by 5°C.What is the temperature of the city the next day?
(a) −5°C
(b) −3°C
(c) 4°C
(d) 7°C

Q6 What is the sum of the additive inverses of −29 and 61?
(a) −90
(b) −32
(c) 90
(d) 32

Q7 On a particular day,the temperature of four places P,Q,R,S are recorded at noon and midnight of the day

At which place is the decrease in temperature the maximum?
(a)P
(b)Q
(c)R
(d)S

Q8 The temperature of a city was found to be 3°C on a particular day .Next day the temperature was found to be −4°C .What is the change in the temperature of the city over the two days?
(a) Decrease by 7°C
(b) Decrease by 1°C
(c) Increase by 7°C
(d) Increase by 1°C

Q9 What is the difference between greatest two-digit positive number and smallest three-digit
negative number?
(a) 199
(b) 110
(c) 1100
(d) 1098

Q10 What is the value of the expression,
(− 216) – (−351)+( −98) –(71)+(28) –(−56) ?
(a) −50
(b) 15
(c) −15
(d) 50

Q11 The temperature in New York city on two consecutive days were 1°C and −6°C.What is the
decrease in the temperature of New York city in two days?
(a) −7°C
(b) 7°C
(c) 5°C
(d) −5°C

INTEGERS (SUBTRACTION AND MULTIPLICATION)

Q1. Find 36 − (−64) and (−64) − 36. Are they equal?
Solution.
36 − (−64) = 36 + 64 = 100
Now, (−64) − 36
= (−64) + (−36) = −100
Here, 100 ≠≠ −100
Thus, they are not equal.

Q2. If a = − 8, b = − 7, c = 6, verify that (a+b) + c = a + (b+c).
Solution.
(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]

Q3. If a = − 9 and b = − 6, show that (a−b) ≠ (b−a).
Solution.
Here, (a − b) = −9 − (−6) = −3
Similarly, (b − a) = −6 − (−9) = 3
∴ (a−b) ≠ (b−a)

Q4. The sum of two integers is − 16. If one of them is 53, find the other.
Solution. Let the other integer be a.
Then,
we have:
53 + a = −16
⇒ a = −16 − 53 = −69
∴ The other integer is −69.

Q5. The sum of two integers is 65. If one of them is − 31, find the other.
Solution. Let the other integer be a. Then,
−31 + a = 65
⇒ a = 65 − (−31) = 96
∴ The other integer is 96.

Q6. The difference of an integer a and (−6) is 4. Find the value of a.
Solution.
We have:
a − (−6) = 4
⇒ a = 4 + (−6) = −2
∴ a = −2

Q7. Write a pair of integers whose sum gives

(i) zero;
Solution. Consider the integers 8 and −8. Then,
we have:
8 + (−8) = 0

(ii) a negative integer;
Solution. Consider the integers 2 and (−9).
Then,
we have: 2 + (−9)= −7,
which is a negative integer.

(iii) an integer smaller than both the integers;
Solution. Consider the integers −4 and −5.
Then, we have: (−4) + (−5) = −9,
which is smaller than −4 and −5.

(iv) an integer greater than both the integers;
Solution. Consider the integers 2 and 6.
Then,
we have: 2 + 6 = 8,
which is greater than both 2 and 6.

(v) an integer smaller than only one of the integers.
Solution. Consider the integers 7 and −4. Then,
we have: 7 + (−4) = 3,
which is smaller than 7 only.

Q8. For each of the following statements, write (T) for true and (F) for false:

(i) The smallest integer is zero.
Solution. F (false). −3, −90 and −100 are also integers.
We cannot determine the smallest integer, since they are infinite.

(ii) − 10 is greater than − 7
Solution. F (false). −10 is less than −7.

(iii) Zero is larger than every negative integer.
Solution.T (true). All negative integers are less than zero.

(iv) The sum of two negative integers is a negative integer. 
Solution. T (true).

(v) The sum of a negative integer and a positive integer is always a positive integer.
Solution. F (false). Example: −9 + 2 = −7

Q9. Multiply:

(i) 16 by 9
Solution. 16 ×× 9 = 144

(ii) 18 by − 6
Solution. 18 ×× (−6)
= −(18×6)
= -(18×6)
= −108

(iii) 36 by − 11
Solution. 36 ×× (−11)
= − (36×11)
= - (36×11)
= −396

(iv) − 28 by 14
Solution. (−28) ××14
= −(28×14) = -(28×14)
= −392

(v) − 53 by 18
Solution. (−53) ×× 18
= −(53×18) = -(53×18)
= −954

(vi) − 35 by 0
Solution. (−35) ×× 0 = 0

(vii) 0 by − 23
Solution. 0 ×× (−23) = 0

(viii) − 16 by − 12
Solution. (−16) ×× (−12) = 192

(ix) − 105 by − 8
Solution. (−105) ×× (−8) = 840

(x) − 36 by − 50
Solution. (−36) ×× (−50) = 1800

(xi) − 28 by − 1
Solution. (−28) ×× (−1) = 28

(xii) 25 by − 11
Solution. 25 ×× (−11)
= − (25×11)
= - (25×11)
= −275

Q10. Find each of the following products:

(i) 3 × 4 × (−5) 
Solution. 3 × 4 × (−5)
= (12) × (−5)
= −60

(ii) 2 × (−5) × (−6)
Solution. 2 × (−5) × (−6)
= (−10) × (−6)
= 60

(iii) (−5) × (−8) × (−3)
Solution. (−5) × (−8) × (−3)
= (−5) × (24)
= −120

(iv) (−6) × 6 × (−10)
Solution. (−6) × 6 × (−10)
= 6 × (60)
= 360

(v) 7 × (−8) × 3
Solution. 7 × (−8) × 3
= 21 × (−8)
= −168

(vi) (−7) × (−3) × 4
Solution. (−7) × (−3) × 4
= 21 × 4
= 84

Q1) If the integers 12,-6, 8,-5, 7,-4, 3 are marked on the number line, the one that comes on the extreme left is:
a) 12
b) -4
c) -6
d) 3

Q2) The difference in temperatures +50⁰C and -50⁰C is:
a) 100⁰C
b) 0⁰C
c) 50⁰C
d)-100⁰C

Q3) The integer x for which |1-x| =3 is:
a) 3,0
b) 4,2
c) -2,3
d) 4,-2

Q4) The numbers between -30 and -15 are :
a) 14
b) 15
c) 16
d) 17

Q5) Multiplicative identity for any integer a is:
a) 0
b) 1
c) a
d) a/b

Q6) Represent each of the following integers on the number line: 3 -1, 5, -4, 8, -10 

Q7) The sum of two integers is (-11).If one of them is 72 ,find the other number.

Q8) Using quicker grouping, find the product of :

(a) 16x 20 x ( -25)

(b) ( -125) x 17 x (-8)

(c) (-50) x( -41) x12

(d) (-25) x 36 x 80

(e) (-700) x 49 + (-700)

(f) (-562) x 96 + (-562) x 4

Q9) Using suitable properties, find the value of :

(a) -58 x 104

(b) (-279) x 1001

(c) 36 x (-99)

(d) (-73) x 8 + 73 x (-92)

(e) 517 x (-36) + 517 x (-64)

Q10) Divide:

(a) (-525) ÷(-25)

(b) (-512) ÷ 32

(c) 2352÷(-42)

(d) (-3128) ÷34

Q11) Fill in the blanks:

(a) 450 x 0 =______ (b) 450 x (-1)=_______ (c) (-450) x 1=_____

(d) (-450) x (-1)=________ (e) 0 ÷(-20)=___ (f) (-20)÷ 1=_______

(g) (-20)÷ (-1)=______ (h) 20÷ (-1)=________ (i) (-20)÷ (-1)=_____

Q12) The product of two integers is (-840). If one of them is (-70), find the other.

Q13) Simplify the following:

(a) 120÷[18 – {20 – 3(9-5)}]

(b) 64 ÷[16 x (-3) – 2 x {17 – 25 }]

Q14) Find the value of :

(a) |-15|

(b)- |-20 |

(c) -50 +| -2 |

(d) 18 - | -36|

(e) 46 - |-5 |-|6|

Q15) Write : (a) Additive inverse of 0
(b) Additive inverse of 15
(c) Additive inverse of -36.

Q16) By how much does 2 exceed ( -5)?

Q17) The product of three integers is ( -85). If the two integers are ( -17) and ( -5), find the third.

Q18) Raghu has 30 marbles. In 5 games he won 3 marbles each and in 7 games he lost 2 marbles each. Find the marbles he has at the end of the games.

Q19) Name 4 real life situations in which integers can be used.

INTEGERS (DIVISION)

Rules on How to Divide Integers

RULE 1: The product of a positive integer and a negative integer is negative. (+) × (-) = (-)
RULE 2: The product of two positive or two negative integers is always positive. (+)× (+)= (+) (-) × (-) = (+)
RULE 3: When you divide 0 by another number the answer is always 0.
RULE 4 : When you divide by 1, the answer is the same as the number you were dividing.
RULE 5 : Any number divided by the same number is 1.
RULE 6 : When you divide two negative numbers, THE NEGATIVE sign of numerator DENOMINATOR GET cancelled with each other.

QUESTIONS BASED ON ABOVE RULES

Q1. Divide:

(i) 65 by −13.
Solution. 65 ÷(−13) = -(65/13) = −5

(ii) −84 by 12.
Solution. (−84) ÷12 = -(84/12) = −7

(iii) −76 by 19.
Solution. (−76) ÷ 19 = −(76/19) = −4

(iv) −132 by 12
Solution. (−132) ÷ 12 = −(132/12) = −11

(v) −150 by 25.
Solution. (−150) ÷ 25 = −(150/25) = −6

(vi) −72 by −18.
Solution. (−72) ÷(−18) = (-72/-18) = 4.
[(-)sign cancelled with each other in numerator and denominator]

(vii) −105 by −21.
Solution. (−105) ÷ (−21) = (−105/−21) = 5
[(-)sign cancelled with each other in numerator and denominator]

(viii) −36 by −1
Solution. (−36) ÷(−1) = (−36/−1) = 36.
[(-)sign cancelled with each other in numerator and denominator]

(ix) 0 by −31.
Solution. 0 ÷ (−31) = -(0/31) = 0

(x) −63 by 63
Solution. (−63) ÷63 = −(63/63 ) = −1

Q2. Fill in the blanks

(i) 72 ÷ (......) = −4.
(ii) −36 ÷ (......) = −4. (iii) (......) ÷ (−4) = 24
(iv) (......) ÷ 25 = 0. (v) (......) ÷ (−1) = 36.
(vi) (......) ÷ 1 = −37 (vii) 39 ÷ (......) = −1.
(viii) 1 ÷ (......) = −1. (ix) −1 ÷ (......) = −1
Answer.
(i). 72 ÷ (x) = −4 ⇒72÷x = −4. ⇒x = 72÷( −4 )= -(72÷4) = −18
(ii) −36 ÷ (x) = −4 ⇒−36÷ x = −4 ⇒x = (−36)÷( −4 )= 9
(iii). (x) ÷ (−4) = 24 ⇒x÷ (-4 ) = 24⇒x = 24×(−4) = -(24÷4) = -96
(iv) (x) ÷ 25 = 0 ⇒x÷ 25 = 0. ⇒ x = 25×0 = 0
(v). (x) ÷ (−1) = 36 ⇒x = 36×(-1) = -36
(vi). (x) ÷ 1 = −37 ⇒x = -37×1 = -37
(vi) 39 ÷ (x) = −1 ⇒x = -1×39 = -39
(viii) 1 ÷ (x) = −1 ⇒x = -1×1 = -1 (ix). −1 ÷ (x) = −1 ⇒−x = (-1)÷(-1)= 1.

Q3.Write (T) for true and (F) for false for each of the following statements.

(i) 0 ÷ (−4) = 0
(ii) (−6) ÷ 0 = 0
(iii) (−5) ÷ (−1) = −5
(iv) (−8) ÷ 1 = −8
(v) (−1) ÷ (−1) = −1
(vi) (−9) ÷ (−1) = 9
Answer.
 (i) True (T). Dividing zero by any integer gives zero.
(ii) False (F). Division by zero gives an indefinite number.
(iii) False (F). Because (-5)÷(-1) = 5÷1 = 5
(iv) True (T). −8÷1 =-(8÷1)= -8
(v) False (F). (−1)÷(−1 )= 1÷1 = 1.
(vi) True (T). (−9)÷(-1)= 9÷1 = 9

I. Perform the following operations on Integers :-
1. (+5) + (+2)       6. (-7) + (-3)         11. (+9) + (-4)
2. (-5) + (-2)         7. (+7) + (-3)        12. (-9) + (+4)
3. (+5) + (-2)        8. (-7) + (+3)        13. (-7) +(-2)
4. (-5) + (+2)        9. (+9) + (+4)       14. (-7) +(+2)
5. (+7) + (+3)     10. (-9) + (-4)         15. (+7) +(-2)

II. Perform the following operations on Integers :-
1. (+5) - (+2)         6. (-7) - (-3)          11. (+9) - (-4)
2. (-5) - (-2)           7. (+7) - (-3)         12. (-9) - (+4)
3. (+5) - (-2)          8. (-7) - (+3)         13. (-7) - (-2)
4. (-5) - (+2)          9. (+9) - (+4)        14. (-7) - (+2)
5. (+7) - (+3)       10. (-9) - (-4)          15. (+7) -(-2)

III. Perform the following operations on Integers :-
1. (+5) X (+2)                   11. (+9) X (-4)
2. (-5) X (-2)                     12. (-9) X (+4)
3. (+5) X (-2)                    13. (-7) X(-2)
4. (-5) X (+2)                    14. (-7) X (+2)
5. (+7) X (+3)                   15. (+7) X (-2)
6. (-7) X (-3)                     16 . -8 / -2
7. (+7) X (-3)                    17. -8/2
8. (-7) X (+3)                    18. 8/(-2)
9. (+9) X (+4)                   19. 24/(-2)
10. (-9) X (-4)                   20. -18/6

IV. Find

(a) (-7)-8-(-25)

(b) (-13) + 32-8-1

(c) (-7) + (-8) + (-90)

(d) 50-(-40)-(-2)

V. 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)

VI. Fill in the blanks using >,< or = sign.

(a) (-8) + (-4) _________ (-8) - (-4)

(b) (-3) + 7 – (19) _________ 15 -- 8 + (-9)

(c) 23 – 41 + 11 _________ 23 –-41 – 11

(d) 39 + (-24) – (15) ______ 36 --(-52) – (-36)

(e) -231 + 79 + 51 ______ -399 + 159 + 81

VII. Fill in the blanks

(a) (-8) + ______=0

(b) 13 + ______=0

(c) 12 + (-12)=______

(d) (-4) + _____=-12

(e)_____-15=-10

VIII. (i) Find each of the following products.

(a) (-20) X (-2) X (-5) X 7

(b) (-1) X (-5) X (-4) X (-6)

(ii) Fill in the blanks

(a) (-3) X ______=27

(b) 5 X _____=-35

(c)_____ X (-8)=(-56)

(d)_____ X (-12)=132

IX. Solve

(a) (-30) / 10 (f)0 / (-12)

(b) 50 / (-5) (g)(-31) / {(-30) + (-1)}

(c) (-36) / (-9) (h)({(-36) + 12} / 3

(d) (-49) / 49 (i){(-6) + 5)} /{(-2 + 1)}

(e) 13 / {(-2) + 1}

X. Fill in the blanks

(a) 369 /______=369

(b) (-75) / ______=-1

(c) (-206) / _____=-1

(d) -87 / _____=87

(e) ______ / 1 = -87

(f) ______/ 48=-1

(g) 20 / _____=-2

(h) ______ /(4)=-3

XI. Solve using suitable properties :-
1) (-5782396) X 9+5782396 X (-1)                   16) (-17) X (-29)
2) 8326429 X (-98) + (-8326429) X (-2)           17) (-27) X (-39)
3) (-7624928) X 997 + (7624928) X (-3)          18) (-37) X (-49)
4) (-98) X (-9) + 98                                          19) 8 X 53 X (-125)
5) (-237) X (-99) + 237                                    20) 8 X 56739 X (-125)
6) (-563) X (-999)+ 563                                   21) (-8) X 32597 X 12
7) 7 X (50-2)                                                    22) 8 X (-63298) X 125
8) 253 X (100-1)                                              23) (-8) X (-53) X 125
9) 567 X (1000-1)                                            24) 8 X (-56739) X (-125)
10) (-41) X 102                                               25) 15 X (-25) X (-4) X (-10)
11) (-34) X 1002                                             26) 23 X (-25) X (-4) X (-10)
12) (-67) X 101                                               27) 627 X (-125) X (-8)
13) (-84) X 99                                                 28) 583 X (-125) X (-5) X 16
14) (-24) X 998                                               29) (-749) X 25 X (-250) X 16
15) (-17) X 9997                                             30) 183X (-25) X 8 X 5

XII. In a class test containing 15 questions, 4 marks are given for every correct answer and (-2) marks for every incorrect answer.(i) Gurpreet attempts all questions but only 9 of her answers are correct. What is her total score? (ii) One of her friends gets only 5 answers correct. What will be her score?

XIII. In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer and 0 for not attempting any of the questions.
(a) Mohan gets 4 correct answers and 6 incorrect answers. What is his score?
(b) Reshma gets 5 correct and 5 incorrect answers. What is her score?
(c) Heena gets 2 correct and 5 incorrect answers out of 7 questions she attempted. What is her score?

XIV. In a test (+5) marks are given for every correct answer and (-2) for incorrect answer
(i) Radhika answered all the questions and scored 30 marks though she got 10 correct answers
(ii) Jay also answered all the questions and scored (-12) marks though he got 4 correct answers. How many incorrect questions did they attempt?

XV. In a class test + 3 marks are given for every correct answer and -2 marks are given for every incorrect answer and no marks for not attempting any question –
i) Radhika scored 20 marks if she has got 12 correct answers. How many questions had she attempted incorrectly?
ii) Mohini scored -5 marks in the test though she had got 7 correct answers. How many questions had she attempted incorrectly?

XVI. An elevator descends into the mine shaft @ 6 min per minute. If it descends from 10m above the ground, how long will it take to reach -350m?

XVII. Suppose we represent the distance above the ground, what will be its positive integer and that below the ground by a negative integer, then answer the following: -
(i) An elevator descends into a mine shaft at the rate of 5 m per minute. What will be its position after 1 hour?
(ii) If it begins descending from 15 m above the ground, what will be its position after 45 minutes?

XVIII. A certain freezing process requires that room temperature be lowered from 40º C at the rate of 5º C every hour. What will be the room temperature 10 hours after the process begins? 

XIX. The temperature at the noon was 10°C above zer o. If it decreases @ 2°C per hour until midnight, at what rate would the temperature will be 8°C below zero? What would be the temperature at midnight?

XX.A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.
(a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
(b) What is the no. of white cement bags it must sell to have neither profit nor loss, if the no. of grey bags sold is 6,400 bags.

Q (21) A shopkeeper earns a profit of Re 1 by selling 1 pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock.
(i) In a particular month she incurs a loss of Rs 5. In this period, she sold 45 pens. How many pencils did she sell in this period?
(ii) In the next month she earns neither profit nor loss. If she sold 70 pens, how many pencils were sold?

Question. –32 + 47
Answer : 15

Question. Find the value of (–23) {(–5) + (25)}
Answer : –460

Question. The sum of two integers is (–16). If one of them is 53, find the other.
Answer : –69

Question. What will be the sum of (–2035) and 285?
Answer : –1750

Question. Subtract –134 from the sum of 37 and –87.
Answer : 84

Question. Find the product of (–25) and (14).
Answer : –350

Question. An elevator descends into a mine shaft at the rate of 6 meter per minute. If the descentent starts from the ground level, how long will it take to reach 240 meter?
Answer : 40 minutes

Question. Find the value of 13 – (15 – 6 3).
Answer : 0

Question. Rohit earns profit of Re. 1 by selling one pen and suffers a loss of 50 paise by selling one pencil. One day Rohit earns Rs. 5. If he sold 25 pens, how many pencils did he sell?
Answer : 40 pencils

Question. Subtract the sum of –1878 and 878 from 2000.
Answer : 3000

Question. Find the sum of (8 + 9) × 10 and 8 + 9 × 10.
Answer : 268

Question. Multiply (–36) by (–50).
Answer : 1800

Question. Divide 324 by (–27).
Answer : –12

Question. What is the difference between [36 – (–64) and (–64) – 36]
Answer : 200

Question. If the sum of two integers is –1600 and one of them is 549, find the other number.
Answer : –2149

Question. Find the product : (–2) × 36 × (–5).
Answer : 360

Question. Multiply : (–2) × (–4) × (–5) × (–8)
Answer : 320

Question. The sum of two integers is 65. If one of them is –35, find the other
Answer : 100

Question. Determine the integer when it is divided by (–9), the answer is 23.
Answer : –207

Question. Find the value of 1569 × 887 – 569 × 887.
Answer : 887000 

Question. The product of two integers is –51. If one integer is –17, find the other.
Answer : 3

Question. Divide (–98) by (–14)
Answer : 7

Question. Which integer if multiplied by (–1) will be 432 ?
Answer : –432

Question. What will be the sum of (–1006) and (–934)?
Answer : –1940

Question. The temperature at 1.00 p.m. was 10°C above zero. If it decreases at the rate of 2°C per hour until 10 p.m., at what time would the temperature be 6°C below zero?
Answer : 9 p.m.

I FILL IN THE BLANKS

1. ________________ is the additive identity and _______________ is the multiplicative identity of integers.

2. (-1) x even number of times = _______________

3. (-1) x odd number of times = _______________

4. 38 ÷ 0 = _______________

5. 0 ÷ 11 = _______________

6. 13 ÷ 1 + _______________

7. 55 + _______________ = 0

8. (-31) + _______________ = 0

9. (-55) + _______________ = -89

10. (-33) + _______________ = 79

11. 1000 + _______________ = - 1000

12. [ (-7) + 9] + (_______________) = 9 + [ -7 + 4]

13. (-6) + 2 = 2 (_______________)

14. 251 ÷ _______________ = 1

15. (-70) ÷ _______________ = 5