Class 7 Maths Notes for Integers

NOTES

CLASS 7
MATHS

Study Material

DOWNLOAD PDF

INTEGERS

Previous Knowledge:
Integers - Integers are bigger collection of numbers which is formed by whole numbers and their
negatives or we can say that all positive and negative numbers including zero are integers.
Example: -3, -2, -1, 0, 1, 2, 3...

Integers on Number Line - On a number line, when we:
● add a positive integer, we move to the right.
● add a negative integer, we move to the left.
● subtract a positive integer, we move to the left.
● subtract a negative integer, we move to the right.

Properties of Addition and Subtraction of Integers
(a) Closure Property: Integers are closed for addition and subtraction both,
i.e. a + b and a – b are again integers, where a and b are any integers.
Example: For any two integers 2 and 3, we have
2+ 3 = 5 an integer and 2 – 3 = -1 is also an integer.

(b) Commutative Property: Addition is commutative for integers,
i.e. a + b = b + a for all integers a and b.
Example: For any two integers say 5 and 4, we have 5+ 4 = 4 + 5 = 9,
but the same does not holds for subtraction as 5– 4 =1 and 4 - 5 = -1.

(c) Associative Property: Addition is associative for integers,
i.e., (a + b) + c = a + (b + c) for all integers a, b and c.
Example: For any three integers say 6, 3 & 7 we have (6 + 3) +7= 6 + (3 + 7)
Again it does not hold under subtraction.

(d) Additive Identity: Integer 0 is the identity under addition
i.e. a + 0 = 0 + a = a for every integer a.
Example: 3 + 0 = 0 + 3 = 3

Multiplication of Integers
The product of a positive and a negative integer is a negative integer, whereas
the product of two negative integers is a positive integer and the product of two
positive integers is always a positive integer.
Example: – 2 × 7 = – 14 and – 3 × – 8 = 24 and 5 × 6 = 30.
Also we can see that the product of even number of negative integers is positive.
whereas the product of odd number of negative integers is negative.

2

Example: (-1) × (-1) × (-1) × (-1) = 1 but (-1) × (-1) × (-1) = -1.

Properties of Multiplication of Integers
(a) Closure Property: Integers are closed under multiplication,
i.e., a × b is an integer for any two integers a and b,
Example: 2 x 3 =6, 6 is also an integer.
(b) Commutative Property: Multiplication is commutative for integers,
i.e., a × b = b × a for any integers a and b
Example: 4 x 3 = 3 x 4 = 12.
(c) Associative Property: Multiplication is associative for
integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b & c.
Example: (2 × 3) × 4 = 2 × (3 × 4) = 24
(d) Multiplicative Identity: The integer 1 is the identity under multiplication,
i.e., 1 × a = a × 1 = a for any integer a.
Example: 1 × 9 = 9 × 1 = 9
(e) Distributive Property: Under addition and multiplication, integers show a property called
distributive property i.e., a × (b + c) = (a × b) + (a × c) for any three integers a, b and c.
Examples:
i) 16 x12 = 16 x (10 +2) = (16 x 10) + (16 x 2) = 160 + 32 =192
ii) -23 x 48 = -23 x (50 - 2) = (-23 x 50) + (-23 x 2) = -1150 + (-46)
= -1150 - 46 = -1196
iii) 52 x (-8) + (-52) x 2 = [52 x (-8)] + [ 52 x (-2)] = 52 x [(-8 -2)] =52 x (-10) = -520.
Properties of Division of Integers
(a) When a positive integer is divided by a negative integer, the quotient
obtained is a negative integer and vice-versa.
2 2
Example: −3= -3
(b) Division of a negative integer by another negative integer gives a positive
integer as quotient.
−5 5
Example: −6=6
Other Properties of Integer: For any integer a, we have (i) a ÷ 0 is not defined and
(ii) a ÷ 1 = a. Example: 4÷0 is not defined and 6 ÷1 = 6

3

Summarization of properties of Integers

SOLVED EXAMPLES
MCQ
Q1.The integer whose product with (-1) gives 1 is
a) 1 b) -1 c) ) d) None of these (Ans: b) -1 )
Q2. 10 ÷ (-5) =
a) 2 b) 5 c) -5 d) -2 (Ans: d) -2)
Q3. If x ÷ 1= -8 then x =
a)8 b) 1 c) -8 d) 8
(Ans: c) -8 )
Q4. The additive identity for integers is
a) 1 b) -1 c) 0 d) None of these (Ans c) 0 )

CASE STUDY BASED QUESTIONS
Q1. The temperature decreases due to increase in altitude at the rate of 6°C per 900 m on Mount
Everest

i) If the temperature on Mt Everest at 8100 m above ground level is -24°C, then the temperature
at 2400m is :
a)14°C b) -2 °C c) 10°C d) -4°C (Ans: 10°C)
ii) At which height will the temperature be -18 °C

4

a) 4000 m b) 4500m c) 7000m d) 7200m (Ans: 7200m)
SHORT ANSWER TYPE QUESTIONS
Q1. Find : (-49) X 18 using distributive property
Solution: (-49)X18
= (-49) X (10+8)
= (-49X 10) + (-49)X 8
= -490 – 392 =- 882 Ans
Q2. Solve the following:
(-15) × 8 + (-15) × 4
Solution:
(-15) × 8 + (-15) × 4
= (-15) × [8 + 4]
= (-15) × 12= -180
Q3. Solve
[32 + 2 × 17 + (-6)] ÷ 15
Solution:
[32 + 2 × 17 + (-6)] ÷ 15
= [32 + 34 – 6] ÷ 15
= [66 – 6] ÷ 15
= 60 ÷ 15= 4

LONG ANSWER TYPE QUESTIONS
1) A shop owner earns a profile of Rs 280 on the sale of a pair of footwear and incurs a loss of
Rs 165 on the sale of a purse. In a particular week, he incurs a loss of Rs 300. If he sold 6 pairs
of footwear in that week, then how many purses did the shop owner sell in that particular week?
Solution:
Profit of 280/- on footwear
Loss of 165/- on purse
Net Loss=300/-
Profit on 6 footwears = 6X 280= 1680/-
Loss 1680+300=1980/-
Hence no. of purse sold= 1980÷165= 12
Ans: 12 purse was sold
Q2 In a class test containing 20 questions, 5 marks are awarded for each correct answer
and 2 marks is deducted for each wrong answer. If Riya get 15 correct answers out of all
the questions attempted. What is her total score?
Solution
Number of questions = 20
Marks awarded for corrected answer = 5
Marks awarded for wrong answer = –2
Number questions attempted correctly = 15
Number questions not attempted correctly = 5
Her total score = (15 × 5) + (–2 × 5) = 75 – 10 = 65

5

---------------------------------------------------------------------------------------------------------------------
PRACTICE QUESTIONS
MCQ
Q1. Write the additive inverse of -34.
a) 34 b) -34 c) -3 d) 4
Q2. Closure property does not hold good in integers for
a)) addition (b) multiplication (c) subtraction (d) division
Q3. Which of the following is true?
(a) (-8) + (-4) > (-8) – (-4) (b) (-8) + (-4) < (-8) – (-4)
(c) (-8) + (-4) = (-8) – (-4) (d) None of these
Q4The multiplicative identity for integers is
(a) 1 (b) -1 (c) 0 (d) 1 and -1
Q5Product of two integers is 256, if one of the integers is (-8), then the other is
(a) 32 (b) -32 (c) 248 (d) -264
Q6 The value of (-27) × (-16) + (-27) × (-14) is
(a) 1110 (b) -810 (c) 810 (d) 1110
Q7 When 0 divided by (-10), we get
(a) – 10 (b) 10 (c) 1 (d) 0
Q8 The smallest positive integer is 0
a) True b) False
Q9 (-9) + (-4) ▭ (-9) – (-4) Fill in the blanks.
(a) >(b) <(c) = d) ≤
Q10 Evaluate -50 ÷ 5 =?
(a) 15(b) -25(c) -10(d) +10
Short Answer Type
Q1. Evaluate using a suitable property:
(a) 22 × 45 + 22 × 55
(b) 63 × (-15) + (-63) × 85
Q2. Put >, < or = sign in the given blank:
(a) (-2) + 5 + (-7) ___ (-9) + (-2) +10
(b) 39 + (-23) -16 ____ 36 + (-22) - (-20)
Q3. Find the product:
(a) 6 × (32 - 2)
(b) (-81) × 104
(c) (-27) × 19 - 27
(d) (-8) × (-3) × (2) x (-1)
(e) 32 × 0 × (-29)
Q4. Evaluate:
(a) (-40) ÷ 10
(b) (-61) ÷ [ (-60) + (-1)]

6

Long Answer Type Questions
Q1. A grocer had a profit of Rs 47 on Monday, a loss of Rs12 on Tuesday and loss of Rs8 on
Wednesday. Find his net profit or loss for 3 days
Q2. Temperature of a room is 22° C. If the temperature decreases at 4° C every hour. What will
be the temperature of the room after 8 hours?
Q3. In a quiz containing 10 questions, for every correct answer 3 marks are given and for every
incorrect answer (-1) is given. Sonia attempts all the questions. She gives 7 correct and 3
incorrect answers. Find her final score
Q4. Q5. Verify a-(-b) = a+b for a =59, b= 23
Q5. A plane is flying at the height of 5000 m above the sea level. At a particular point, it is
exactly above a submarine floating 1200 m below the sea level. What is the vertical distance
between them?
Q6. In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0, – 30 in three successive
rounds. Which team scored more? Can we say that we can add integers in any order?

Case Study Questions
Q1.An elevator descends at the rate of 4 m/min. If the elevator start descending 25 m above
the ground level, how long will it take to descend 20 m?

Q2.An air conditioner cools a room by 4oC/min. If the temperature of the room is 45oC before
switching on the air conditioner. Find temperature of the room after switching on the air
conditioner for 6 min.

7

ANSWERS

MCQ Short Answer Long Answer
Ques Ques

Q1 a) 1a) 2200 1 Loss of
Rs27
Q2 d) 1b) -6300 2 -10°C

Q3 b) 2a) < 3 18

Q4 a) 2b) < 4 82

Q5 b) 3a) 180 5 6200m

Q6 c) 3b) -8424 6 Team B
Yes
Q7 d) 3c) -540

Q8 b) 3d) -48

Q9 b) 3e) 0

Q10 c) 4a) -4

4b) -1

8

PRACTICE TEST-1
Mathematics
Class-VII
General Instructions: Section-A contains 4 questions of 1 mark each.Section –B contains 3
questions of 2 marks each. Section-C contains 2 questions of 3 marks each. Section-D contains
1question of 4 mark
M.Marks:20 Time: 45 min

SECTION-A
Q1 Evaluate: (-49) ÷ (-7) 1
a) 14 b) 7 c)-7 d) 42
Q2 1
a × (5 + c) = a × 5 + a × c is called
a) commutative property
b) associative property
c) distributive property
d) closure property
Q3 1
If (- 50) ÷ x = 1, then x is equal to
a) 1 b)50 c) – 50 d) 100
Q4 1
Find the value of 6 – (-3) :
a) 3 b) -3 c) 9 d) -9
SECTION-B
Q5 Find the product : (-8) x (-3) x (2) x (-1) 2
Q6 Use the sign of >, < or = in the box to make the statements true. 2
(– 8) + (– 4) (–8) – (– 4)

Q7 Suppose we represent the distance above the ground by a positive integer and 2
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 metre per minute.
What will be its position after one hour?
(ii) If it begins to descend from 15 m above the ground, what will be its
position after 45 minutes?

SECTION-C
Q8 Find the product, using suitable properties: 3
26 × (– 48) + (– 48) × (–36)
Q9 In a quiz, team A scored -30, 10 and team B scored 5, -30 in two successive 3
rounds. Which team scored more?

9

SECTION-D
Q10. The average monthly temperature of
Jan Feb March April May June
°
Avrg. Temp. In Drass(( c) -32 -20 -6 2 14 21

Avrg. Temp. In Churu(°c) 22 25 32 35 40 44

i) Show the increase in temperature in Drass from March to April on the number line
below.

Find the difference in temperature between Churu and Drass in January

PRACTICE TEST-2
Mathematics
Class-VII
General Instructions: Section-A contains 5 questions of 1 mark each.Section –B contains 6
questions of 2 marks each. Section-C contains 3 questions of 3 marks each. Section-D contains
1question of 4 marks
M.Marks:30 Time: 90 min
SECTION-A
Q1 Evaluate: (–10) + 3 = 1
b) 14 b) 7 c)-7 d) 42
Q2 Write the additive inverse of -34 1
1 1
a) – 1 b) c) 34 d)
 34 34
Q3 If (- 5) ÷ x = 5, then x is equal to 1

b) 1 b)50 c) – 50 d) -1
Q4 Find the value of 6 – (-13) : 1
a) 3 b) -13 c) 19 d) -19
Q5 a × (– b) = (– a) × b E)
e) commutative property f) associative property
g) distributive property h) closure property

10

SECTION-B
Q6 Find the product : (-10) × (-3) × (-2) × (-1) 2
Q7 Use the sign of >, < or = in the box to make the statements true. 2
(– 18) + (– 4) (–8) – (– 14)

Q8 A grocer had a profit of 47 on Monday, a loss of 12 on Tuesday and 2
loss of 8 on Wednesday. Find his net profit or loss for 3 days.
Q9 Find the product, using suitable properties: 2
16 × (– 4) + (– 4) × (–36)
Q10 Evaluate: (-61) ÷ [ (-60) + (-1)] 2

Q11 Find the product : 6 x (30 - 2) 2
SECTION-C
Q12 3
Verify a-(-b) = a+b for a =59, b= 23
Q13 3
Evaluate using a suitable property:
(a) 22 x 45 + 19 x 55
(b) 63 x (-15) + (-63) x 85
Q14 Temperature of a room is 22° C. If the temperature decreases at 4° C every 3
hour. What will be the temperature of the room after 8 hours?
SECTION-D
Q15 4

i) By observing the above number line, state which of the following statements is
true?
(a) B is 2 (b) A is – 4 (c) B is -13 (d) B is – 4

ii) By observing the above number line, state which of the following statements is
not true?
(a) B is greater than -10 (b) A is greater than 0
(c) B is greater than A (d) 6 is smaller than

iii)Next three consecutive numbers in the pattern 11, 8, 5, 2,______ ,__ ,__ are
(a) 0, – 3, – 6 (b)-1,-5,-8 (c) – 2, — 5, – 8 (d) -1,-4, -7

iv) B represents which integer ?

11

Study Materials
Notes

Model Papers Class 6 Notes

Sample Papers Class 7 Notes
Half Yearly Sample Papers Class 8 Notes

Class 9 Notes
Important Resources
Class 10 Notes
Periodic Table
Class 11 Notes
Writing Skills / Formats

Maps of India / World Class 12 Notes

Books and Solutions

NCERT Books
NCERT Book Solutions
HC Verma Chapter Wise Solutions
RD Sharma Solutions
CGBSE Solutions