NCERT Solutions for Class 7 Maths Chapter 1 Integers
NCERT Solutions for Class 7 Maths Chapter 1 Integers - The first chapter of class 7 starts with recollecting the concepts of integers studied in the previous class of NCERT. The first exercise explained in the NCERT class 7 maths chapter 1 solutions are based on these recollected concepts. In NCERT solutions for class 7 maths chapter 1, you will study more about the integers, their properties, and operations. There are a total of 4 exercises with 30 questions in this NCER book chapter. All the questions are explained in the CBSE NCERT solutions for class 7 maths chapter 1.
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The NCERT solutions are prepared by expert teachers to help students. NCERT Class 7 maths chapter 1 solutions are important for a student. All the topics included in NCERT Class 7 Maths chapter 1 solutions are extremely important for higher classes as well. In this NCERT Solutions for Class 7 Maths Chapter 1, we will study important topics of NCERT solutions for class 7 like properties of addition, subtraction, multiplication, and division of Integers. Here you will get NCERT Class 7 Maths chapter 1 solutions to all four exercises.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.2
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?
Answer: First, we complete the number line.
Now, the integers marked by:
B = -6
D = -4
H = 0
J = 2
M = 5
O = 7
Answer: The given number are: 7, –5, 4, 0 and – 4
Arranging them in ascending order (increasing order)
On a number line, as we move towards the right, the number increases.
Answer:
(a) 7, 3, – 1, – 5,
The pattern is :
(b) – 2, – 4, – 6, – 8,
The pattern is :
(c) 15, 10, 5, 0,
The pattern is :
(d) – 11, – 8, – 5, – 2,
The pattern is :
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.3.5
Answer:
(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.
Answer:
(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.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.4.1
1. Find:
(i) 6 × (–19)
(ii) 12 × (–32)
(iii) 7 × (–22)
Answer:
Multiplying a positive integer and a negative integer, we multiply them as whole numbers and put a minus sign (–) before the product. We thus get a negative integer
(i)
(ii)
(iii)
1. Find:
(a) 15 × (–16) (b) 21 × (–32)
(c) (– 42) × 12 (d) –55 × 15
Answer: We know, multiplication of a positive and negative integer is given by:
(a)
(b)
(c)
(d)
2. Check if (a) 25 × (–21) = (–25) × 21 (b) (–23) × 20 = 23 × (–20)
Write five more such examples.
Answer: We know, when multiplying a positive integer and a negative integer, we multiply them as whole numbers and put a minus sign (–) before the product. We thus get a negative integer.
(a)
L.H.S =
R.H.S =
Therefore, L.H.S = R.H.S
(b)
L.H.S =
R.H.S =
Therefore, L.H.S = R.H.S
Five more examples:
Q. Find: (–31) × (–100), (–25) × (–72), (–83) × (–28)
Answer: We know,
Multiplication of two negative integers :
NCERT Soltions for Class 7 Maths Chapter 1 Integers Topic 1.4.3
Answer: We know,
If the number of negative integers in a product is even, then the product is a positive integer and if the number of negative integers in a product is odd, then the product is a negative integer.
Hence, the product is positive whereas the product is negative
(ii) What will be the sign of the product if we multiply together:
(a) 8 negative integers and 3 positive integers?
(b) 5 negative integers and 4 positive integers?
(c) (–1), twelve times?
(d) (–1), 2m times, m is a natural number?
Answer: We know,
If the number of negative integers in a product is even, then the product is a positive integer and if the number of negative integers in a product is odd, then the product is a negative integer
And, any number of positive integers will always give a positive integer.
So, the sign of the product will be decided by the number of negative integers.
(a) 8 negative integers and 3 positive integers: Even number of negative integers, hence product is positive.
(b) 5 negative integers and 4 positive integers: Odd number of negative integers, hence product is negative.
(c) (–1), twelve times: Even number of negative integers, hence product is positive.
(d) (–1), 2m times, m is a natural number: Even number of negative integers, hence product is positive.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.5.6
(i) Is 10 × [(6 + (–2)] = 10 × 6 + 10 × (–2)?
Answer:
L.H.S =
R.H.S =
Therefore,L.H.S = R.H.S
Hence,
(ii) Is (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)?
Answer:
L.H.S =
R.H.S =
Therefore, L.H.S = R.H.S
Hence,
(ii) Is (–15) × [(–7) – (–1)] = (–15) × (–7) – (–15) × (–1)?
Answer:
L.H.S =
R.H.S =
Therefore, L.H.S = R.H.S
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.5.7
Q. Find (– 49) × 18; (–25) × (–31); 70 × (–19) + (–1) × 70 using distributive property.
Answer: We know,
Distributive law: for any integers a, b and c,
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.6
Find:
(a) (–100) ÷ 5 (b) (–81) ÷ 9
(c) (–75) ÷ 5 (d) (–32) ÷ 2
Answer: When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient
(a)
(b)
(c)
(d)
Find: (a) 125 ÷ (–25) (b) 80 ÷ (–5) (c) 64 ÷ (–16)
Answer: When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient.
(a)
(b)
(c)
Find: (a) (–36) ÷ (– 4) (b) (–201) ÷ (–3) (c) (–325) ÷ (–13)
Answer: When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+).
(a)
(b)
(c)
NCERT Solutions for Class 7 Maths Chapter 1 Integers Topic 1.7
Q. Is (i) 1 ÷ a = 1?
(ii) a ÷ (–1) = – a? for any integer a.
Take different values of a and check.
Answer: (i) is true only for .
(ii)
Taking,
Hence, this is true for every integer.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.1
(a) Observe this number line and write the temperature of the places marked on it.
(b) What is the temperature difference between the hottest and the coldest places among the above?
(c) What is the temperature difference between Lahulspiti and Srinagar?
(d) Can we say the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?
Answer:
(a) The temperature of the places in degree Celsius (°C) marked on it are :
Places | Temperature |
Lahaul Spiti | |
Srinagar | |
Shimla | |
Ooty | |
Bangalore |
(b) The hottest temperature is and coldest is
The temperature difference between them =
(c) The temperatures at Lahulspiti is and Srinagar is
The temperature difference between Lahulspiti and Srinagar is =
(d) The temperatures at Srinagar is and Shimla is
The temperature of Srinagar and Shimla took together =
which is less than the temperature of Shimla.
But, it is not less than the temperature at Srinagar.
Answer: Given, Jack’s scores in five successive rounds are
Therefore, his total score =
His total score at the end was
Answer: The temperature of Srinagar on Monday =
According to question,
The temperature of Tuesday =
The temperature of Srinagar on Tuesday =
Again, according to question
The temperature of Wednesday=
The temperature of Srinagar on Wednesday =
Answer: The plane is flying at the height of 5000 m above the sea level
The distance of the plane from sea level =
Also, the submarine floating 1200 m below the sea level
The distance of the submarine from sea level =
Distance between them =
Answer: Given,
The amount deposited in the bank account =
Amount withdrawn from bank account is=
Balance in account = Amount deposited in bank account + Amount withdrawn from the bank account
Therefore, the balance in Mohan’s account after the withdrawal is
Answer: We will represent the distance travelled towards west with negative integer.
Distance travelled towards east =
Distance travelled towards west =
Distance travelled from A =
As the distance is negative, so final position of Rita from A is towards the west direction.
5 | -1 | -4 |
-5 | -2 | 7 |
0 | 3 | -3 |
Answer: Taking Rows-
Taking Columns-
Taking Diagonals-
As the sum of one of the diagonals is not equal to 0, it is not a magic square.
1 | -10 | 0 |
-4 | -3 | -2 |
-6 | 4 | -7 |
Answer: Taking Rows-
Taking Columns-
Taking Diagonals-
As the sum of all the rows, columns and diagonals are equal, this is a magic square.
8. Verify for the following values of a and b.
(i)
(ii)
(iii)
(iv)
Answer:
(i)
L.H.S =
R.H.S =
L.H.S = R.H.S
Hence verified.
(ii)
L.H.S =
R.H.S =
L.H.S = R.H.S
Hence verified.
(iii)
L.H.S =
R.H.S =
L.H.S = R.H.S
Hence verified.
(iv)
L.H.S =
R.H.S =
L.H.S = R.H.S
Hence verified.
9. Use the sign of >, < or = in the box to make the statements true.
(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
Answer:
(Note: On a number line, the number on the right is greater than a number towards its left.)
(a) (– 8) + (– 4) (–8) – (– 4)
L.H.S =
R.H.S =
Clearly, (b) (– 3) + 7 – (19) 15 – 8 + (– 9)
L.H.S =
R.H.S =
Clearly,
(c) 23 – 41 + 11 23 – 41 – 11
L.H.S =
R.H.S =
Clearly,
(d) 39 + (– 24) – (15) 36 + (– 52) – (– 36)
L.H.S =
R.H.S =
Clearly,
(e) – 231 + 79 + 51 –399 + 159 + 81
L.H.S =
R.H.S =
Clearly,
He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?
Answer: Let the number of steps moved down be represented by positive integers and the number of steps moved up by negative integers.
Given,
Monkey is at the step = 1
Now,
The step after:
1 ^{ st } jump =
2 ^{ nd } jump =
3 ^{ rd } jump =
4 ^{ th } jump =
5 ^{ th } jump =
6 ^{ th } jump =
7 ^{ th } jump =
8 ^{ th } jump =
9 ^{ th } jump =
10 ^{ th } jump =
11 ^{ th } jump =
Therefore, after 11 jumps, the monkey reaches the water level which is at the ninth step.
After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down in every move. In how many jumps will he reach back the top step?
Answer: Let the number of steps moved down be represented by positive integers and the number of steps moved up by negative integers.
Given, Monkey is at the step = 9
Now,
The step after:
1 ^{ st } jump =
2 ^{ nd } jump =
3 ^{ rd } jump =
4 ^{ th } jump =
5 ^{ th } jump =
Therefore, after 5 jumps, the monkey will reach back at the top.
If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following; (a) – 3 + 2 – ... = – 8 (b) 4 – 2 + ... = 8. In (a) the sum (– 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?
Answer: If we represent the down steps by negative and up steps by positive then:
Moves in (i):
Also,
Moves in part (ii):
Therefore, the sum +8 represents going up by eight steps.
NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.2
1. Write down a pair of integers whose:
(a) sum is –7 (b) difference is –10 (c) sum is 0
Answer: A pair of integers whose:
(a) sum is –7 :
(b) difference is –10 :
(c) sum is 0 :
Answer:
(a) A pair of negative integers whose difference gives 8 :
(b) A negative integer and a positive integer whose sum is –5:
:
(c) A negative integer and a positive integer whose difference is –3:
Answer: Given,
Team A scored :
Team A's total =
Team B scored :
Team B's total =
Therefore, both the team scored same.
Yes, we can add integers in any order.
Answer:
(i) (–5) + (– 8) = (– 8) + ( )
By the commutative property
(ii) –53 + = –53
is the additive identity. The number added to gives the same number.
(iii) 17 + = 0
By additive identity property.
(iv) [13 + (– 12)] + ( ) = 13 + [(–12) + (–7)]
By associative property
(v) (– 4) + [15 + (–3)] = [– 4 + 15] +
By associative property
NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.3
1. Find each of the following products:
(a) 3 × (–1) (b) (–1) × 225
(c) (–21) × (–30) (d) (–316) × (–1)
(e) (–15) × 0 × (–18)
Answer:
(a)
(b)
(c)
Product of two negative integers is a positive integer
(d)
(e)
1. Find each of the following products:
(f) (–12) × (–11) × (10) (g) 9 × (–3) × (– 6)
(h) (–18) × (–5) × (– 4) (i) (–1) × (–2) × (–3) × 4
(j) (–3) × (–6) × (–2) × (–1)
Answer:
Product of even number of negative integers is an even integer.
(f)
(g)
(h)
(i)
(j)
2 (a). Verify the following:
18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]
Answer:
L.H.S =
R.H.S =
L.H.S = R.H.S
Hence, verified.
2 (b). Verify the following:
[(–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]
Answer:
L.H.S =
R.H.S
Therefore, L.H.S = R.H.S
Hence verified.
Answer:
(i) For any integer a, , i.e, the additive inverse of the given integer.
(ii) The integer whose product with gives the following are:
4. Starting from (–1) × 5, write various products showing some pattern to show (–1) × (–1) = 1.
Answer:
Given,
Therefore,
Answer: Using suitable properties of multiplication:
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Answer: Given,
Initial temperature =
Also, Change in temperature per hour =
Therefore,Change in temperature after 10 hours =
Hence, Final temperature =
(i) Mohan gets four correct and six incorrect answers. What is his score?
Answer: Given,
Total questions =
Marks for correct answer =
Marks for incorrect answers =
Marks for unattempted question =
According to question,
Mohan gets four correct and six incorrect answers
Total marks =
Therefore, Mohan scored 8 marks.
(ii) Reshma gets five correct answers and five incorrect answers, what is her score?
Answer: Given,
Total questions =
Marks for correct answer =
Marks for incorrect answers =
Marks for unattempted question =
According to question,
Reshma gets five correct answers and five incorrect answers
Total marks =
Therefore, Reshma scored 15 marks.
(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?
Answer: Given,
Total questions =
Marks for correct answer =
Marks for incorrect answers =
Marks for unattempted question =
According to question,
Heena gets two correct and five incorrect answers.
Therefore, number of unattempted questions =
Total marks =
Therefore, Heena scored 0 marks.
(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?
Answer: Given,
Profit earned by selling 1 bag of white cement =
Profit earned by selling 3000 bags of white cement=
Loss on 1 bag of grey cement =
Loss of 5000 bags of grey cement =
Total earnings =
This means that the company incurred a loss of
(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.
Answer: Given,
Profit earned by selling 1 bag of white cement =
Loss on 1 bag of grey cement =
Loss on 6400 bags of grey cement =
To be neither in profit nor loss, the profit from white cement must be
Number of white cement bags to be sold =
Therefore the company has to sell 4000 white cement bags.
Answer:
(a)Given,
The product is positive, therefore there should be even number of negative integers.
(b) Given,
The product is negative, therefore there should be odd number of negative integers.
(c)
The product is negative, therefore there should be odd number of negative integers.
(d)
The product is positive, therefore there should be even number of negative integers.
NCERT Soltions for Class 7 Maths Chapter 1 Integers Exercise 1.4
(h) [(–36) ÷ 12] ÷ 3 (i) [(– 6) + 5)] ÷ [(–2) + 1]
Answer: Points to keep in mind:
When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient.
When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put a minus sign (–) before the quotient.
When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put a positive sign (+).
(a)
(b)
(c)
(d)
(e)
(f )
(g)
(h)
(i)
2. Verify that for each of the following values of a , b and c .
(a) a = 12, b = – 4, c = 2 (b) a = (–10), b = 1, c = 1
Answer:
(a) a = 12, b = – 4, c = 2
L.H.S =
R.H.S =
Therefore.
Hence verified.
(b) a = (–10), b = 1, c = 1
L.H.S =
R.H.S =
Therefore.
Hence verified.
3. 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
Answer:
(a) Given,
A number divided by 1 gives the number itself.
(b)
The product is negative, therefore there must be odd number of negative integers.
(c)
A number divided by itself gives 1
(d)
The product is positive, therefore there must be even number of negative integers.
(e)
A number divided by 1 gives the number itself.
(f)
The product is negative, therefore there must be odd number of negative integers.
(g)
The product is negative, therefore there must be odd number of negative integers.
(h)
The product is negative, therefore there must be odd number of negative integers.
Answer:
Five pairs of integers such that are:
Answer: Given,
The temperature at 12 noon =
Final temperature =
The decrease in temperature =
Time taken for the temperature to decrease by =
Time taken for the temperature to decrease by =
Now,
Time until midnight =
The decrease in temperature in =
Therefore, the temperature at midnight =
Therefore, the temperature at mid-night will be below zero.
Answer: Given,
Marks for every correct answer =
Marks for every wrong answer =
(i) According to question,
Marks obtained by Radhika =
Number of correct answers =
Marks obtained for correct answers =
Marks obtained for incorrect answers = Total marks – Marks obtained for correct answers
Number of incorrect answers =
Therefore, Radhika attempted 8 questions incorrectly.
(ii)
According to question,
Marks obtained by Mohini =
Number of correct answers =
Marks obtained for correct answers =
Marks obtained for incorrect answers = Total marks – Marks obtained for correct answers
Number of incorrect answers =
Therefore, Mohini attempted 13 questions incorrectly.
Answer: Given,
Initial height =
Final depth =
Total distance the elevator has to descend = Final position - Initial position
=
Also,
Time the elevator takes to descend =
Time the elevator takes to descend =
Integers Class 7 Maths Chapter 1- Topics
- 1.1 Introduction
- 1.2 Recall
- 1.3 Properties of Addition and Subtraction of Integers
- 1.3.1 Closure under Addition
- 1.3.2 Closure under Subtraction
- 1.3.3 Commutative Property
- 1.3.4 Associative Property
- 1.3.5 Additive Identity
- 1.4 Multiplication of Integers
- 1.4.1 Multiplication of a Positive and a Negative Integers
- 1.4.2 Multiplication of two Negative Integers
- 1.4.3 Product of three or more Negative Integers
- 1.5 Properties of Multiplication of Integers
- 1.5.1 Closure under Multiplication
- 1.5.2 Commutativity of Multiplication
- 1.5.3 Multiplication by Zero
- 1.5.4 Multiplicative Identity
- 1.5.5 Associativity for Multiplication
- 1.5.6 Distributive Property
- 1.5.7 Making Multiplication Easier
- 1.6 Division of Integers
- 1.7 Properties of Division of Integers
NCERT Solutions for Class 7 Maths Chapter-Wise
Chapter No. | Chapter Name |
Chapter 1 | Integers |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | Comparing quantities |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 | Visualising Solid Shapes |
NCERT Solutions for Class 7 Subject Wise
Important Points of Class 7 Maths Chapter 1 Integers
- Integers are closed for both addition and subtraction. That is, if a and b are any integers then a + b and a – b are also integers.
- The addition is commutative for the integers, such that for all integers 'a' and 'b'.
- The addition is associative for the integers, such that, for all the integers 'a', 'b' and 'c'.
- Integer 0 is the identity under addition. That is, for every integer 'a'.
- Integers are closed under multiplication. That is, is an integer for any two integers 'a' and 'b'.
- Multiplication is commutative for the integers. That is, for any integers 'a' and 'b.'
- The integer 1 is the identity under multiplication, such that, for any integer 'a'.
- Multiplication is associative for the integers, such that, for any three integers a, b and c.
If a student is familiar with the CBSE NCERT solutions for Class 7 Maths chapter 1 Integers, then good marks in the exam is not a difficult task. Also, the NCERT solutions for Class 7 Maths chapter 1 Integers help in solving homework problems
Also Check NCERT Books and NCERT Syllabus here:
Frequently Asked Question (FAQs) - NCERT Solutions for Class 7 Maths Chapter 1 Integers
Question: How many exercise in NCERT solution Class 7 Maths Chapter Integers?
Answer:
There are 4 exercises in NCERT solution Class 7 Maths Integers
Question: Write example of integers.
Answer:
Here is an example of integers;
-4,-3,-2,-1,0,1,2,3,4
Question: What is Integers?
Answer:
An Integer is a whole number that can be positive, negative, or zero.
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