# NCERT Solutions for Class 7 Maths Chapter 1 Integers (EX 1.1) Exercise 1.1

## NCERT Solutions for Class 7 Maths Chapter 1 Integers (EX 1.1) Exercise 1.1

### Important Points to Note before Solving Exercise 1.1

• Integers are always closed under addition. Generally, for any two integers a and b, a + b is an integer.

• Integers are always closed under subtraction. So, if a & b are two integers then a – b will also be an integer.

• The addition will be commutative for integers. Generally, for any two integers a & b, we can say that a + b = b + a.

• Subtraction can not be commutative for integers.

• Addition will be associative for integers. Generally, for any integers a, b & c, we can say that a + (b + c) = (a + b) + c

• Zero will be an additive identity for integers. Generally, for any integer a, a + 0 = a = 0 + a

• When multiplying a positive integer & a negative integer, we can multiply them as whole numbers and put a minus sign (-) before the product. We will get a negative integer. Generally, for any two positive integers a and b we can say that a × (-b) = (-a) × b = -(a × b).

• The product of two negative integers will always be a positive integer. Generally, for any two positive integers a & b, (-a) × (-b) = a × b.

• Integers will be closed under multiplication.

• Multiplication will be commutative for integers. Generally, for any two integers a & b, a × b = b × a.

• The product of zero and a negative integer is zero, i.e,  a × 0 = 0 × a=0

• 1 will be the multiplicative identity for integers. Eg, a × 1 = 1 × a = a

• Multiplication will be associative for integers, i.e,  (a × b) × c = a × (b × c)

• The distributive property of multiplication over addition will be true for integers. Generally, a × (b + c) = a × b + a × c

• The distributive property of multiplication over subtraction is also true for integers. Generally, a × (b–c) = a × b – a × c

 Chapter 1 - Integers Other Exercises in PDF Format Exercise 1.2 4 Questions & Solutions Exercise 1.3 9 Questions & Solutions Exercise 1.4 7 Questions & Solutions
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## Access NCERT Solutions for Maths Class 7 Chapter 1 – Integers

### Exercise 1.1

1. Following number line shows the temperature in degree Celsius $\left( ^{\circ }\text{C} \right)$ at different places on a particular day:

a. Observe this number line and write the temperature of the places marked on it.

Ans: First find the distance between two marks on the number line. Observe that there are a total of five partitions between every two consecutive numbers written say $0,5$. Hence, one partition will represent ${{1}^{\circ }}C$.

Therefore, the temperature of the places marked on it is:

 Place Temperature Banglore ${{22}^{\circ }}C$ Ooty ${{14}^{\circ }}C$ Shimla ${{5}^{\circ }}C$ Srinagar $-{{2}^{\circ }}C$ Lahulspiti $-{{8}^{\circ }}C$

b. What is the temperature difference between the hottest and the coldest places among the above?

Ans: From the table we can see that the temperature of the hottest place is Bangalore which is ${{22}^{\circ }}\text{C}$ and the temperature of the coldest place Lahulspiti $-{{8}^{\circ }}\text{C}$ and their difference will be

Difference = Temperature of Bangalore – Temperature of Lahulspiti

Difference $=22-\left( -8 \right)=22\text{+}8\text{=3}{{\text{0}}^{\circ }}\text{C}$.

c. What is the temperature difference between Lahulspiti and Srinagar?

Ans: From the table we can see that the temperature of the Srinagar is $-{{2}^{\circ }}\text{C}$ and the temperature of Lahulspiti is $-{{8}^{\circ }}\text{C}$ and their difference will be

Difference = Temperature of Srinagar – Temperature of Lahulspiti

Difference $=-2-\left( -8 \right)=-2+8={{6}^{\circ }}\text{C}$.

d. Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

Ans: From the table we can see that the temperature of the Srinagar is $-{{2}^{\circ }}\text{C}$ and the temperature of Shimla is ${{5}^{\circ }}\text{C}$ and their sum will be

Sum = Temperature of Shimla – Temperature of Srinagar

Sum $=5+\left( -2 \right)=5-2={{3}^{\circ }}\text{C}$.  …..(1)

Temperature of Shimla $={{5}^{\circ }}\text{C}$.  …..(2)

From (1) and (2), the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla.

Temperature of Srinagar $=-{{2}^{\circ }}\text{C}\,$.  …..(3)

From (1) and (3), the temperature of Srinagar and Shimla taken together is not less than the temperature at Srinagar.

2. In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s scores in five successive rounds were$25,-5,-10,15$ and $10$, what was his total at the end?

Ans: Jack’s scores in five successive rounds are$25,-5,-10,15\text{ and }10$. Then the total marks got by Jack will be the sum of all these marks i.e.,

$25+\left( -5 \right)+\left( -10 \right)+15+10=25-5-10+15+10$

$\Rightarrow 25-15+5+10=35$

Therefore, Jack scored $35$ marks in the quiz.

3. At Srinagar temperature was $-{{5}^{\circ }}\text{C}$ on Monday and then it dropped by ${{2}^{\circ }}\text{C}$ on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by${{4}^{\circ }}\text{C}$. What was the temperature on this day?

Ans: It is given that on Monday, temperature at Srinagar is $-{{5}^{\circ }}\text{C}$. On Tuesday, temperature dropped by ${{2}^{\circ }}\text{C}$ i.e., the temperature became $2$ less than Monday.

$\therefore$  Temperature on Tuesday$=-{{5}^{\circ }}\text{C}-{{2}^{\circ }}\text{C}=-{{7}^{\circ }}\text{C}$  ….. (1)

On Wednesday, temperature rose up by ${{4}^{\circ }}\text{C}$ i.e., the temperature became $4$ more than Tuesday. Hence from (1),

$\therefore$ Temperature on Wednesday $=-{{7}^{\circ }}\text{C}\,\text{+}\,{{\text{4}}^{\circ }}\text{C}=-{{3}^{\circ }}\text{C}$

4. A plane is flying at the height of $5000\,\text{m}$above the sea level. At a particular point, it is exactly above a submarine floating $1200\text{ m}$below the sea level. What is the vertical distance between them? Ans: Given, the height of a place above the sea level is $5000\text{ m}$ and a floating submarine is $1200\text{ m}$ below the sea level. Let us denote the distance above the sea level by $+$ sign and the distance below the sea level by  $-$ sign.

Hence, Distance of plane from sea level $=5000m$

Distance of submarine from sea level $=-1200m$

$\therefore$  The vertical distance between the plane and the submarine is $5000-\left( -1200 \right)=6200\text{ m}$.

Thus, the vertical distance between the plane and the submarine is $6200\text{ m}$.

5. Mohan deposits ₹$2,000$ in his bank account and withdraws ₹$1,642$from it, the next day. If withdrawal of an amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s accounts after the withdrawal?

Ans: Deposit and Withdrawal are opposite of each other. Therefore, if we are representing withdrawal by $-$, we should represent deposit by $+$.

Given, Deposit amount $=$ ₹$2,000$ and Withdrawal amount $=$ ₹$1,642$. In integer representation, deposit $=+2000$ and withdrawal $=-1642$.

$\therefore$  Balance$=2,000-1,642$ $=$ ₹$358$

Therefore, the balance in Mohan’s account after withdrawal is ₹$358$.

6. Rita goes $20$km towards east from a point A to the point B. From B, she moves $30$ km towards west along the same road. If the distance towards east is represented by a positive integer, then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A?

Ans: East and West are opposite of each other. Therefore, if we are representing east by $+$, we should represent west by $-$.

Let $A$ be the point of origin i.e., $A$ will lie at $0$ on the number line.

Given, Rita goes $20$ km towards east from a point $A$ to the point $B$. From $B$, she moves $30$ km towards the west along the same road.

Plotting the given information on the number line we get,

Distance from $A$ to $B$$=20\text{ km}$

Distance from $B$ to final point $=30\text{ km}$

Distance from $A$ to the final point $=20+\left( -30 \right)=-10\,\text{km}$.

Therefore, Rita is $10$ km west from her initial position $A$ and will be represented by the integer $-10$.

7. In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

i.

 5 -1 -4 -5 -2 7 0 3 -3

Ans: In a magic square each row, column and diagonal have the same sum. So let us check whether the given square is a magic square or not.

Sum of row $1$ $=5+\left( -1 \right)+\left( -4 \right)=0$  …..(1)

Sum of row $2$ $=\left( -5 \right)+\left( -2 \right)+7=-7+7=0$  …..(2)

Sum of row $3=$ $0+3+\left( -3 \right)=3-3=0$  …..(3)

Sum of column $1=$ $5+\left( -5 \right)+0=5-5=0$  …..(4)

Sum of column $2=$ $\left( -1 \right)+\left( -2 \right)+3=-3+3=0$  …..(5)

Sum of column $3=$ $\left( -4 \right)+7+\left( -3 \right)=7-7=0$  …..(6)

Sum of diagonal $1=$ $5+\left( -2 \right)+\left( -3 \right)=5-5=0$  …..(7)

Sum of diagonal $2=$ $\left( -4 \right)+\left( -2 \right)+0=-6$  …..(8)

From (1) to (8) we can conclude that this box is not a magic square because all the sums are not equal.

ii.

 1 -10 0 -4 -3 -2 -6 4 -7

Ans: In a magic square each row, column and diagonal have the same sum. So let us check whether the given square is a magic square or not.

Sum of row $1=$ $1+\left( -10 \right)+0=1-10=-9$  …..(1)

Sum of row $2=$ $\left( -4 \right)+\left( -3 \right)+\left( -2 \right)=-7-2=-9$  …..(2)

Sum of row $3=$ $\left( -6 \right)+4+\left( -7 \right)=-2-7=-9$  …..(3)

Sum of column $1=$ $1+\left( -4 \right)+\left( -6 \right)=1-10=-9$  …..(4)

Sum of column $2=$ $\left( -10 \right)+\left( -3 \right)+4=-13+4=-9$  …..(5)

Sum of column $3=$ $0+\left( -2 \right)+\left( -7 \right)=0-9=-9$  …..(6)

Sum of diagonal $1=$ $1+\left( -3 \right)+\left( -7 \right)=1-10=-9$  …..(7)

Sum of diagonal $2=$ $0+\left( -3 \right)+\left( -6 \right)=-9$  …..(8)

From (1) to (8) we can conclude that this box is a magic square because all the sums are equal.

8. Verify $a-\left( -b \right)=a+b$ for the following values of$a\,\text{and }b$:

i. Given, $a=21,b=18$

Ans: Given, $a=21,b=18$. We have to verify $a-\left( -b \right)=a+b$.

LHS $=21-\left( -18 \right)=21+18=39$  ….. (1)

RHS $=a+b=21+18=39$  ….. (2)

From (1) and (2), since LHS $=$RHS therefore, it is verified that $a-\left( -b \right)=a+b$.

ii. Given, $a=118,b=125$

Ans: Given, $a=118,b=125$. We have to verify $a-\left( -b \right)=a+b$.

LHS $=118-\left( -125 \right)=118+125=243$  ….. (1)

RHS $=118+125=243$  ….. (2)

From (1) and (2), since LHS $=$RHS therefore, it is verified that $a-\left( -b \right)=a+b$.

iii. Given, $a=75,b=84$

Ans: Given, $a=75,b=84$. We have to verify $a-\left( -b \right)=a+b$.

LHS $=75-\left( -84 \right)=75+84=159$  ….. (1)

RHS $=a+b=75+84=159$  ….. (2)

From (1) and (2), since LHS $=$RHS therefore, it is verified that $a-\left( -b \right)=a+b$.

iv. Given, $a=28,b=11$

Ans: Given, $a=28,b=11$. We have to verify $a-\left( -b \right)=a+b$.

LHS $=28-\left( -11 \right)=28+11=39$  ….. (1)

RHS $=28+11=39$  ….. (2)

From (1) and (2), since LHS $=$RHS therefore, it is verified that $a-\left( -b \right)=a+b$.

9. Use the sign of $>,<\,\,\text{or}\,=$ in the blank to make the statements true:

a. $\left( -8 \right)+\left( -4 \right)\,\_\_\left( -8 \right)-\left( -4 \right)$.

Ans: $\left( -8 \right)+\left( -4 \right)=-12$ and $\left( -8 \right)-\left( -4 \right)=-4$

$\Rightarrow \text{ }-12\,\,<\,\,-4$.

$\Rightarrow \left( -8 \right)+\left( -4 \right)\,<\,\,\left( -8 \right)-\left( -4 \right)\,$

b. $\left( -3 \right)+7-\left( 19 \right)\_\_15-8+\left( -9 \right)$

Ans: $\left( -3 \right)+7-\left( 19 \right)\,\,=-15$ and $15-8+\left( -9 \right)=-2$

$\Rightarrow -15\,\,<-2$

$\Rightarrow \left( -3 \right)+7-\left( 19 \right)\,<15-8+\left( -9 \right)$

c. $23-41+11\_\_23-41-11$

Ans: $23-41+11=-7$ and $23-41-11=-29$

$\Rightarrow -7>-29$

$\Rightarrow 23-41+11>23-41-11$

d. $39+\left( -24 \right)-\left( 15 \right)\_\_36+\left( -52 \right)-\left( -36 \right)$

Ans: $39+\left( -24 \right)-\left( 15 \right)\,=0$ and $36+\left( -52 \right)-\left( -36 \right)=20$

$\Rightarrow 0<20$

$\Rightarrow 39+\left( -24 \right)-\left( 15 \right)<36+\left( -52 \right)-\left( -36 \right)$

e. $\left( -231 \right)+79+51\_\_\left( -399 \right)+159+81$

Ans: $\left( -231 \right)+79+51=-101$ and $\left( -399 \right)+159+81=-159$

$\Rightarrow -101>-159$

$\Rightarrow \left( -231 \right)+79+51>\left( -399 \right)+159+81$

10. A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step:

i. He jumps $3$ steps down and then jumps back $2$ steps up. In how many jumps will he reach the water level?

Ans: Given that the monkey jumps $3$ steps down and jumps back $2$ steps up. We can represent the path of the monkey as:

First jump $=1+3=4$ steps

Second jump $=4-2=2$ steps

Third jump $=2+3=5$ steps

Fourth jump $=5-2=3$ steps

Fifth jump $=3+3=6$ steps

Sixth jump $=6-2=4$ steps

Seventh jump $=4+3=7$ steps

Eighth jump $=7-2=5$ steps

Ninth jump $=5+3=8$ steps

Tenth jump $=8-2=6$ steps

Eleventh jump $=6+3=9$ steps

Therefore, the monkey will reach the ninth step in $11$ jumps.

ii. 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?

Ans: Given that the monkey jumps four steps up and then jumps down $2$ steps down. We can represent the path of the monkey as:

First jump $=9-4=5$ steps

Second jump $=5+2=7$ steps

Third jump $=7-4=3$ steps

Fourth jump $=3+2=5$ steps

Fifth jump $=5-4=1$ steps

Therefore, the monkey reaches back on the first step in the fifth jump.

iii. If the number of steps moved down is represented by negative integers and the number of steps move 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?

Ans:  (a) $-3+2-3+2-3+2-3+2-3+2-3=-8$

(b)  $4-2+4-2+4=8$

Thus, sum $8$ in (b) represents going up by eight steps.

## CBSE Class 7 Maths Chapter 1 Exercise 1.1 Solutions

In class 6, students have learned about the fundamental definition and meaning of Integers and Whole Numbers. In class 7, they will learn in detail about integers, the properties of integers, and the operations of integers. Class 7 Chapter 1 covers a variety of significant topics and subtopics. Some of them have been listed below.

• Introduction to integers

• Recalling of Concepts

• Properties of Addition and Subtraction of Integers

2. Closure under Subtraction

3. Commutative Property

4. Associative Property

• Multiplication Of Integers

1. Closure under Multiplication

2. Commutativity of Multiplication

3. Multiplication By Zero

4. Associativity for Multiplication

5. Distributive Property

6. Making Multiplication Easier

• Division of Integers

• Properties of Division of Integers

Class 7 Maths Chapter 1 Exercise 1.1 PDF deals with the introduction to Integers. It lays out all the fundamental concepts about integers that are necessary for you to understand the rest of the chapter easily. It is important that you solve the Class 7 Maths Chapter 1 Integers Exercise 1.1 with full concentration in order to effectively learn the subsequent parts. NCERT Solutions for Class 7 Maths Integers Exercise 1.1 includes all possible and important question types from the Introduction to Integers part of this chapter. Class 7 Maths Exercise 1.1 questions and answers contain detailed step by step solutions that make first time learning and revision sessions simple and effective.

A subject like Maths can seem intimidating and daunting, especially in the formative years of your student life, such as Class 7 and Class 8. It is so because of the element of uncertainty and unpredictability associated with it, unlike theory subjects. Since Maths is very logic and aptitude based subject, complete conceptual clarity requires the systematic practice of the subject. Vedantu’s NCERT Solutions help you do just that.

Vedantu’s Exercise 1.1 Class 7 PDF has been drafted in a manner that makes learning about integers interesting, engaging, and fun, and successful. It includes all the requisite formulas, examples, answers, that you need to understand clearly and study efficiently.

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1. Give an overview of the chapter.

Integers are the numbers that have no fractional part or decimal. The difference between two consecutive integers is one unit. These can be negative or positive. The familiarity of an integer will help you in dealing with real-life problems. For example, calculating lengths or other dimensions, counting money, increase in price, age, etc. Without a proper understanding of integers, one cannot attain computing efficiency. Many students face difficulties in understanding the concepts of integers.

Natural Numbers: The collection of all the counting numbers is called a set of natural numbers. It is denoted by N = {1,2,3,4….}.

Whole Numbers: The total collection of natural numbers which consists of zero is known as a set of whole numbers. It is denoted by W = { 0, 1, 2, 3, 4, 5, … }.

2. Explain the properties of multiplication of integers.

Below are the properties of multiplication of integers.

Closure Under Multiplication

• For every integer a and b, a×b=Integer

Commutative Property of Multiplication

• For every integer a and b, a×b=b×a

Multiplication by Zero

• For every integer a, a×0=0×a=0

Multiplicative Identity

• For every integer a, a×1=1×a=a. Here 1 is the multiplicative identity for integers.

Associative Property of Multiplication

• For every integer a, b  and c,  (a×b)×c=a×(b×c)

Distributive Property of Integers

• Under multiplication and addition, integers determine the distributive property.

i.e., For every integer a, b  and c,  a×(b+c)=a×b+a×c

These properties make calculations easier.

Product of an even number of negative integers is positive and product of an odd number of negative integers is negative.

Addition of Integers: In this section of chapter 1 of NCERT Solutions for Class 7 Maths, you will learn about the mathematical operations of integers which are complicated and confusing as you have to be careful with ‘+’ and ‘-’ sign while calculating the answer. The rule is to add when you have two positive or negative numbers. However, in the case of the former, you will put ‘+’ sign with the final answer whereas ‘-’ sign in the latter cases.

Subtraction of Integers: In this section of NCERT Class 7 Maths Chapter 1 will teach you subtraction of integers on a number line. You will learn about the rules of subtracting negative numbers and additive inverse. Our subject experts have used easy and simple language along with the short cut techniques to teach you about integers and their calculations.

4. How will Vedantu’s NCERT solutions guide me?

Our NCERT Solutions are the perfect study material for the students of Class 7. The solutions provided by us will help them gain a better understanding of various characteristics related to Maths. All our Solutions are written in a very simple language to make better use of it.

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5. What do you mean by Integers according to Chapter 1 of Class 7 Maths NCERT?

Integers are handy while performing various arithmetic operations, like addition, subtraction, multiplication, and division. An integer can primarily be described as a number that can be written with no fractional component. For example, 8, 67, 1, and −1956 are integers, while 1.125 and √5 cannot be termed under the category of integers. Integers are a crucial component of the Number System. For more elaborate explanations, visit the Vedantu website or app. You will also find numerous study modules on Vedantu.

6. What do you mean by commutative property according to Chapter 1 of Class 7 Maths NCERT?

When two integers are added, regardless of their order, the sum stays the same since they are commutative under addition. When two integers are added together, the result is always the same. Similarly the commutative property of integer multiplication says that the outcome is unaffected by the order of the operands or the integers. As a result, integer operations such as multiplication and addition are commutative. Practice as many problems as you can to completely grasp the concept of commutative property.

7. What do you mean by associative property according to Chapter 1 of Class 7 Maths NCERT?

When three or more numbers are put together in any sequence, their total or product remains the same. This is known as the associative property of numbers in mathematics. To put it another way, no matter what sequence we put the parenthesis around the numbers, the answer will always be the same. Only addition and multiplication are associative with the associative property in arithmetic. Practice as many problems as you can to comprehend the notion of associative property thoroughly.

8. What do you mean by additive identity according to Chapter 1 of Class 7 Maths NCERT?

A real number can be added to zero or another real number, and you'll receive the same real number either way. This can be referred to as the additive identity. The zeroth digit is referred to as the additive identity since it is the identity element. Any element to which an identity element is introduced remains unaltered after the addition. It is important to understand this concept before proceeding to the exercises. Visit the Vedantu site if you require more problems with this concept.

9. How to download the Solutions for Class 7 Math Chapter 1 Exercise 1.1?

The solutions are available on the Vedantu site.

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