NCERT Solutions for Class 7 Maths Chapter 1: Integers - Exercise 1.1

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:

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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:

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, 

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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.

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. 

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:

(Image will be uploaded soon)

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:

(Image will be uploaded soon)

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

1. Closure under Addition

2. Closure under Subtraction

3. Commutative Property

4. Associative Property

5. Additive 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. 

NCERT Solutions for Class 7 Maths Integers Exercise 1.1 includes all solved examples, solutions to all practice exercises, and an ample amount of problem sums to practice. This helps you clear all your doubts and solve sums from this chapter confidently. CBSE Class 7 Maths Chapter 1 Exercise 1.1 Solutions will not only help you get a good grip on the chapter Integers but also help you master the concepts and perform better in your exams. Learning exercise 1.1 class 7 will help you build a solid conceptual foundation. This will help you solve complex problems all throughout your student life.

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