NCERT Solutions for Class 7 Maths Chapter 1 Integers

NCERT Solutions for Class 7 Maths Chapter 1 Integers: Students who are studying in class 7 must go through Integers Class 7 Maths Chapter 1 solutions to understand the topic more deeply. Integers Class 7 Maths Chapter 1 solutions include concepts such as the Introduction of Integers, Properties of Addition and Subtraction of Integers, Multiplication of Integers, Multiplication of Positive and Negative Integers, Division of Integers, Multiplication of Two Negative Integers, etc. The subject matter expert of Physics Wallah developed Integers Class 7 Maths Chapter 1 solutions for the students who are preparing to appear in the CBSE board examination. Students can check those Integers Class 7 Maths Chapter 1 solutions in this article below.

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Class 7 Maths Chapter 1 Integers Solutions

Students prepping for CBSE class 7 exam must go through Class 7 Maths Chapter 1 Integers Solutions below

Question 1:

Following number line shows the temperature in degree celsius (°C) at different places on a particular day.

(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 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) By observing the given data, the temperatures of these cities are as follows.

Lahulspiti : −8°C

Srinagar : −2°C

Shimla : 5°C

Ooty : 14°C

Bangalore : 22°C

(b) Temperature at the hottest place, i.e., Bangalore = 22°C

Temperature at the coldest place, i.e., Lahulspiti = −8°C

Temperature difference = 22°C − (−8°C)

= 30°C

Therefore, the temperature difference between the hottest and the coldest places is 30ºC.

(c) Temperature at Lahulspiti = −8°C

Temperature at Srinagar = −2°C

Temperature difference = −2°C − (−8°C)

= 6°C

Therefore, the temperature difference between Lahulspiti and Srinagar is 6ºC.

(d) Temperature at Srinagar = −2°C

Temperature at Shimla = 5°C

Temperature of Srinagar and Shimla taken together = −2°C + 5°C

= 3°C

3°C <  5°C

3°C <  Temperature of Shimla Yes, the temperature of Srinagar and Shimla taken together is less than the temperature of Shimla. However, 3°C < −2°C

Hence, the temperature of Srinagar and Shimla taken together is not less than the temperature of Srinagar.

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Question 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?

Answer: Jack’s scores in five successive rounds are 25, −5, −10, 15, and 10. Total score of Jack at the end will be the sum of these scores.

Therefore, Jack’s total score at the end = 25 − 5 − 10 + 15 + 10 = 35

Question 3: At Srinagar temperature was − 5°C on Monday and then it dropped by 2°C on Tuesday.

What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

Answer: Temperature on Monday = −5°C

Temperature on Tuesday = Temperature on Monday −2°C

= −5°C − 2°C = −7°C

Temperature on Wednesday = Temperature on Tuesday + 4°C

= −7°C + 4°C = −3°C

Therefore, the temperature on Tuesday and Wednesday was −7ºC and −3ºC respectively.

Question 4: 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?

Answer: Height of plane = 5000 m

Depth of submarine = −1200 m

Distance between plane and submarine = 5000 m − (−1200) m

= 5000 m + 1200 m = 6200 m

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

Answer: Since the amount withdrawn is represented by a negative integer, the amount deposited will be represented by a positive integer.

Amount deposited = Rs 2000

Amount withdrawn = −Rs 1642

Balance in Mohan’s account = Money deposited + Money withdrawn

= 2000 + (−1642) = 2000 − 1642 = 358

Therefore, balance in Mohan’s account after withdrawal is Rs 358.

Question 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?

Answer: Since the distance towards east is represented by a positive integer, the distance travelled towards west will be represented by a negative integer.

Distance travelled in east direction = 20 km

Distance travelled in west direction = −30 km

Distance travelled from A = 20 + (−30) = −10 km

Therefore, we will represent the distance travelled by Rita from point A by a negative integer, i.e., −10 km (i.e., Rita is now in west direction).

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

Answer: It can be observed that in square (i), every row and column add up to give 0. However, the sum of one of its diagonals is not 0.

As − 4 − 2 = −6 ≠ 0,

Therefore, (i) is not a magic square.

Similarly, in square (ii), each row, column, and diagonal add up to give −9. Therefore,

(ii) is a magic square.

Question 8: Verify a − (−b) = a + b for the following values of a and b.

(i) a = 21, b = 18

(ii) a = 118, b = 125

(iii) a = 75, b = 84

(iv) a = 28, b = 11

Answer:

(i) a = 21, b = 18

a − (−b) = 21 − (−18) = 21 + 18 = 39

a + b = 21 + 18 = 39

∴a − (−b) = a + b = 39

(ii) a = 118, b = 125

a − (−b) = 118 − (−125) = 118 + 125 = 243

a + b = 118 + 125 = 243

∴a − (−b) = a + b = 243

(iii) a = 75, b = 84

a − (−b) = 75 − (−84) = 75 + 84 = 159

a + b = 75 + 84 = 159

∴ a − (−b) = a + b = 159

(iv) a = 28, b = 11

a − (−b) = 28 − (−11) = 28 + 11 = 39

a + b = 28 + 11 = 39

∴ a − (−b) = a + b = 39

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Question 9:  Use the sign of >, < or = in the box to make the statements true:

(a) (-8) + (-4) ….. (-8) - (-4)

Solution: We have,

(-8) + (-4)

= -8 – 4

= - 12

Also,

(-8) – (-4)

= - 8 + 4

= - 4

Hence,

-12 < - 4

(-8) + (-4) < (-8) - (-4)

(b) (-3) + 7 – (19) ….. 15 – 8 + (-9)

Solution: We have,

(-3) + 7 – (19)

= - 3 + 7 – 19

= - 22 + 7

= - 15

Also,

15 – 8 + (-9)

= 15 – 8 – 9

= - 2

Hence,

- 15 < - 2

(-3) + 7 – (19) < 15 – 8 + (-9)

(c) 23 – 41 + 11 ….. 23 – 41 – 11

Solution: We have,

23 - 41 + 11

= - 7

Also,

23 – 41 – 11

= 23 – 52

= - 29

Hence,

- 7 > - 29

23 – 41 + 11 > 23 – 41 – 11

(d) 39 + (-24) – (15) ….. 36 + (-52) – (-36)

Solution: We have,

39 + (-24) – (15)

= 39 – 24 - 15

= 39 – 39

= 0

Also,

36 + (-52) – (- 36)

= 36 – 52 + 36

= 72 – 52

= 20

Hence,

0 < 20

39 + (-24) – (15) < 36 + (-52) – (-36)

(e) – 231 + 79 + 51 ….. – 399 + 159 + 81

Solution: We have,

- 231 + 79 + 51

= - 231 + 130

= - 101

Also,

- 399 + 159 + 81

= - 399 + 240

= - 159

Hence,

- 101 > - 159

– 231 + 79 + 51 >

Integers Class 7 Maths Chapter 1 Solutions Summary

In Class 7 Maths, Chapter 1 focuses on Integers. Integers are a set of numbers that include all positive whole numbers, negative whole numbers, and zero. They are used to represent quantities that can be both above and below zero.

1. Understanding Integers:

• Positive integers are numbers greater than zero, like 1, 2, and 3.

• Negative integers are numbers less than zero, such as -1, -2, and -3.

• Zero is neither positive nor negative but is an integer itself.

2. Number Line: A number line is a useful tool to visualize integers. It is a straight line with zero in the middle, positive integers on the right, and negative integers on the left. This helps in understanding the order and distance between integers.

3. Addition and Subtraction of Integers:

• To add integers, if both numbers have the same sign, add their absolute values and keep the common sign. If they have different signs, subtract the smaller absolute value from the larger one and use the sign of the number with the larger absolute value.

• To subtract integers, add the opposite of the number being subtracted. For example, subtracting -3 is the same as adding +3.

4. Multiplication and Division of Integers:

• When multiplying or dividing integers, if both integers have the same sign, the result is positive. If they have different signs, the result is negative.

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Class 7 Maths Chapter 1 Integers Solutions FAQs

Q1. What is the integer?
Ans. An integer is any number including 0, positive numbers, and negative numbers. For example, 1, 2, 4, 10, -15, -52, -896, etc are Integer numbers. 

Q2. What is the first chapter of maths in class 7th?

Ans. The first chapter of Maths in class 7th is Integers. There are three exercises included in NCERT class 7 chapter 1.

Q3. What is the formula of integers Class 7?

Ans. There are both positive and negative numbers included in Integers.  If a positive and a negative integer are multiplied the result is a negative integer, whereas the multiplication of two negative integers results in a positive integer. There is a commutative property followed by the Integers i.e., a × b = b × a.

Q4. Which is the hardest chapter in Maths?  

Ans. Quadratic Equations is the hardest chapter in Mathematics. 

Q5. Is 0 an integer?

Ans. Yes, 0 is an Integer as Zero, known as a neutral integer because it is neither negative nor positive, is a whole number.