Contents

NCERT Solutions for Class 7 Maths Chapter 1 Integers are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 1 Integers.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 7 |

Subject |
Maths |

Chapter |
Chapter 1 |

Chapter Name |
Integers |

Exercise |
Ex 1.1, Ex 1.2, Ex 1.3, Ex 1.4 |

Number of Questions Solved |
30 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 7 Maths Chapter 1 Integers

### Chapter 1 Integers Exercise 1.1

**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)** From the given number line, we find that the temperature of the indicated places as under :

**(b)** The hottest place is Bangalore (22 °C) and the coldest place is Lahulspiti (-8°C). The temperature difference between the hottest and the coldest places

= 22 °C – (-8 °C)

= 22 °C +8 °C = 30 °C

**(c)** The temperature difference between Lahulspiti and Srinagar

= -2 °C – (-8 °C)

= -2 °C +8 °C = 6 °C

**(d)** Yes, we can say that the temperature of Srinagar and Shimla taken together is less than the temperature at Shimla as -2 + 5 = 3 and 3 < 5. This temperature is not less than the temperature at Srinagar.

**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?

**Solution.**

Jack’s scores in five successive rounds were given as 25, -5, -10, 15 and 10.

Jack’s total score

=25 +(-5)+ (-10)+ 15+ 10

= 25-5-10+15 + 10 = 50-15 = 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?

**Solution.**

At Srinagar, temperature was on Monday = -5 °C

Since, the temperature was dropped by 2 °C on Tuesday, therefore, temperature was on Tuesday = (-5-2) °C = -7°C

Also, on Wednesday the temperature rose by 4 °C.

∴ Temperature on Wednesday= (-7 + 4) °C = -3 °C

**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?

**Solution.**

Vertical distance between the plane and the submarine

= 5000 m + 1200 m = 6200 m

**Question 5.**

Mohan deposits ₹ 2,000 in his bank account and withdraws ₹ 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.

**Solution.**

Amount deposited will be represented by a positive integer.

Balance in Mohan’s account after withdrawal

= (+ ₹ 2000) + (- ₹ 1642)

= ₹ (2000-1642)

= ₹ 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?

**Solution.**

The distance towards west will be represented by a negative integer.

Rita’s movement is shown as under :

Since, Rita moves 20 km towards east from a point A, so she reaches B and then from B she moves 30 km towards west along the same road and reaches C.

Thus, her final position from A will be represented by the integer -10.

**Question 7.**

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

**Solution.**

In square (i) :

**Row 1 :** 5 + (-1) + (-4) = 5-1-4 =0

**Row 2 :** (-5) + (-2) + 7 =-5-2 + 7 = 0

**Row 3 :** 0 + 3 + (-3) =0+3-3 =0

**Column 1 :** 5 + (-5) + 0= 5- 5 + 0= 0

**Column 2 :** (-1) + (-2) + 3 = -1 -2 + 3 = 0

**Column 3 :** (-4) + 7 + (-3) = -4 + 7- 3 = 0

**Diagonal 1 :** 5 + (-2) + (-3) = 5 – 2 – 3 =0

**Diagonal 2 :** (-4) + (-2) + 0 = -4 – 2 + 0 = -6

∵ The sum of digits along the diagonal 2 ≠ 0.

Thus, it is not a magic square.

In square (ii) :

**Row 1 :** 1 + (-10) + 0 = 1-10+0 = -9

**Row 2 :** (-4) +(-3) +(-2) = -4-3-2 = -9

**Row 3 :** (-6) + 4 + (-7) = -6 + 4 – 7 = -9

**Column 1 :** 1 + (-4) + (-6) = 1- 4- 6 = -9

**Column 2 :** (-10) + (-3) + 4 = -10-3 + 4 = -9

**Column 3 :** 0 + (-2) + (-7) = 0-2-7 =-9

**Diagonal 1 :** 1 + (-3) + (-7) = -9

**Diagonal 2:** 0 + (-3) + (-6) = 0- 3- 6 = -9

∵ Each row, column and diagonal have the same sum.

Thus, it is a magic square.

**Question 8.**

Verify a – (-b) = a + b for the following values of a and b:

- a = 21, b = 18
- a = 118, b = 125
- a = 75, b = 84
- a = 28, b = 11

**Solution.**

- L.H.S. = a – (-b) = 21 – (-18) = 21 +18 = 39

R.H.S. = a + b = 21 +18 =39

∴ L.H.S. = R.H.S. - L.H.S. = a – (-b) = 118 – (-125) = 118 +125 = 243

R.H.S. = a + b = 118+125 = 243

∴ L.H.S. = R.H.S. - L.H.S. = a – (-b) = 75 – (-84) = 75+ 84 = 159

R.H.S. = a + b =75 + 84 = 159 - L.H.S. = a – (-b) = 28 – (-11) = 28+ 11 = 39

R.H.S. = a + b = 28 + 11 = 39

**Question 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

**Solution.**

**Question 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?

**(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?

**(iii)** 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?

**Solution.**

**(i)** While going down the monkey jumps 3 steps down and then jumps back 2 steps up. To reach the water level he is to jump as under:

-3+ 2 -3 + 2 – 3 +2 – 3 + 2 – 3 + 2 – 3 = -8 Hence, he takes 11 jumps to reach the water level.

**(ii)** After drinking water, he jumps back as under to reach the top step as under : 4 – 2+ 4 – 2+ 4 = 8

Hence, he takes 5 jumps to reach back the top.

**(iii)** **(a)** – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 = -8

**(b)** 4 – 2 + 4 – 2 + 4 = 8

In **(b)** the sum 8 represents going up 8 steps.

### Chapter 1 Integers Exercise 1.2

**Question 1.**

Write down a pair of integers whose:

**(a)** sum is -7

**(b)** difference is -10

**(c)** sum is 0

**Solution.**

**(a)** A pair of integers whose sum is -7 can be (-1) and (-6).

∵ (-1) + (-6) = -7

**(b)** A pair of integers whose difference is -10 can be (-11) and (-1)

∵ -11 – (-1) = -11+1 = -10

**(c)** A pair of integers whose sum is 0 can be 1 and (-1).

∵ (-1) + (1) = 0.

**Question 2.**

**(a)** Write a pair of negative integers whose difference gives 8.

**(b)** Write a negative integer and a positive integer whose sum is -5.

**(c)** Write a negative integer and a positive integer whose difference is -3.

**Solution.**

**(a)** A pair of negative integers whose difference gives 8 can be -12 and -20.

∵ (-12) – (-20) = -12+20 =8 .

**(b)** A negative integer and a positive integer whose sum is -5 can be -13 and 8.

∵ (-13) + 8 = -13 +8 = -5

**(c)** A negative integer and a positive integer whose difference is -3 can be -1 and 2.

∵ (-1) – 2 = – 1 -2 = -3

**Question 3.**

In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, -40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?

**Solution.**

Total scores of team A = (-40) + 10 +0

= -40 + 10 + 0 = -30

and, total scores of team B = 10 + 0 + (-40)

= 10 + 0 – 40 = -30

Since, the total scores of each team are equal.

∴ No team scored more than the other but each have equal score.

Yes, integers can be added in any order and the result remains unaltered. For example, 10 +0 +(-40) = -30 = -40 +0 +10

**Question 4.**

Fill in the blanks to make the following statements true:

**(i)** (-5) + (-8) = (-8) + (………)

**(ii)** -53 + ……. = -53

**(iii)** 17+ …… = 0

**(iv)** [13 + (-12)] + (……) = 13 + [(-12) + (-7)]

**(v)** (-4) + [15 + (-3)] = [-4 + 15] + ……

**Solution.**

**(i)** (-5) + (-8) = (-8) + (-5)

**(ii)** -53 + 0 = -53

**(iii)** 17 + (-17) = 0

**(iv)** [13 + (-12)] + (-7) = (13) + [(-12) + (-7)]

**(v)** (-4) + [15 + (-3)] = [(-4) + 15] + (-3)

### Chapter 1 Integers Exercise 1.3

**Question 1.**

Find each of the following products :

**(a)** 3 x (-1)

**(b) **(-1) x 225**
(c)** (-21) x (-30)

**(d)**(-316)

**x (-1)**

**(e)**(-15) x O x (-18)

**(f)**(-12) x (-11) x (10)

**(g)**9 x (-3) x (-6)

**(h)**(-18) x (-5) x (-4)

**(i)**(-1) x (-2) x (-3) x 4 Sol. (a) 3 x (-1) = – (3 x 1) = -3

**(j)**(-3) x (-6) x (-2) x (-1)

**Solution.**

**(a)**3 x (-1) = – (3 x 1) = -3

**(b)**(-1) x 225 = – (1 x 225) = -225

**(c)**(-21) x (-30) = 21 x 30 =630

**(d)**(-316) x (-1) = 316 x 1 = 316

**(e)**(-15) x 0 x (-18) = [(-15) x 0] x (-18) = 0 x (-18) = 0

**(f)**(-12) x (-11) x (10) = [(-12) x (-11)] x (10)

= (132) x (10) =1320

**(g)**9 x (-3) x (-6) = [9 x (-3)] x (-6) = (-27) x (-6) = 162

**(h)**(-18) x (-5) x (-4) = [(-18) x (-5)] x (-4)

= 90 x (-4) – -360

**(i)**(-1) x (-2) x (-3) x 4 = [(-1) x (-2)] x [(-3) x 4]

= (2)x (-12) = -24

**(j)**(-3) x (-6) x (-2) x (-1) = [(-3) x (-6)] x [(-2) x (-1)] = (18) x (2) = 36

**Question 2.**

Verify the following:

**(a)** 18 x [7 + (-3)] = [18 x 7] + [18 x (-3)]

**(b)** (-21) x [(-4) + (-6)] = [(-21) x (-4)] + [(-21) x (-6)]

**Solution.**

**(a)** We have,

18 x [7 + (-3)] = 18 x 4 = 72

and, [18 x 7] + [18 x (-3)] = 126 – 54 =72

18 x [7 + (-3)] = [18 x 7] + [18 x (-3)]

**(b)** We have,

(-21) x [(-4) + (-6)] = (-21) x (-4 -6)

= (-21)(-10) = 210 and, [(-21) x (-4) + [(-21) x (-6)]

= 84+126 =210

∴ (-21) x [(-4) + (-6)] = [(-21) x (-4)] + [(-21) x (-6)]

**Question 3.**

**(i)** For any integer a, what is (-1) x a equal to?

**(ii)** Determine the integer whose product with (-1) is

**(a)** -22

**(b)** 37

**(c)** 0

**Solution.**

**(i)** For any integer a, (-1) x a = -a.

**(ii) **We know that the product of any integer and (-1) is the additive inverse of integer.

The integer whose product with (-1) is

**(a)** additive inverse of -22, t. e., 22.

**(b)** additive inverse of 37, i.e., -37.

**(c)** additive inverse of 0, i.e., 0.

**Question 4.
**Starting from (-1) x 5, write various products showing some pattern to show (-1) x (-1) = 1.

**Solution.**

(-1) x 5 = -5

(-1) x 4 = -4 = [-5 – (-1)] = -5 +1

(-1) x 3 = -3 = [-4 – (-1)] = -4 +1

(-1) x 2 = -2 = [-3 – (-1)] = -3 +1

(-1) x 1 = -1 = [-2 – (-1)] = -2 +1

(-1) x 0 = 0 = [-1 – (-1)] = -1 +1

(-1) x (-1) =[0 – (-1)] = 0 + 1 = 1

**Question 5.
**Find the product, using suitable properties :

**(a)**26 x (-48) + (-48) x (-36)

**(b)**8 x 53 x (-125)

**(c)**15 x (-25) x (-4) x (-10)

**(d)**(-41) x 102

**(e)**625 x (-35) +(-625) x 65

**(f)**7 x (50-2)

**(g)**(-17) x (-29)

**(h)**(-57) x (-19) + 57

**Solution.**

**(a)**We have, 26 x (-48) + (-48) x (-36)

= (-48) x 26 + (-48) x (-36)

= (-48) x [26 + (-36)]

= (-48) x (26 – 36)

=(-48) x (-10)= 480

**(b)**We have,

8 x 53 x (-125) = [8 x (-125)] x 53

= (-1000) x 53 = -53000

**(c)**We have,

15 x (-25) x (-4) x (-10)

=15 x [(-25) x (-4)] x (-10)

= 15 x (100) x (-10)

= (15 x 100) x (-10)

= 1500 x (-10) = -15000

**(d)**We have,

(-41) x 102 = (-41) x (100 +2)

= (-41) x 100 + (-41) x 2 = -4100 – 82 = -4182

**(e)**We have, 625 x (-35) + (-625) x 65

= 625 x (-35) + (625) x (-65)

= 625 x [(-35)+ (-65)]

= 625 x (-100) = -62500

**(f)**7 x (50-2) = 7 x 50 – 7 x 2

= 350 -14 =336

**(g)**(-17) x (-29) = (-17) x [(-30) + 1]

= (-17) x (-30) + (-17) x 1 = 510 – 17 = 493

**(h)**(-57) x (-19)+ 57 =57 x 19 + 57 x 1

= 57 x (19 +1)

= 57 x 20 = 1140

**Question 6.**

A certain freezing process requires that room temperature be lowered from 40 °C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

**Solution.**

Initial room temperature = 40 X

Temperature lowered every hour = (-5) °C

Temperature lowered in 10 hours = (-5) x 10 °C = -50 °C

∴ Room temperature after 10 hours = 40 X – 50 X = -10 °C

**Question 7.**

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect, answer and 0 for questions not attempted.

**(i)** Mohan gets four correct and six incorrect answers. What is his score?

**(ii)** Reshma gets five correct answers and five incorrect answers, what is her score?

**(iii)** Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

**Solution.**

**(i)** Marks awarded for one correct answer = 5

Marks scored for 4 correct answer = 5 x 4 = 20

Marks awarded for one incorrect answer = (-2)

Marks scored for 6 incorrect answer = (-2) x 6 = -12

Hence, Mohan’s score = 20 – 12 = 8 marks.

**(ii)** Reshma’s score for 5 correct answers = 5 x 5 = 25 marks

Reshma’s score for 5 incorrect answers = (-2) x 5 = -10 marks

Hence, Reshma’s score = 25-10 =15 marks

**(iii)** Heena’s score for 2 correct and 5 incorrect answers

= (5 x 2) + {(-2) x 5}

= 10+ (-10) = 10 – 10 =0.

**Question 8.**

A cement company earns a profit of ? 8 per bag of white cement sold and a loss of ? 5 per bag of grey cement sold.

**(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?

**(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?

**Solution.**

Profit on sale of 1 bag of white cement = ₹ 8

Loss on sale of 1 bag of grey cement = – ₹ 5

**(a)** Profit on sale of 3000 bags of white cement

= ₹ (3000 x 8)

= ₹ 24,000

Loss on sale of 5000 bags of grey cement = ₹ (5000 x -5)

= – ₹ 25,000

Difference between the two = ₹ 24,000 – ₹ 25,000 = – ₹ 1,000

Hence, there is a loss of ₹ 1000.

**(b)** Loss on the sale of 6400 bags of grey cement = ₹ (6400 x 5) = ₹ 32,000

In order to have neither profit nor loss, the profit on the sale of white cement should be ? 32,000.

Number of white cement bags sold

Hence, 4000 bags of white cement should be sold to have neither profit nor loss.

Replace the blank with an integer to make it a true statement.

**(a)** (-3) x = 27

**(b)** 5 x = -35

**(c)** 7 x (-8) = -56

**(d)** (-11) x (-12) = 132

**Solution.**

**(a)** (-3) x (-9) = 27

**(b)** 5 x (-7) = (-35)

**(c)** 7 x (-8) = (-56)

**(d)** (-11) x (-12) =132

### Chapter 1 Integers Exercise 1.4

**Question 1.**

Evaluate each of the following:

**Solution.**

**Question 2.**

values of a, b and c.

**(a)** a = 12, b = -4, c = 2

**(b)** a = (-10), b = 1, c = 1

**Solution.**

**Question 3.**

Fill in the blanks :

**Solution.**

**Question 4.**

Write five pairs of integers (a, b) such that = -3. One such pair is (6, – 2) because .

**Solution.**

Five pairs of integers (a, b) such that a + b = -3 are : (-6,2), (-9, 3), (12,-4), (21,-7), (-24, 8)

Note : We may write many such pairs of integers.

**Question 5.**

The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2 °C per hour until mid-night, at what time would the temperature be 8 °C below zero? What would be the temperature at mid-night?

**Solution.**

Difference in temperatures +10 °C and -8

= [10 – (-8)] °C = (10 + 8)° C = 18 °C

Decrease in temperature in one hour = 2°C

Number of hours taken to have temperature 8 °C below zero

So, at 9 P.M., the temperature will be 8 °C below zero

Temperature at mid-night = 10 °C – (2 x 12) °C

= 10°C – 24 °C = -14 °C

**Question 6.**

In a class test (+ 3) marks are given for every correct answer and (- 2) marks are given for every incorrect answer and no marks for not attempting any question, (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores – 5 marks in this test though she has got 7 correct, answers. How many questions has she attempted incorrectly?

**Solution.**

**(i)** Marks given for 12 correct answers at the rate of + 3 marks for each answer = 3 x 12 = 36 Radhika’s score = 20 marks

∴ Marks deducted her for incorrect answers = 20 – 36 = -16

Marks given for one incorrect answer = -2

Number of incorrect answers

**(ii)** Marks given for 7 correct answers at the rate of + 3 marks for each answer = 3 x 7 = 21 Mohini’s score = -5

∴ Marks deducted for incorrect answers

= – 5 – 21 = -26

Marks given for one incorrect answer = -2

∴ Number of incorrect answers

**Question 7.**

An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m.

**Answer.**

Difference in heights at two positions = 10 m – (- 350 m) = 360 m

Rate of descent = 6 m/minute

∴ Time taken minutes

= 60 minutes = 1 hour

Hence, the elevator will take 1 hour to reach – 350 m.

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