NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.4

NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4

The NCERT Solutions for Class 7 Maths Chapter 1 Integers Exercise 1.4 aligned with CBSE syllabus provides step-by-step answers and explanations for the problems related to integers. This exercise focuses on the multiplication of integers, which is an essential concept in mathematics. Students learn how to multiply positive and negative integers, understanding that the product of two positive integers or two negative integers is a positive integer, while the product of a positive integer and a negative integer is a negative integer. The NCERT solutions in this exercise are designed to help students grasp the rules of multiplication with integers, which is a foundational skill for more advanced mathematical operations.

NCERT Solutions for Class 7 Maths Chapter 1 Ex 1.4

Class 7 Maths Ex 1.4 Question 1

Evaluate each of the following.

(a) (–30) ÷ 10

(b) 50 ÷ (–5)

(c) (–36) ÷ (–9)

(d) (– 49) ÷ (49)

(e) 13 ÷ [(–2) + 1]

(f) 0 ÷ (–12)

(g) (–31) ÷ [(–30) + (–1)]

(h) [(–36) ÷ 12] ÷ 3

(i) [(– 6) + 5)] ÷ [(–2) + 1]

Sol.

(a) (–30) ÷ 10
= -30 / 10
= -3

(b) 50 ÷ (–5)
= 50 / -5
= -10

(c) (–36) ÷ (–9)
= -36 / -9
= 4

(d) (–49) ÷ (49)
= -49 / 49
= -1

(e) 13 ÷ [(–2) + 1] = 13 / (-2 + 1)
= 13 / -1
= -13

(f) 0 ÷ (–12)
= 0 / -12
= 0

(g) (–31) ÷ [(–30) + (–1)] = -31 / (-30 – 1)
= -31 / -31
= 1

(h) [(–36) ÷ 12] ÷ 3
= (-36 / 12) / 3
= -3 / 3
= -1

(i) [(–6) + 5)] ÷ [(–2) + 1] = (-6 + 5) / (-2 + 1)
= -1 / -1
= 1

Class 7 Maths Ex 1.4 Question 2

Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) 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

Sol.

(a)
Given:
a÷(b+c)+(a÷b)+(a÷c)

a=12, b=-4, c=2

Putting the given values in L.H.S. = 12÷(−4+2)

= 12 ÷ (-2) = 12 x (-1/2) = -12/2 = 6

Putting the given values in R.H. S=[12÷(−4)]+(12÷2)
=(12 x -1/4) + 6=- -3 + 6 = 3

Since,

L.H.S. ≠ R.H.S

Hence verified.

(b) Given:

a÷(b+c)+(a÷b)+(a÷c)

a=-10, b=1, c=1

Putting the given values in L.H.S. = −10÷(1+1)

=-10÷(2)=-5

Putting the given values in R.H. S=[−10÷1]+[−10÷1]

=-10-10-20

Since,

L.H.S. ≠ R.H.S

Hence verified.

Class 7 Maths Ex 1.4 Question 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

Sol.

(a) 369 ÷ 1 = 369

(b) (-75) ÷ 75 = -1

(c) (-206) ÷ (-206) = 1

(d) -87 ÷ (-1) = 87

(e)-87 ÷ 1 = -87

(f) (-48) ÷ 48 = -1

(g) 20 ÷ (-10) = -2

(h) (-12) ÷ (4) = -3

Class 7 Maths Ex 1.4 Question 4

Q 4: Write five pairs of integers (a, b) such that a ÷ b = -3. One such pair is (6, -2) because 6 + (-2) = -3.

Solution:

(a) (24, -8) because 24 ÷ (-8) = -3

(b) (-12, 4) because (-12) ÷ 4 = -3

(c) (15, -5) because 15 ÷ (-5) = -3

(d) (18, -6) because 18 ÷ (-6) = -3

(e) (60, -20) because 60 ÷ (-20) = -3

Class 7 Maths Ex 1.4 Question 5

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

Solution:

The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at midnight?
Solution:
Temperature at 12 noon was 10°C above zero i.e. +10°C

Rate of decrease in temperature per hour = 2°C

Number of hours from 12 noon to midnight = 12
∴ Change in temperature in 12 hours

= 12 × (-2°C) = -24°C

∴ Temperature at midnight
= +10°C + (-24°C) = -14°C

Hence, the required temperature at midnight =-14°C

Difference in temperature between + 10°C and -8°C

= +10°C – (-8°C) = +10°C + 8°C = 18°C

Number of hours required = 18∘C /2∘C = 9 hours

∴ Time after 9 hours from 12 noon = 9 pm.

Class 7 Maths Ex 1.4 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?

Sol.

Given that:

+3 marks are given for each correct answer. (-2) marks are given for each incorrect answer. Zero marks for not attempted questions.

(i) Marks obtained by Radhika for 12 correct answers = (+3) × 12 = 36

Marks obtained by Radhika for correct answers = 12 × 3 = 36

Total marks obtained by Radhika = 20

∴ Marks obtained by Radhika for incorrect answers = 20 – 36 = -16

Number of incorrect answers =(−16)÷(−2)=(−16)(−2)=8

Hence, the required number of incorrect answers = 8

(ii) Marks scored by Mohini = -5

Number of correct answers = 7

∴ Marks obtained by Mohini for 7 correct answers = 7 × (+3) – 21

Marks obtained for incorrect answers = -5 – 21 = (-26)

∴ Number of incorrect answers = (-26) ÷ (-2) = 13

Hence, the required number of incorrect answers – 13.

Class 7 Maths Ex 1.4 Question 7

An elevator descends into a nine 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.

Sol.

The present position of the elevator is at 10 in above the ground level.

Distance moved by the elevator below the ground level = 350 m

∴ Total distance moved by the elevator = 350 m + 10 m = 360 m

Rate of descent = 6 m/min.

Total time taken by the elevator

\(=\frac{360 \mathrm{m}}{6 \mathrm{m} / \mathrm{min}}\)

= 60 minutes = 1 hour

Hence, the required time = 1 hour.

NCERT Solutions for Class 7 Maths Chapter 1 Integers Other Exercise

• NCERT Solutions for Class 7 Maths Ex 1.1
• NCERT Solutions for Class 7 Maths Ex 1.2
• NCERT Solutions for Class 7 Maths Ex 1.3

NCERT Solutions for Class 7 Maths Chapter 1 Integers Ex 1.4 PDF Download

The NCERT Solutions for class 7 Maths chapter 1 Integers exercise 1.4 are available for PDF download on the Infinity Learn platform. These NCERT solutions provide a detailed explanation of the multiplication of integers, a key concept in the Class 7 Maths curriculum as per the CBSE Maths syllabus for class 7. Students can easily grasp the rules for multiplying positive and negative integers through these step-by-step solutions.

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In addition to providing NCERT solutions, Infinity Learn also offers Infinity Tuition, a comprehensive tutoring program designed specifically for students of class 7. Infinity Tuition focuses on building a strong foundation in various subjects, including Maths, through personalized attention and interactive learning methods.

NCERT Solutions for Class 7 Maths Other Chapters

• Chapter 2 Fractions and Decimals
• Chapter 3 Data Handling
• Chapter 4 Simple Equations
• Chapter 5 Lines and Angles
• Chapter 6 The Triangles and Its Properties
• Chapter 7 Congruence of Triangles
• Chapter 8 Comparing Quantities
• Chapter 9 Rational Numbers
• Chapter 10 Practical Geometry
• Chapter 11 Perimeter and Area
• Chapter 12 Algebraic Expressions
• Chapter 13 Exponents and Powers
• Chapter 14 Symmetry
• Chapter 15 Visualizing Solid Shapes

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FAQs on NCERT Solutions for Class 7 Maths Ex 1.4

How many questions are there in Class 7 Maths Chapter 1 Exercise 1.4 of NCERT textbook?

In Class 7 Maths Chapter 1 Exercise 1.4 of the NCERT textbook, there are 9 questions. These questions focus on the division of integers and the properties of this operation.

What does Class 7 Maths Chapter 1 deal with?

Class 7 Maths Chapter 1 deals with integers. It introduces the concept of integers, which includes positive and negative whole numbers and zero. The chapter covers the representation of integers on a number line, addition and subtraction of integers, and their properties.

What is the focus of Exercise 1.4 in Class 7 Maths Chapter 1?

Exercise 1.4 deals with the division of integers and explores the properties of this operation.

Where can I find solutions for Class 7 Maths Chapter 1 Exercise 1.4?

You can find solutions for Class 7 Maths Chapter 1 Exercise 1.4 on Infinity Learn. These solutions are available in simple PDF format for easy access and reference.

How can I download NCERT Solutions from Infinity Learn app?

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