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.

Infinity Learn offers a user-friendly interface for students to access and download the PDF of NCERT Solutions for Class 7 Maths Exercise 1.4. By downloading the PDF, students can study the solutions at their own pace and refer to them anytime, even without an internet connection. This convenience allows for a more flexible and effective learning experience.

In addition to providing NCERT solutions, Infinity Learn also offers Infinity Learn, a comprehensive tutoring program designed specifically for students of class 7. Infinity learn 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

Why to Choose Infinity Learn Class 7 Maths Chapter 1 Integers Ex 1.4 Solutions

Choosing Infinity Learn for NCERT Class 7 Maths Chapter 1 Integers Exercise 1.4 solutions offers several advantages for students looking to excel in their mathematics studies:

• Expertly Crafted Solutions: Infinity Learn’s solutions are meticulously designed by experienced educators well-versed with the intricacies of the CBSE syllabus. This ensures that students receive accurate and comprehensive explanations for each problem, aiding in a deeper understanding of the concepts.
• Interactive Learning Experience: Infinity Learn provides an interactive platform that makes learning more engaging and effective. The use of visual aids, animations, and interactive exercises helps students grasp complex concepts more easily.
• Personalized Attention: With Infinity Learn, students have access to personalized tutoring options that cater to their individual learning pace and style. This personalized approach ensures that each student’s unique needs are addressed, leading to better comprehension and retention of concepts.
• Convenience and Accessibility: The solutions are available in a downloadable PDF format, allowing students to access them anytime and anywhere. This flexibility enables students to study at their own pace and convenience.
• Comprehensive Learning Resource: Infinity Learn offers a holistic learning experience by providing not just solutions but also additional resources such as sample papers, revision notes, and practice quizzes. This comprehensive approach helps students prepare thoroughly for their exams.
• Building a Strong Foundation: The focus on conceptual clarity and problem-solving skills ensures that students build a strong foundation in mathematics. This not only helps them excel in their current class but also prepares them for future academic challenges.

Choosing Infinity Learn for NCERT Class 7 Maths exercise 1.4 solutions provides students with a well-rounded and effective learning experience that enhances their understanding of mathematics and boosts their academic performance.

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?

To download NCERT Solutions from the Infinity Learn app, first, install the app from the Google Play Store or Apple App Store. Once installed, open the app and sign up or log in. Navigate to the NCERT Solutions section and select your class and subject. You'll see a list of chapters; choose the one you need solutions for, and you'll be able to view and download the solutions in PDF format. The downloaded solutions can be accessed from the Downloads section of the app or your device's file manager.