In Class 7, students are introduced to a new and essential concept in mathematics – Integers. Chapter 1 of RD Sharma’s Class 7 Maths focuses on helping students understand integers, their properties, and their role in various mathematical operations. Integers include all the whole numbers, both positive and negative, as well as zero. For example, -3, -2, -1, 0, 1, 2, 3, and so on are integers. Integers are used to represent situations where both positive and negative values are involved, such as in temperature changes, bank balances, and even elevations above or below sea level.
The concept of integers goes beyond simple counting numbers. It expands our understanding to include numbers that represent opposite values. For instance, if a person is 5 meters above sea level, this can be represented by +5. On the other hand, if they are 5 meters below sea level, it is represented by -5. Integers are thus important for solving real-life problems that involve changes in conditions, direction, or magnitude. This chapter helps students explore integers through various examples, real-world applications, and exercises. It introduces students to the basic operations of addition, subtraction, multiplication, and division of integers. It emphasizes how to handle operations with both positive and negative numbers, such as adding and subtracting positive and negative integers. These operations follow specific rules that are essential to learn as they form the foundation for higher-level math concepts. The chapter also covers the representation of integers on a number line, which helps students visualize how integers are placed relative to one another. Understanding the position of integers on the number line makes it easier to compare, add, or subtract them.
Also Check: RD Sharma Solutions for Class 7 Maths
With RD Sharma’s Class 7 Maths Solutions, students can solve a variety of problems and practice different concepts from this chapter. The solutions provided are step-by-step, which help students grasp the methods behind solving each problem, ensuring they build a strong foundation in understanding integers. Mastery of this chapter is crucial as it lays the groundwork for more complex topics in higher classes. In summary, Chapter 1 of RD Sharma Class 7 Maths gives a solid introduction to integers, covering both theoretical concepts and practical applications. Understanding these concepts will help students confidently work with numbers in everyday situations.
Download Class 7 RD Sharma Solutions for Chapter 1 Integers
Download the Class 7 RD Sharma Solutions for Chapter 1 – Integers to master the essential concepts of integers with ease. These solutions are designed to help students understand the fundamental operations involving integers, such as addition, subtraction, multiplication, and division. With detailed step-by-step explanations, the solutions simplify complex problems, making it easier for students to grasp each concept. Whether you're preparing for exams or looking to strengthen your foundation in mathematics, these solutions will provide the necessary guidance and practice to build confidence. Download now and enhance your understanding of integers with RD Sharma's expert solutions!
Access Answers to RD Sharma Solutions for Class 7 Maths Chapter 1 Integers
Q1. Find the product of the following:
(i) 12 × 7
(ii) (-15) × 8
(iii) (-25) × (-9)
(iv) 125 × (-8)
Solution:
(i) Given 12 × 7
We need to find the product of these two numbers.
12 × 7 = 84
This is because multiplying two numbers with the same sign gives the product of their absolute values.
(ii) Given (-15) × 8
We need to find the product of these two numbers.
(-15) × 8 = -120
When multiplying a negative and a positive number, the product is negative, and we take the absolute values of the numbers.
(iii) Given (-25) × (-9)
We need to find the product of these two numbers.
(-25) × (-9) = + (25 × 9) = +225
When multiplying two negative numbers, the product is positive, and we multiply their absolute values.
(iv) Given 125 × (-8)
We need to find the product of these two numbers.
125 × (-8) = -1000
When multiplying a positive number by a negative number, the product is negative.
Q2. Find the product of the following:
(i) 3 × (-8) × 5
(ii) 9 × (-3) × (-6)
(iii) (-2) × 36 × (-5)
(iv) (-2) × (-4) × (-6) × (-8)
Solution:
(i) Given 3 × (-8) × 5
We calculate step-by-step:
3 × (-8) × 5 = 3 × (-8 × 5)
= 3 × -40 = -120
Multiplying a positive number with a negative number gives a negative result.
(ii) Given 9 × (-3) × (-6)
We calculate step-by-step:
9 × (-3) × (-6) = 9 × (+18) = +162
Multiplying two negative numbers gives a positive result.
(iii) Given (-2) × 36 × (-5)
We calculate step-by-step:
(-2) × 36 × (-5) = (-2 × 36) × (-5)
= -72 × -5 = +360
Multiplying two negative numbers results in a positive product.
(iv) Given (-2) × (-4) × (-6) × (-8)
We calculate step-by-step:
(-2) × (-4) × (-6) × (-8) = (-2 × -4) × (-6 × -8)
= +8 × +48 = +384
Multiplying two negative numbers results in a positive product.
Q3. Find the value of:
(i) 1487 × 327 + (-487) × 327
(ii) 28945 × 99 – (-28945)
Solution:
(i) Given 1487 × 327 + (-487) × 327
By using integer multiplication rules:
1487 × 327 + (-487) × 327 = 486249 – 159249
= 327000
(ii) Given 28945 × 99 – (-28945)
By using integer multiplication rules:
28945 × 99 – (-28945) = 2865555 + 28945
= 2894500
Q4. Find the integer whose product with ‘-1’ is:
(i) 58
(ii) 0
(iii) -225
Solution:
(i) Given 58
To find the integer that gives 58 when multiplied by -1:
58 × (-1) = -58
(ii) Given 0
To find the integer that gives 0 when multiplied by -1:
0 × (-1) = 0
(iii) Given -225
To find the integer that gives -225 when multiplied by -1:
-225 × (-1) = 225
Q5. Divide:
(i) 102 by 17
(ii) -85 by 5
(iii) -161 by -23
(iv) 76 by -19
(v) 17654 by -17654
(vi) (-729) by (-27)
(vii) 21590 by -10
(viii) 0 by -135
Solution:
(i) Given 102 ÷ 17
102 ÷ 17 = 6
(ii) Given -85 ÷ 5
-85 ÷ 5 = -17
(iii) Given -161 ÷ -23
-161 ÷ -23 = 7
(iv) Given 76 ÷ -19
76 ÷ -19 = -4
(v) Given 17654 ÷ -17654
17654 ÷ -17654 = -1
(vi) Given (-729) ÷ (-27)
(-729) ÷ (-27) = 27
(vii) Given 21590 ÷ -10
21590 ÷ -10 = -2159
(viii) Given 0 ÷ -135
0 ÷ -135 = 0
Q6. Find the value of:
A. 36 ÷ 6 + 3
Solution: 36 ÷ 6 + 3 = 6 + 3 = 9
B. 24 + 15 ÷ 3
Solution: 24 + 15 ÷ 3 = 24 + 5 = 29
C. 120 – 20 ÷ 4
Solution: 120 – 20 ÷ 4 = 120 – 5 = 115
D. 32 – (3 × 5) + 4
Solution: 32 – (3 × 5) + 4 = 32 – 15 + 4 = 21
E. 3 – (5 – 6 ÷ 3)
Solution: 3 – (5 – 6 ÷ 3) = 3 – (5 – 2) = 0
F. 21 – 12 ÷ 3 × 2
Solution: 21 – 12 ÷ 3 × 2 = 21 – 8 = 13
G. 16 + 8 ÷ 4 – 2 × 3
Solution: 16 + 8 ÷ 4 – 2 × 3 = 16 + 2 – 6 = 12
H. 28 – 5 × 6 + 2
Solution: 28 – 5 × 6 + 2 = 28 – 30 + 2 = 0
I. (-20) × (-1) + (-28) ÷ 7
Solution: (-20) × (-1) + (-28) ÷ 7 = 20 – 4 = 16
J. (-2) + (-8) ÷ (-4)
Solution: (-2) + (-8) ÷ (-4) = -2 + 2 = 0
K. (-15) + 4 ÷ (5 – 3)
Solution: (-15) + 4 ÷ (5 – 3) = -15 + 2 = -13
L. (-40) × (-1) + (-28) ÷ 7
Solution: (-40) × (-1) + (-28) ÷ 7 = 40 – 4 = 36
M. (-3) + (-8) ÷ (-4) -2 × (-2)
Solution: (-3) + (-8) ÷ (-4) -2 × (-2) = 3 + 2 + 4 = 3
N. (-3) × (-4) ÷ (-2) + (-1)
Solution: (-3) × (-4) ÷ (-2) + (-1) = -6 – 1 = -7