Integers - Exercise 1.3 | Class 7 Mathematics Chapter 1/ Class 7 Maths - Ex.1.3 - Chapter 1New Ncert

Here’s a detailed 1000-word description of **Class 7 Mathematics Chapter 1, Exercise 1.3 (Integers) from the NCERT textbook**: --- *Class 7 Mathematics – Chapter 1: Integers (Exercise 1.3)* *Introduction to Integers* Mathematics is a subject that helps us understand numbers and their properties in various ways. One fundamental concept in arithmetic and algebra is **integers**, which form the basis of many mathematical operations. In Class 7 Mathematics, Chapter 1 is entirely dedicated to the study of integers, their properties, and operations. *What Are Integers?* Integers are a set of numbers that include: *Positive numbers* (1, 2, 3, …) *Negative numbers* (-1, -2, -3, …) **Zero (0)**, which is neither positive nor negative. The set of integers is represented as **{…, -3, -2, -1, 0, 1, 2, 3, …}**. *Overview of Exercise 1.3* Exercise 1.3 in Chapter 1 focuses on the **multiplication of integers**. In the previous exercises, students have learned about the addition and subtraction of integers. Now, in this part, they explore how multiplication works when negative numbers are involved. *Multiplication of Integers* The multiplication of integers follows specific rules: #### *Rules for Multiplication of Integers* 1. *Positive × Positive = Positive* Example: *3 × 4 = 12* 2. *Negative × Positive = Negative* Example: *(-3) × 4 = -12* 3. *Positive × Negative = Negative* Example: *3 × (-4) = -12* 4. *Negative × Negative = Positive* Example: *(-3) × (-4) = 12* These rules form the foundation of multiplication operations involving integers. *Understanding Multiplication Through Number Line* To visualize integer multiplication, we can use a number line. For example: *Multiplying a positive number by a negative number* means moving in the negative direction. *Multiplying two negative numbers results in a positive* because two negative signs cancel each other. Example: *(-2) × 3* Start at 0 and move 2 steps to the left three times. The result is **-6**. Example: *(-2) × (-3)* Here, reversing direction twice results in a positive number. The answer is **6**. *Properties of Multiplication of Integers* The multiplication of integers follows several mathematical properties: #### *1. Closure Property* The product of any two integers is always an integer. Example: *(-5) × 4 = -20* (which is also an integer). #### *2. Commutative Property* The order of multiplication does not change the result. Example: **(-3) × 5 = 5 × (-3) = -15**. #### *3. Associative Property* When multiplying three integers, grouping does not change the result. Example: *(2 × -3) × 4 = 2 × (-3 × 4)* Calculation: *-6 × 4 = -24* and **2 × -12 = -24**. The results are equal. #### *4. Multiplicative Identity* Any number multiplied by *1* remains unchanged. Example: **(-7) × 1 = -7**. #### *5. Multiplication by Zero* Any integer multiplied by *0* is **0**. Example: **8 × 0 = 0**. *Solving Problems in Exercise 1.3* The problems in Exercise 1.3 include direct multiplication, word problems, and applying properties to simplify expressions. #### *Examples of Questions* 1. Multiply the following: a) (-5) × (-3) b) 7 × (-6) c) (-9) × (-8) *Solution:* a) (-5) × (-3) = 15 b) 7 × (-6) = -42 c) (-9) × (-8) = 72 2. Simplify using properties: a) (-2) × (-3) × 5 b) (-4) × (6 × -2) c) (-7) × 8 + (-7) × 2 *Solution:* a) (-2 × -3) × 5 = 6 × 5 = 30 b) -4 × (6 × -2) = -4 × -12 = 48 c) (-7 × 8) + (-7 × 2) = -56 + (-14) = -70 3. *Word Problems:* If the temperature drops 2°C every hour for 5 hours, what is the total temperature drop? A submarine descends 50 meters every minute. What is its depth after 6 minutes? *Solution:* 2 × 5 = -10°C (Total drop in temperature) 50 × (-6) = -300 meters (Submarine depth) *Why Is Multiplication of Integers Important?* Understanding how to multiply integers is crucial for advanced mathematics. This concept is applied in: *Physics* (motion, forces, temperature changes). *Economics* (profit/loss calculations). *Programming* (handling positive and negative values in computations). *Conclusion* Exercise 1.3 in Class 7 Mathematics is a key step in understanding integer operations. By learning the multiplication of integers and its properties, students develop a strong foundation for algebra and problem-solving. Practicing these concepts thoroughly will help in mastering more complex mathematical topics in higher classes. NEW NCERT Class 7 Maths Exercise 1.3 new ncert maths class 7 chapter 1 integers class 7 maths ch 1 class 7 maths exercise 1.3 class 7 maths ex.1.3 q.1 class 7 integers ranveer maths chapter1 class 7 ncert maths class 7 ncert maths exercise 1.3