CBSE Class 6 Maths: Mastering Integers Ex 6.2

Hello, young mathematicians! Have you ever wondered about numbers that are less than zero? Or how to measure temperature below freezing? That's where integers come in! In CBSE Class 6 Maths, Chapter 6, we dive deep into the fascinating world of Integers. Specifically, in Exercise 6.2, we'll learn how to perform basic operations like addition and subtraction of integers. Our primary tool will be the powerful number line, which helps us visualize these operations. Understanding this concept is not just for exams; it helps you grasp real-world situations involving debt, altitude, temperature changes, and much more. By the end of this lesson, you'll be a pro at adding and subtracting positive and negative numbers with confidence!

What are Integers? And Using the Number Line

Integers are a collection of numbers that include all natural numbers (1, 2, 3, ...), zero (0), and the negative numbers (-1, -2, -3, ...). Think of them as whole numbers and their opposites. They don't include fractions or decimals. Integers help us represent quantities that can be positive (above zero), negative (below zero), or exactly zero. For example, if you gain 5 rupees, it's +5. If you owe 5 rupees, it's -5. If you have neither, it's 0.

The number line is a straight line where every point corresponds to a number. For integers, we mark 0 at the center. Positive integers are marked to the right of 0, and negative integers are marked to the left of 0. The further a number is to the right, the greater its value. The further a number is to the left, the smaller its value. For example, 3 is greater than -5, and -1 is greater than -4.

When we add or subtract integers, especially in Class 6, using the number line is a fantastic way to visualize the operation. It makes understanding why we move left or right much clearer. We start at the first number and then move based on the operation and the second number's sign.

Adding Integers Using a Number Line

  1. Step 1: Locate the First Integer — Start by finding the position of the first integer in your sum on the number line. This is your starting point.
  2. Step 2: Determine Direction of Movement — Look at the second integer. If you are adding a positive integer, you will move to the RIGHT. If you are adding a negative integer, you will move to the LEFT.
  3. Step 3: Count Steps — Count the number of steps equal to the absolute value (the number part without the sign) of the second integer, in the direction determined in Step 2. The point where you land is your answer.
  4. Example: Find 3 + (-5) — 1. Start at 3 on the number line. 2. We are adding (-5), which is a negative integer, so we move to the LEFT. 3. Move 5 steps to the left from 3. (3 -> 2 -> 1 -> 0 -> -1 -> -2) You land on -2. So, 3 + (-5) = -2.
  5. Example: Find -2 + 6 — 1. Start at -2 on the number line. 2. We are adding 6, which is a positive integer, so we move to the RIGHT. 3. Move 6 steps to the right from -2. (-2 -> -1 -> 0 -> 1 -> 2 -> 3 -> 4) You land on 4. So, -2 + 6 = 4.

Subtracting Integers Using a Number Line

  1. Step 1: Locate the First Integer — Just like with addition, start by marking the first integer on the number line. This is your starting position.
  2. Step 2: Convert Subtraction to Addition (Key Rule!) — This is the most important step for subtraction. Remember this rule: Subtracting a positive integer is the same as adding its negative. (e.g., a - (+b) is a + (-b)) Subtracting a negative integer is the same as adding its positive. (e.g., a - (-b) is a + (+b))
  3. Step 3: Apply Addition Rules — Once you've converted the subtraction problem into an addition problem (Step 2), follow the rules for adding integers on a number line (move right for adding positive, move left for adding negative). The final point is your answer.
  4. Example: Find 5 - (-3) — 1. Start at 5 on the number line. 2. We are subtracting (-3). According to our rule, subtracting a negative is like adding a positive. So, 5 - (-3) becomes 5 + (+3) or simply 5 + 3. 3. Now, from 5, add 3 (move 3 steps to the RIGHT). (5 -> 6 -> 7 -> 8) You land on 8. So, 5 - (-3) = 8.
  5. Example: Find -4 - 2 — 1. Start at -4 on the number line. 2. We are subtracting 2 (which is +2). Subtracting a positive is like adding its negative. So, -4 - 2 becomes -4 + (-2). 3. Now, from -4, add (-2) (move 2 steps to the LEFT). (-4 -> -5 -> -6) You land on -6. So, -4 - 2 = -6.

YoLearn AI Tutor's Exam Tip: Mastering Integer Operations

When solving problems with integers, especially addition and subtraction, always pay close attention to the signs. A common mistake is getting confused between a - (-b) and a + (-b). Remember that a - (-b) transforms into a + b (subtracting a negative is adding a positive), while a + (-b) means a - b (adding a negative is subtracting a positive).

If you find yourself stuck, quickly draw a small number line. It's a powerful visual aid that can prevent simple errors and help you verify your answer. Practice these conversions mentally, and soon you won't need the number line for every problem, but it's always there as your reliable helper!

Practice Questions with Solutions

  • Q: Solve 7 + (-4) using a number line. A: Step 1: Start at 7 on the number line. Step 2: You are adding -4, so move 4 steps to the left. Step 3: Counting 4 steps left from 7: (7 -> 6 -> 5 -> 4 -> 3). Final answer: 7 + (-4) = 3
  • Q: Solve -5 + 8 using a number line. A: Step 1: Start at -5 on the number line. Step 2: You are adding 8, so move 8 steps to the right. Step 3: Counting 8 steps right from -5: (-5 -> -4 -> -3 -> -2 -> -1 -> 0 -> 1 -> 2 -> 3). Final answer: -5 + 8 = 3
  • Q: Evaluate 6 - (-2) using a number line. A: Step 1: Start at 6 on the number line. Step 2: The expression is 6 - (-2). Remember, subtracting a negative is the same as adding a positive, so this becomes 6 + 2. Step 3: From 6, move 2 steps to the right (because you are adding +2). Step 4: Counting 2 steps right from 6: (6 -> 7 -> 8). Final answer: 6 - (-2) = 8
  • Q: Evaluate -3 - 4 using a number line. A: Step 1: Start at -3 on the number line. Step 2: The expression is -3 - 4. Subtracting a positive is the same as adding a negative, so this becomes -3 + (-4). Step 3: From -3, move 4 steps to the left (because you are adding -4). Step 4: Counting 4 steps left from -3: (-3 -> -4 -> -5 -> -6 -> -7). Final answer: -3 - 4 = -7

Frequently Asked Questions

What are integers in simple terms?

Integers are whole numbers, including positive numbers (like 1, 2, 3), negative numbers (like -1, -2, -3), and zero. They are used to count quantities that can be above, below, or at a reference point like sea level or zero temperature.

How do you add a negative integer on a number line?

To add a negative integer on a number line, you always move to the left. For example, to solve 5 + (-3), you start at 5 and move 3 steps to the left, landing on 2.

What does it mean to subtract a negative integer?

Subtracting a negative integer is the same as adding a positive integer. For example, 7 - (-2) is equivalent to 7 + 2, which equals 9. On a number line, you would move to the right.

Why is the number line important for learning integers?

The number line provides a visual way to understand the concept of positive and negative numbers and how operations like addition and subtraction affect their values. It helps in building a strong foundation for more complex integer calculations later on.