Integers Class 6 NCERT: Concepts, Number Line Rules, & Solved Practice Questions

Welcome, young mathematicians! Have you ever wondered what happens when we go below zero? Imagine a freezing winter night in Shimla where the temperature drops below zero to minus 5 degrees Celsius, or deep-sea diving where you descend 100 meters below sea level. To represent these physical situations, our standard whole numbers (0, 1, 2, 3...) are not enough. This is where integers come to the rescue! In this chapter on integers class 6 ncert, we will master negative numbers, learn how to plot them on a horizontal number line, and understand rules to add and subtract them. Grab your virtual YoLearn sketchpad and let's explore this beautiful mathematical landscape together!

The Big Picture: What are Integers?

To understand the collection of integers, let's look at the numbers we already know. We have Natural Numbers (1, 2, 3...) and Whole Numbers (0, 1, 2...). Now, imagine attaching a minus sign (-) to each natural number. We get numbers like -1, -2, -3, and so on. These are called negative integers. The positive integers (1, 2, 3...) represent forward steps, profit, or heights. Negative integers represent backward steps, losses, or depths. Zero is an integer, but it is neither positive nor negative. It acts as the balance point. Together, positive integers, zero, and negative integers form the complete set of integers.

How to Plot Integers on a Horizontal Number Line

  1. Step 1: Draw the base line — Draw a straight horizontal line and mark a point in the center, labeling it as zero (0).
  2. Step 2: Mark positive integers — Move to the right of zero at equal distances. Mark these consecutive points as 1, 2, 3, 4, 5, etc.
  3. Step 3: Mark negative integers — Move to the left of zero at the exact same equal intervals. Mark these points as -1, -2, -3, -4, -5, etc.
  4. Step 4: Understand order and value — Remember the golden rule: Any number to the right on a number line is always greater than any number to its left. Thus, 2 is greater than -3, and -1 is greater than -5.

Golden Rules for Adding and Subtracting Integers

  • Same Signs: When adding two integers with the same sign, add their numerical values and keep the common sign. Example: (-3) + (-4) = -7.
  • Different Signs: When adding two integers with different signs, subtract the smaller numerical value from the larger one, and apply the sign of the integer with the larger value. Example: (-8) + (+5) = -3.
  • Subtracting Negatives: Subtracting a negative number is equivalent to adding its positive counterpart. Example: 6 - (-3) becomes 6 + 3 = 9.
  • Opposites Add up to Zero: An integer and its opposite add up to zero. Example: (+7) + (-7) = 0. They are also known as additive inverses.

Step-by-Step Worked Examples

  • Example 1: Find the value of (-5) + (+8) using the sign rules. - Step 1: Identify the signs. One is negative (-5), and one is positive (+8). - Step 2: Since they have different signs, find the difference of their absolute values: 8 - 5 = 3. - Step 3: Identify the number with the larger absolute value, which is +8. - Step 4: Apply its positive sign to the difference. Answer is +3.
  • Example 2: Subtract (-12) from (-20). - Step 1: Set up the equation: (-20) - (-12). - Step 2: Convert the subtraction of a negative number into addition: (-20) + 12. - Step 3: These have opposite signs. Find the difference: 20 - 12 = 8. - Step 4: Keep the sign of the larger number (-20 is further from zero than 12). Answer is -8.

Practice Questions with Solutions

  • Q: Write the opposite of each statement: (a) Increase of 8, (b) 30 km North, (c) Loss of Rs 700. A: Step 1: Identify the mathematical action being described. Step 2: Swap the keyword with its mathematical opposite (Increase vs Decrease, North vs South, Loss vs Gain). Final answer: (a) Decrease of 8, (b) 30 km South, (c) Gain of Rs 700.
  • Q: Arrange the following integers in ascending order: -8, 5, 0, -3, -12, 4. A: Step 1: Identify negative integers: -8, -3, -12. Find the smallest first. -12 is farthest to the left on the number line, so it is the smallest, followed by -8, and then -3. Step 2: Place zero in the middle because it is greater than all negative integers but smaller than positive ones. Step 3: Arrange positive integers: 4, 5. Final answer: -12, -8, -3, 0, 4, 5.
  • Q: Solve: (-9) + (+4) + (-6) + (+15) A: Step 1: Group the positive and negative integers together: (4 + 15) + [(-9) + (-6)] Step 2: Add the positive integers: 4 + 15 = 19. Step 3: Add the negative integers using the same-sign rule: (-9) + (-6) = -15. Step 4: Now combine the two totals: 19 + (-15). Step 5: Subtract the absolute values: 19 - 15 = 4. Keep the sign of the larger value (+19). Final answer: 4
  • Q: Find the value of: 50 - (-40) - (-2) A: Step 1: Convert the double negatives into addition: 50 + 40 + 2. Step 2: Add the first two numbers: 50 + 40 = 90. Step 3: Add the final number: 90 + 2 = 92. Final answer: 92

Frequently Asked Questions

Is zero a positive or a negative integer?

Zero is a unique integer that is neither positive nor negative. It acts as the neutral dividing point on the number line between negative integers and positive integers.

Why is -10 smaller than -2?

On a horizontal number line, the values decrease as we move to the left. Since -10 lies further to the left than -2, it has a lower mathematical value.

What is the additive inverse of an integer?

The additive inverse of an integer is its opposite value with the opposite sign. When you add an integer and its additive inverse, the sum is always zero (e.g., the additive inverse of -5 is +5).