Integers on number lines

key notes :

What Are Integers?

• Integers are a set of whole numbers and their negatives, including zero.

… -4, -3, -2, -1, 0, 1, 2, 3, 4 …\text{… -4, -3, -2, -1, 0, 1, 2, 3, 4 ..}… -4, -3, -2, -1, 0, 1, 2, 3, 4 …

• Positive integers: 1, 2, 3, …
• Negative integers: -1, -2, -3, …
• Zero (0) is neither positive nor negative.

✅ Integers do not include fractions or decimals.

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📏 Number Line – Introduction

A number line is a straight, horizontal or vertical line used to represent numbers in order.

• It is evenly spaced.
• The center of the number line is 0.
• Positive integers lie to the right of 0.
• Negative integers lie to the left of 0.

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🔹 Representing Integers on a Horizontal Number Line

luaCopyEdit<--- -4 --- -3 --- -2 --- -1 --- 0 --- 1 --- 2 --- 3 --- 4 --->

🧠 Rules:

• Move right for positive numbers.
• Move left for negative numbers.
• Equal distance is maintained between all integers.

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🔹 Representing Integers on a Vertical Number Line

     ↑
     3
     2
     1
     0
    -1
    -2
    -3
     ↓

• Upwards → Positive integers
• Downwards → Negative integers
• 0 remains at the center

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📌 How to Plot Integers on Number Lines

✅ Steps:

• Draw a line (horizontal or vertical).
• Mark zero (0) in the middle.
• Place positive integers to the right (or above).
• Place negative integers to the left (or below).
• Use equal spacing between numbers.
• Plot (draw a dot) where the given integer lies.
• Label the point clearly.

🧠 Example:

To plot -3 and 2 on a number line:

• -3: Start at 0, move 3 units left, and mark it.
• 2: Start at 0, move 2 units right, and mark it.

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🌍 Real-Life Examples of Integers on Number Lines

Context	Negative Integers	Positive Integers
Thermometer	Below 0°C (cold)	Above 0°C (warm)
Bank balance	Debt (₹-500)	Savings (₹+500)
Elevation	Below sea level (-100 m)	Above sea level (+200 m)
Lifts/Elevators	Basement floors (B1 = -1)	Floors above ground
Game scores	Penalties (-10 points)	Points scored (+10)

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🔍 Practice Exercises

Q1. Mark the following integers on a number line:
-5, -2, 0, 3, 6

Q2. Which integer is farthest to the left on the number line?
a) -4 b) -6 c) -1 d) 0

Q3. On a vertical number line, what is 2 units above -1?

Q4. Fill in the blanks:
a) -3 is to the ______ of -1 on the number line.
b) 0 is ______ -2 and 2.

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📝 Important Points to Remember

• Integers extend infinitely in both directions on the number line.
• The farther right a number is, the greater it is.
• Negative integers are always less than 0.
• Distance from 0 is called absolute value (e.g., |-3| = 3).
• Always maintain equal spacing when drawing number lines.

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🎯 Summary

• Integers can be positive, negative, or zero.
• A number line helps us visualize integers and compare them easily.
• Always start from zero, and move left (negative) or right (positive).
• Integers are used in everyday life to show gain/loss, temperature, elevation, and more.

Learn with an example

let’s practice!