Integers Class 6 Chapter Notes

Key points

• Integers include all positive numbers, all negative numbers and zero: ..., -3, -2, -1, 0, 1, 2, 3, ...
• Positive integers are greater than zero; negative integers are less than zero; zero is neither positive nor negative.
• On a number line, numbers increase as we move right and decrease as we move left.
• Every positive integer has a corresponding negative integer: +5 and -5 are opposites.
• The integer with greater position on the number line is greater. Example: -2 is greater than -5 because -2 lies to the right of -5.
• To add a positive integer, move right on the number line. To add a negative integer, move left.
• To subtract an integer, add its opposite. Example: 6 - (-2) = 6 + 2 = 8.
• When comparing negative numbers, the number closer to zero is greater. Example: -1 is greater than -8.
• Integer signs are used in real life for temperature below zero, loss, debt, depth below sea level and floors below ground level.

Important definitions

Integer

A number from the set of positive numbers, negative numbers and zero.

Positive integer

An integer greater than zero, usually written as 1, 2, 3 and so on. The plus sign is often not written.

Negative integer

An integer less than zero, written with a minus sign such as -1, -2, -3.

Zero

The integer 0, which is neither positive nor negative and lies between positive and negative integers.

Number line

A straight line with numbers marked at equal distances, used to represent and compare integers.

Opposite integers

Two integers that are at the same distance from zero but on opposite sides, such as +4 and -4.

Ascending order

Arrangement from the smallest integer to the greatest integer.

Descending order

Arrangement from the greatest integer to the smallest integer.

Understanding integers through the number line

The easiest way to understand integers is to use a number line. Zero is placed in the middle. To the right of zero are positive integers such as 1, 2, 3 and to the left of zero are negative integers such as -1, -2, -3. Moving right means the value is increasing, so 4 is greater than 1. Moving left means the value is decreasing, so -5 is less than -2. This is why many students make mistakes with negative numbers: although 8 is greater than 2, -8 is not greater than -2. In negative integers, the number closer to zero is greater. Integers help us write opposite situations in real life. A gain of ₹50 can be written as +50, while a loss of ₹50 can be written as -50. A temperature of 5°C above zero is +5°C, while 5°C below zero is -5°C.

Where integers are used in daily life

Positive integers, negative integers and zero

How to compare and arrange integers

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Rules for addition and subtraction of integers

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Short worked examples

• Compare -4 and -9. -4 is to the right of -9 on the number line. Therefore, -4 > -9.
• Arrange 3, -2, 0, -6, 5 in ascending order. Ascending means smallest to greatest. On the number line the order is -6, -2, 0, 3, 5.
• Find -3 + 7 and 6 - (-4). -3 + 7 = 4 because we move 7 steps right from -3. Also, 6 - (-4) = 6 + 4 = 10.

Exam tip: avoid sign mistakes

In Class 6 integer questions, most errors happen with negative signs. Always remember: right side means greater on the number line. Do not say -9 is greater than -3 just because 9 is bigger than 3; actually -3 is greater because it is closer to zero. In subtraction questions, circle the sign before the second number and convert subtraction into adding the opposite. Write one step clearly, such as 7 - (-2) = 7 + 2, because teachers often give marks for correct sign handling.

Must remember formulas and sign rules

• a + 0 = a and a - 0 = a for any integer a.
• a + (-a) = 0 because opposite integers cancel each other.
• To add a positive number: move right on the number line.
• To add a negative number: move left on the number line.
• To subtract an integer: add its opposite.
• Greatest negative integer is -1 because it is closest to zero on the left side.
• There is no smallest negative integer in Class 6 integer set because numbers continue as ..., -100, -101, -102 and so on.
• Zero is greater than every negative integer and less than every positive integer.

Quick revision checks

• Q: Is zero a positive integer? A: No. Zero is neither positive nor negative.
• Q: Which is greater: -7 or -2? A: -2 is greater because it is closer to zero and lies to the right of -7.
• Q: What is the opposite of +12? A: -12.
• Q: Calculate 5 + (-8). A: Start at 5 and move 8 steps left. The answer is -3.

Frequently Asked Questions