Integers
Overview
Integers are a collection of all positive numbers, negative numbers, and zero. In Class 6, we learn how to represent integers on a number line, compare them, and perform basic operations like addition and subtraction. Integers help us describe real-life situations such as temperature below zero, depth below sea level, or money owed. Understanding integers builds a strong foundation for higher mathematics and everyday problem-solving skills.
Typed Notes
What Are Integers?
Natural numbers are 1, 2, 3, … and whole numbers add zero to them. But what about temperatures like –5°C or a loss of ₹10? We need numbers less than zero. Negative numbers such as –1, –2, –3 fill this gap. Together, all negative numbers, zero, and all positive numbers form the set of integers. We write them as: …, –4, –3, –2, –1, 0, 1, 2, 3, 4, … Every natural number has a negative counterpart called its opposite or additive inverse.
Integers on a Number Line
Draw a straight line and mark 0 in the middle. Mark 1, 2, 3, 4 equally spaced to the right and –1, –2, –3, –4 to the left. This is the integer number line. Moving right means increasing value; moving left means decreasing value. So –3 is less than –1 because –3 is further left. We compare integers using this idea: –5 < –2 < 0 < 3 < 7. The number line also helps us add and subtract integers by counting jumps in the correct direction.
Addition of Integers
To add two integers, use the number line or simple rules. Adding two positive integers gives a larger positive number: 4 + 3 = 7. Adding two negative integers gives a larger negative number: (–4) + (–3) = –7. When signs differ, subtract the smaller absolute value from the larger and keep the sign of the bigger number. Example: 5 + (–3) = 2 because 5 – 3 = 2 and 5 is bigger. Example: –7 + 4 = –3 because 7 – 4 = 3 and –7 has the bigger absolute value.
Subtraction of Integers
Subtracting an integer means adding its additive inverse (opposite). Rule: a – b = a + (–b). Example: 6 – 9 = 6 + (–9) = –3. Example: –4 – 3 = –4 + (–3) = –7. Example: –5 – (–2) = –5 + 2 = –3. This rule makes subtraction easy because we always convert it to addition. On the number line, subtracting a positive number means moving left, and subtracting a negative number means moving right. Always change the sign of the number being subtracted, then add.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Integers include negative numbers, zero, and positive numbers: …, -3, -2, -1, 0, 1, 2, 3, …
- 02On a number line, numbers increase from left to right; negative numbers lie to the left of zero.
- 03The absolute value (magnitude) of an integer is its distance from zero, always positive.
- 04When adding a negative integer, we move left on the number line; adding a positive integer means moving right.
- 05Subtracting an integer is the same as adding its opposite: a – b = a + (–b).
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Find the sum: (–8) + 5
Subtract: 4 – (–6)
The temperature in Shimla was –3°C in the morning and rose by 7°C by afternoon. What was the afternoon temperature?
Arrange in ascending order: –5, 3, –1, 0, –8
Find: (–6) – (–4) + (–2)
Integers extend whole numbers by including negative numbers. They are represented on a number line where values increase to the right. We compare integers by their position on the line. Addition follows sign rules, and subtraction is converted to addition by using the additive inverse. These concepts help solve real-life problems involving temperatures, floors below ground, and financial losses.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.Which of the following is the smallest integer?
Q2.What is (–3) + (–5)?
Q3.What is 7 – (–3)?
Q4.The additive inverse of –9 is:
Mark karo — dashboard par progress dikhega.