Class 6 ยท Maths ยท Ganita Prakash
Chapter 10 ๐ก๏ธ
Chapter 10 ๐ก๏ธ
The Other Side of Zero
Integers โ Quick, colourful revision notes for your test!
Chapter Contents
10.1 What Are Integers?
A positive number has a '+' sign (usually dropped: 3 means +3). A negative number has a 'โ' sign and is less than zero. Together with 0, these are called integers. Zero itself is neither positive nor negative.
Think of a building with floors above and below the ground:
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
Fig 1: Floors above ground = positive, floors below ground = negative, ground = 0
Integers on the Number Line
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
Fig 2: Negative numbers sit to the left of 0, positives to the right
Numbers get bigger as you move right on the number line. So: 2 < 5, โ3 < 2, and โ5 < โ3 (a "more negative" number is always smaller).
Adding & Subtracting Integers
Starting Number + Movement = Target Number
Target Number โ Starting Number = Movement needed
Moving right = positive movement; moving left = negative movement.
Target Number โ Starting Number = Movement needed
Moving right = positive movement; moving left = negative movement.
From 9 to 3: you move 6 steps backward, so 9 + (โ6) = 3, and 3 โ 9 = โ6.
Subtracting a negative = adding the positive! (+7) โ (โ5) = (+7) + (+5) = 12. This trick makes tricky subtractions much easier.
10.2 The Token Model
Imagine green (+) tokens and red (โ) tokens. A zero pair = one green + one red token together โ their combined value is 0, so they cancel out!
@edugrown ๐ @edugrown ๐ @edugrown ๐
@edugrown ๐ @edugrown ๐ @edugrown ๐
Fig 3: Cancel matching zero pairs โ whatever's left over is your answer
Stuck subtracting because you don't have enough tokens? Just add extra zero pairs (they don't change the value!) until you have enough to take away.
10.3 Integers in Real Life
| Context | Positive means | Negative means |
|---|---|---|
| Bank account | Credit (money in) | Debit (money owed) |
| Temperature | Above 0ยฐC | Below 0ยฐC |
| Sea level | Above sea level | Below sea level |
| Building floors | Above ground | Below ground (basement) |
๐ฏ Quick Summary
- Integers = ...โ3,โ2,โ1, 0, 1, 2, 3... ; 0 is neither positive nor negative.
- On the number line, bigger numbers are to the right; smaller (more negative) to the left.
- Target โ Start = Movement; Start + Movement = Target.
- Subtracting a negative = adding a positive (and vice versa).
- Token model: a (+) and (โ) token together form a "zero pair" that cancels out.
- Integers show up everywhere: bank credits/debits, temperature, sea level, building floors.
โ๏ธ Notes by @edugrown โ happy revising! ๐