Master Chapter 10 Class 6 - The other side of Zero (Ganita Prakash) with comprehensive NCERT Solutions, Practice Questions, MCQs, Sample Papers, Case Based Questions, and Video lessons.
Start Learning NowWelcome to Chapter 10, The Other Side of Zero, from your Class 6 Maths book, Ganita Prakash.
This is a truly exciting chapter because it expands our entire idea of what a number is. So far in your journey, you have learned about:
Counting Numbers (1, 2, 3...)
Zero (0)
Fractions (like 1/2 or 3/4)
All of these numbers are either zero or greater than zero. They all live on a "number ray" that starts at 0 and goes to the right. This chapter asks a simple but powerful question: what is on the other side of zero?
We will investigate the numbers that come before 0—numbers that are less than 0. This new, complete set of numbers is called the Integers.
This chapter uses a fantastic and intuitive analogy, "Bela's Building of Fun," to help you master this new concept. We will learn how to visualise, compare, and operate on these new numbers.
Integers are the complete set of whole numbers, including positives, negatives, and zero.
Positive Numbers: These are the numbers you already know (+1, +2, +3...), which are greater than 0.
Negative Numbers: These are the new numbers we will study (–1, –2, –3...), which are less than 0.
Zero (0): This is the central point, which is neither positive nor negative.
To understand this, we'll use the "Building of Fun." The Ground Floor is 0.
Floors above ground are positive: +1 (Food Court), +2 (Art Centre), etc.
Floors below ground are negative: –1 (Toy Store), –2 (Video Games), etc.
The building analogy makes comparing integers easy. A higher floor is a greater number.
It's easy to see that +4 > +1.
More importantly, Floor –3 (Cinema) is lower than Floor –1 (Toy Store). This means –3 < –1.
Any positive number is always greater than any negative number.
We will use the lift in the building to understand addition and subtraction.
Addition as Movement: We will use the formula Starting Floor + Movement = Target Floor.
If you are on Floor +1 (Food Court) and press the "+3" button (go up 3), you land on Floor +4. So, (+1) + (+3) = +4.
If you are on Floor +1 and press the "–4" button (go down 4), you land on Floor –3. So, (+1) + (–4) = –3.
Subtraction as "Finding the Movement": We will use the formula Target Floor - Starting Floor = Movement needed.
To get from the +2 (Art Centre) to +5 (Sports), you must press +3. So, (+5) - (+2) = +3.
To get from the +2 (Art Centre) to –3 (Cinema), you must press –5. So, (–3) - (+2) = –5.
To get from –1 (Toys) to –4 (Ghost House), you must press –3. So, (–4) - (–1) = –3.
The Token Model: We will also learn a second method for operations, using positive and negative tokens. A positive token and a negative token cancel each other out, forming a "zero pair".
You already use integers every day! We will see how they apply to:
Temperature: Temperatures below °0° (e.g., –4°°).
Money: Credits (positive) and Debits or loans (negative).
Geography: Heights above sea level (positive) and below sea level (negative).
Understanding integers, especially how to add and subtract negative numbers, is one of the most important skills in mathematics. It can be tricky at first, but the "Building of Fun" model makes it logical and clear.
At Teachoo, we walk you through every example, from the building lift to the token method, to make sure you master these new rules and build a strong foundation.
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