Ch 10 of Ganita Prakash — "The Other Side of Zero" — takes students beyond the natural numbers they are familiar with and into the world of negative numbers and integers. Through real-life contexts like temperature, altitude, and debt, students discover why negative numbers are necessary and how to work with them on a number line.
Natural numbers (1, 2, 3…) are not enough to describe all situations. Temperature drops below zero, lifts go to underground floors, bank accounts can be overdrawn, and sea levels can be above or below a reference point. Negative numbers allow us to represent quantities "less than zero" or "in the opposite direction".
Integers include all positive numbers, zero, and negative numbers: …, −3, −2, −1, 0, 1, 2, 3, … On the number line, positive integers are to the right of zero and negative integers to the left. Zero is the boundary between positive and negative. Every integer has a unique position on the number line.
On the number line, a number to the right is always greater than a number to the left. This means: every positive integer is greater than every negative integer, and zero is greater than every negative integer. Among negative integers, −1 > −2 > −3 (closer to zero means larger). For example: −5 < −2 < 0 < 3 < 7.
Addition on the number line: adding a positive number means moving right, adding a negative number means moving left. Same signs: add absolute values and keep the sign. Different signs: subtract the smaller absolute value from the larger and take the sign of the larger. For example: (−5) + 3 = −2 (start at −5, move 3 right).
Subtracting an integer is the same as adding its opposite (additive inverse): a − b = a + (−b). For example: 3 − 5 = 3 + (−5) = −2. And (−2) − (−7) = (−2) + 7 = 5. This rule makes subtraction of integers consistent and systematic.
Download the official NCERT PDF for Ch 10 "The Other Side of Zero" from the NCERT website: https://ncert.nic.in/textbook/pdf/fegp110.pdf. You can also download the complete Ganita Prakash textbook: https://ncert.nic.in/textbook/pdf/fegp1ps.zip
Zero is neither positive nor negative. It is the boundary between positive and negative integers on the number line. Zero is an integer, but it has no sign.
This follows from the rules of mathematics. If (−1) × (−1) were anything other than 1, the distributive property (a fundamental rule of arithmetic) would break down. Also, intuitively: "the opposite of the opposite" returns you to the original.
Negative numbers appear in temperatures below zero (like −10°C in winter), bank overdrafts/debts, altitudes below sea level (like the Dead Sea at −430 m), underground floors in buildings, and in sports when a team scores below par in golf.
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