Maths Notes Class 6 Chapter 10 Ganita Prakash

The Other Side of Zero

Integers: Numbers that include positive numbers, negative numbers, and zero. Examples: -3, 0, 2, etc.

Positive Numbers: Numbers greater than zero (e.g., +1, +2).

Negative Numbers: Numbers less than zero (e.g., -1, -2).

Zero: It is neither positive nor negative and acts as a central reference point on the number line.

Number Line:

The number line represents both positive and negative numbers, with zero in the middle. Negative numbers lie to the left of zero, and positive numbers lie to the right.

Example:

⋯−3,−2,−1, 0, 1, 2, 3,…

Building of Fun (Floor Concept):

• In a building, floors can be labeled with integers, where:
  • Ground floor = 0
  • Above ground floors = positive integers
  • Below ground floors = negative integers
  • Movement can be represented as pressing lift buttons, either going up (+) or down (-).

Addition and Subtraction:

• Adding positive numbers moves you up (right on the number line), and adding negative numbers moves you down (left on the number line).
• Example: Starting at floor 0, pressing +2 takes you to floor 2. Pressing -1 from there takes you back to floor 1.

Basic Addition:

• (+1) + (+2) = +3 (Moving right)
• (+3) + (−1) = +2 (Moving left)

Subtraction:

Subtraction can be thought of as finding the movement between floors:

• (+5)−(+3)=+2
• (+2)−(−3)=+5 (Subtraction of negative is the same as addition of the corresponding positive).

Inverse:

• Every number has an inverse such that the sum of a number and its inverse is zero.
  • Example: The inverse of+3 is -3, because +3 + (−3) = 0.

Integers in Other Places

• Banking: Positive numbers represent credits (money added), and negative numbers represent debits (money deducted).
• Temperature: Positive numbers represent temperatures above freezing (0°C), and negative numbers represent temperatures below freezing.

Special Rules for Addition and Subtraction (Brahmagupta’s Rules):

• Adding two positive numbers yields a positive result.
• Adding two negative numbers yields a negative result.
• Adding a positive and a negative number: Subtract the smaller value from the larger, and the sign of the larger number is the result.
• Subtracting a negative number is the same as adding the corresponding positive number.

Token Model:

• Positive tokens (representing positive numbers) and negative tokens (representing negative numbers) can be used for performing operations.
• A zero pair (one positive and one negative token) cancels each other out.

Comparing Integers:

• Numbers on the left of the number line are smaller, and those on the right are larger:
• −4<−3<−2<−1<0<1<2<3

Explorations with Grids:

• Grid puzzles and number arrangements to explore integer properties, such as finding sums of rows and columns to create specific totals.