Operations with Integers
Class 7 Mathematics · Ganita Prakash Part 2 · Chapter 2
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2- Mathematics
7- Mathematics
- Science
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- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Social Science
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
- Space weighted by chapter size
- Charts from the book's own data
- Traps corrected
Summary
This chapter completes arithmetic on integers by developing multiplication and division of positive and negative numbers, after a recap of addition and subtraction using the number line and token models. Using a "bag of tokens" model, you see that placing tokens means a positive multiplier and removing them means a negative multiplier, leading to the sign rules: the product (or quotient) of two numbers with the same sign is positive, and with opposite signs is negative. Patterns in multiplication tables confirm these rules, first stated historically by Brahmagupta using "fortune" (positive) and "debt" (negative). Multiplication of integers is commutative \((a\times b = b\times a)\), associative \((a\times(b\times c)=(a\times b)\times c)\), and distributive over addition \((a\times(b+c)=a\times b + a\times c)\). The sign of a product of many integers is positive when there is an even number of negative factors and negative when odd. Real contexts — exam scores with negative marking, a mine elevator, temperature drops — show integers at work.