What is financial infrastructure?

The network of banks, payment systems and stock markets that helps manage money

What are the main things a bank does?

Holds deposits and lends money as loans

How do banks make money?

They pay lower interest on deposits and charge higher interest on loans

Earning interest on previous interest as well as on the original amount

What is the product of two negative integers?

It is positive, e.g. \((-4)\times(-2) = 8\).

What is the sign of the product of a positive and a negative integer?

It is negative, e.g. \(4\times(-2) = -8\).

What is the additive inverse of \(-18\)?

It is \(18\), since \(-18 + 18 = 0\).

Is integer multiplication commutative?

Yes — \(a \times b = b \times a\) for all integers.

A room cools 5°C per hour from 32°C; what is the temperature after 10 hours?

\(32 + 10\times(-5) = 32 - 50 = -18\,^\circ\text{C}\).

Operations with Integers

Q: Who first stated the rules for multiplying positive and negative numbers?

Brahmagupta, using "fortune" (positive) and "debt" (negative).

Class 7 Mathematics · Ganita Prakash Part 2 · Chapter 2

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CBSE Class 7 · Mathematics

8 chapters: lakhs and crores to fractions

Marks booster + cheatsheet: key concepts in 2 lines each, common traps
Triangle inequality, Ch 7
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Five congruence conditions to equations

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Integer sign rules, Ch 2
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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.

Recap of integers, number line and tokensMultiplication of integers and sign rulesDivision of integersCommutative, associative and distributive propertiesInteger word problems

Key terms

Integer

A whole number that may be positive, negative or zero.

Additive inverse

The number that adds to a given number to give zero; the inverse of \(a\) is \(-a\).

Sign rule for multiplication

Same signs give a positive product; opposite signs give a negative product.

Commutative property

For any integers, \(a \times b = b \times a\).

Associative property

For any integers, \(a \times (b \times c) = (a \times b) \times c\).

Distributive property

For any integers, \(a \times (b + c) = a \times b + a \times c\).

Extra questions & answers

Try one from this chapter

The product of two negative integers is:

Flashcards & interactive practice