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 \(\tfrac{3}{4}\times\tfrac{2}{5}\)?

\(\dfrac{3\times2}{4\times5}=\dfrac{6}{20}=\dfrac{3}{10}\).

What is the reciprocal of \(\tfrac{3}{5}\)?

Its reciprocal is \(\dfrac{5}{3}\), and \(\tfrac{3}{5}\times\tfrac{5}{3}=1\).

How do you divide one fraction by another?

Multiply the first fraction by the reciprocal of the second: \(\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}\).

Evaluate \(\tfrac{2}{3}\div\tfrac{3}{5}\).

\(\dfrac{2}{3}\times\dfrac{5}{3}=\dfrac{10}{9}\).

When is a product less than both the numbers multiplied?

When both numbers are between 0 and 1, e.g. \(\tfrac{3}{4}\times\tfrac{2}{5}=\tfrac{3}{10}\).

When multiplying by a number between 0 and 1, what happens to the product?

The product is smaller than the other number.

When the divisor is between 0 and 1, how does the quotient compare to the dividend?

The quotient is greater than the dividend.

Why does the area of a rectangle illustrate fraction multiplication?

A rectangle with fractional sides has area equal to the product of those sides.

Simplify \(\tfrac{12}{7}\times\tfrac{5}{24}\).

Cancel the common factor 12: \(\dfrac{1\times5}{7\times2}=\dfrac{5}{14}\).

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Chapter 8: Working with Fractions — Class 7 Mathematics

Mathematics · 15 chapters

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Chapter 8: Working with Fractions

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Brahmagupta's rule for multiplying fractions is:

Summary

This chapter develops multiplication and division of fractions with meaning. Multiplying a fraction by a whole number repeats it (\(\tfrac{2}{5}\times 3 = \tfrac{6}{5}\)), and multiplying two fractions uses Brahmagupta's rule \(\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{a\times c}{b\times d}\), which you also see as the area of a rectangle with fractional sides. Common factors can be cancelled before multiplying to keep numbers small. A key insight is how the size of a product depends on the factors: multiplying by a number between 0 and 1 makes the product smaller than the other number, while multiplying by a number greater than 1 makes it larger. Division is turned into multiplication using the reciprocal: \(\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}\). When the divisor is between 0 and 1 the quotient is bigger than the dividend; when it is greater than 1 the quotient is smaller. The chapter is rich in history — Brahmagupta, Bhaskaracharya's Lilavati, and the Shulbasutra — and applies fractions to many everyday sharing and measuring problems.

Multiplying fractions by whole numbers and fractionsBrahmagupta's rule and area modelCancelling common factors and lowest formReciprocals and dividing fractionsSize of products and quotients; word problems

Key terms

Fraction

A number of the form \(\dfrac{a}{b}\) representing parts of a whole.

Multiplication of fractions

Brahmagupta's rule: \(\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{a\times c}{b\times d}\).

Reciprocal

The fraction \(\dfrac{b}{a}\) of \(\dfrac{a}{b}\); a fraction times its reciprocal is \(1\).

Division of fractions

Multiplying the dividend by the reciprocal of the divisor.

Cancelling common factors

Dividing numerator and denominator by common factors before multiplying.

Lowest form

A fraction whose numerator and denominator share no common factor other than 1.

Important questions

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Fraction

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A number of the form \(\dfrac{a}{b}\) representing parts of a whole.

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Practice quiz · Working with Fractions

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Working with Fractions

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