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Multiplication of Rational Numbers

Rational Numbers II - Concepts

Identity Property

Commutative Property

Multiplicative Inverse

Division of Rational Numbers

Multiplication of Rational Numbers

Rational Numbers between Two Rational Numbers

Properties of Rational Numbers

Simplification of Rational Numbers

Class - 8th IMO Subjects

Concept Explanation

Multiplication of Rational Numbers

Multiplication of rational numbers:

Recall that the product of two given fractions is a fraction whose numerator is the product of the numerators of the given fractions and whose denominator is the product of the denominators of the given fractions. In other words,

Product of two given fractions $large =frac{Product;of;their;numerators}{Product;of;their;denominators}$

This rule is also true for the product of rational numbers.

$large therefore$ Product of two rational numbers $large =frac{Product;of;their;numerators}{Product;of;their;denominators}$

Thus, if $large frac{a}{b}$ and $large frac{c}{d}$ are any two rational numbers, then

$large frac{a}{b}times frac{c}{d}=frac{atimes c}{btimes d}$

Example: Multiply:

$large (i);frac{3}{4}byfrac{5}{7}$ $large (ii);frac{3}{7}byleft ( frac{-4}{5} right )$ $large (iii);left ( frac{-5}{9} right )by;4$ $large (iv);left ( frac{-36}{7} right )byleft ( -frac{28}{9} right )$

Solution: We have,

$large (i);frac{3}{4}times frac{5}{7}=frac{3times 5}{4times 7}=frac{15}{28}$

$large (ii);frac{3}{4}times left ( frac{-4}{5} right )=frac{3times -4}{7times 5}=frac{-12}{35}$

$large (iii);left ( frac{-5}{9} right )times 4=frac{-5}{9}times frac{4}{1}=frac{(-5)times 4}{9times 1}=frac{-20}{9}$

$large (iv);left ( frac{-36}{7} right )times left ( -frac{28}{9} right )=left ( frac{-36}{7} right )times left ( frac{-28}{9} right )$ $large left [ therefore -frac{28}{9}=frac{-28}{9} right ]$

$large =frac{(-36)times (-28)}{7times 9}=frac{1008}{63}=16$

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Multiply: $large frac{5}{7};by;frac{-3}{4}$
A. $frac{-12}{28}$	B. $frac{-13}{28}$	C. $frac{-16}{28}$	D. $frac{-15}{28}$
Right Option : D
View Explanation

Question : 2

Multiply: $large frac{8}{-9};by;frac{-7}{-16}$
A. $frac{-7}{18}$	B. $frac{-8}{18}$	C. $frac{-6}{18}$	D. -1
Right Option : A
View Explanation

Question : 3

By what number we should multiply $LARGE frac{-15}{28}$ so that the product may be $large frac{-5}{7}$ ?
A. $large frac{4}{3}$	B. $large frac{5}{3}$	C. $large frac{6}{3}$	D. $large frac{16}{3}$
Right Option : A
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Exponents and Power II

Prerequiste

Visualising Soild Shapes

Ratio and Proportion

Introduction to Trigonometry

Constructions

Quadrilaterals II

Quadrilaterals I

Linear Equations in One Variable II

Linear Equations in One Variable I

Cube and Cube Roots

Square and Square Root II

Square and Square Root I

Rational Numbers II

Rational Numbers I

Mensuration I

Exponents and Power I

Direct and Inverse Variation II

Direct and Inverse Variation I

Algebraic Expressions

Comparing Quantities III

Comparing Quantities II

Comparing Quantities I

Playing With Numbers

Introduction to Graphs

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State Government Services

Banking And Insurance

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Sainik School Entrance

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Multiplication of Rational Numbers

Multiplication of Rational Numbers

Students / Parents Reviews [10]

Yatharthi Sharma

Archit Segal

Manish Kumar

Ayan Ghosh

Shivam Rana

Hiya Gupta

Cheshta

Om Umang

Prisha Gupta

Aman Kumar Shrivastava