Multiplication of Rational Numbers


 
 
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
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Question : 1

Simplify:  frac{5}{9}times frac{2}{9}=

Right Option : C
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Explanation
Question : 2

Multiply: large frac{-11}{13};by;frac{-21}{7}

Right Option : C
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Explanation
Question : 3

By what number should dpi{80} frac{-6}{8}  be multiplied in order to produe frac{2}{3}   ?

Right Option : B
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Explanation
 
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