Division of Rational Numbers


 
 
Concept Explanation
 

Division of Rational Numbers

Division of Rational Numbers:

Recall that division of fractions is the inverse of multiplication. In case of rational number also, division is the inverse of multiplication as defined below:

Division: If x and y are two rational numbers such that large yneq 0, then the result of dividing x and y is the rational number obtained on multiplying x by the reciprocal of y.

When x is divided by y, we write large xdiv y

Thus, we have large x+y=xtimes frac{1}{y}

If large frac{a}{b} and large frac{c}{d} are two rational numbers such that large frac{c}{d}neq 0, then

       large frac{a}{b}div frac{c}{d}=frac{a}{b}times left ( frac{c}{d} right )^{-1}=frac{a}{b}times frac{d}{c}

Dividend: The number to be divided is called the dividend.

Divisor: The number which divides the dividend is called the divisor.

Quotient: When dividend is divided by the divisor, the result of the division is called the quotient.

If large frac{a}{b} is divided by large frac{c}{d}, then large frac{a}{b} is the dividend, large frac{c}{d} is the divisor, and

large frac{a}{b}div frac{c}{d}=frac{a}{b}times left ( frac{c}{d} right )^{-1}=frac{a}{b}times frac{d}{c} is the quotient.

Example:  Divide:

large (i);frac{3}{5}byfrac{4}{25}             large (ii);frac{-8}{9}byfrac{4}{3}                large (iii);frac{-16}{21}byfrac{-4}{3}     large (iv);frac{-8}{13}byfrac{3}{-26}

Solution   large (i);;frac{3}{5}div frac{4}{25}=frac{3}{5}times frac{25}{4}=frac{3times 25}{5times 4}=frac{3times 5}{1times 4}=frac{15}{4}

large (ii);;frac{-8}{9}div frac{4}{3}=frac{-8}{9}times frac{3}{4}=frac{-8times 3}{9times 4}=frac{-2times 1}{3times 1}=frac{-2}{3}

large (iii);;frac{-16}{21}div frac{-4}{3}=frac{-16}{21}times frac{3}{-4}=frac{-16times 3}{21times (-4)}=frac{4times 1}{7times 1}=frac{4}{7}

large (iv);;frac{-8}{13}div frac{3}{-26}=frac{-8}{13}times frac{-26}{3}=frac{(-8)times (-26)}{13times 3}=frac{8times 26}{13times 3}=frac{8times 2}{1times 3}=frac{16}{3}

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of cloth is required for each trouser ?

Right Option : A
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Explanation
Question : 2

Divide the sum of large frac{65}{12} and large frac{12}{7} by their difference.

Right Option : A
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Explanation
Question : 3

Divide:   frac{2}{3}by frac{-7}{12}

Right Option : A
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Explanation
 
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