Equivalent Rational Numbers


 
 
Concept Explanation
 

Equivalent Rational Numbers

The rational numbers which represent the same value when converted to the lowest form are called Equivalent Rational Numbers. In case of a fraction if we multiply or divide the numerator and the denominator with the same number we get a rational number whose value is the same as the original fraction when it is converted to the lowest form are called Equivalent Rational Numbers

Equivalent Rational Numbers In Case of Multiplication:

the rational obtained by multiplying the numerator and the denominator of the original rational number is known as Equivalent Rational Numbers In Case of Multiplication.  If frac{p}{q} is a rational number and m is a non-zero integer, then

frac{p}{q}=frac{ptimes m}{qtimes m}

Rational number   frac{ptimes m}{qtimes m}    is a rational number equivalent to   frac{p}{q}  .

Illustration: Find the equivalent rational number for frac{3}{4}

Solution:Let us multiply the numerator and the denominator with 3

frac{3}{4}=frac{3times 3}{4times 3}=frac {9}{12}

Hence frac {9}{12} is equivalent to frac {3}{4}

Equivalent Rational Numbers In Case of Division:

The rational obtained by dividing the numerator and the denominator of the original rational number is known as Equivalent Rational Numbers In Case of Division.  If frac{p}{q} is a rational number and m is a non-zero integer and is a common divisor of p and q, then

frac{p}{q}=frac{pdiv m}{qdiv m}

Rational number   frac{pdiv m}{qdiv m}    is a rational number equivalent to   frac{p}{q}  .

Illustration: Find the equivalent rational number for frac{12}{27}

Solution:Let us divide the numerator and the denominator with 3

frac{12}{27}=frac{12div 3}{27div 3}=frac {4}{9}

Hence frac {4}{9} is equivalent to frac {12}{27}

Illustration: Find four equivalent  to the rational number frac{4}{5}

Solution: Let us fine the equivalent rational numbers

frac{4}{5}=frac{4times 3}{5times 3}=frac {12}{15}

frac{4}{5}=frac{4times 5}{5times 5}=frac {20}{25}

frac{4}{5}=frac{4times -7}{5times -7}=frac {-28}{-35}

frac{4}{5}=frac{4times -12}{5times -12}=frac {-48}{-60}

Hence  frac{12}{15}, frac{20}{25},frac{-28}{-35}, frac{-48}{-60}  are the four equivalent rational number to the rational number frac{4}{5}.

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

The value of x for which the two rational numbers large large frac{2}{x};and;frac{2}{3}  are equivalent, is _____________

Right Option : C
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Question : 2

The value of y for which the two rational numbers large large large frac{4}{y};and;frac{2}{3}  are equivalent, is _____________

Right Option : B
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Explanation
Question : 3

The value of b for which the two rational numbers large large frac{2}{3};and frac{7}{b}  are equivalent, is ____________

Right Option : C
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Explanation
 
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