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

Which of the following pair of rational number is/are equivalent?
A. $frac{50}{105}, frac{10}{5}$	B. $frac{3}{7} , frac{15}{20}$	C. $frac{5}{6}, frac{20}{24}$	D. $frac{5}{6}, frac{-20}{24}$
Right Option : C
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Question : 2

Find the rational number equivalent to $large frac{3}{7}$
A. $large frac{9}{14}$	B. $large frac{21}{9}$	C. $large frac{7}{3}$	D. $large frac{9}{21}$
Right Option : D
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Question : 3

Determine the smallest equivalent rational number of $large frac{210}{462}$
A. $large frac{7}{11}$	B. $large frac{5}{11}$	C. $large frac{5}{13}$	D. $large frac{7}{9}$
Right Option : B
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