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Equivalent Rational Numbers

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									                      Equivalent Rational Numbers

Equivalent Rational Numbers
Equivalent Rational Numbers are number that the same value but are represented differently. A group of
natural numbers, whole numbers, Integers and Fractions are all the subsets of Rational numbers. So we
define rational numbers, as the numbers which can be expressed in form of p / q, where p and q are the
integers and q <> 0 are all rational numbers. Now we are going to learn about Equivalent Rational
Numbers. We can write rational numbers in any form. As if we write 2/5, its equivalent rational
numbers can be attained by multiplying the numerators and the denominators by the same number and
we get the series of equivalent rational numbers for any given rational numbers. These Rational
Numbers Questions can be infinite in number. So here equivalent rational numbers for 2 / 5 are

                        = (2 * 2) / ( 5 * 2) = 4 /10

                        Or = (2 * 3) / ( 5 * 3) = 6/15

                         Or = (2 * 4) / ( 5 * 4 ) = 8 / 20
and the series goes on. All these rational numbers have their standard form = 2 / 5.



                                      Know More About :- 2 Digit Division with Remainders


    Math.Edurite.com                                                            Page : 1/3
Similarly if the two rational numbers are given to you and you need to find if they are Equivalent
Rational Numbers or not, then we will convert these Rational numbers into their standard form and
observe that if the two rational numbers are equivalent , then they have the same standard form.

 Let us learn it more clearly with an example. Check if 3/12 and 9/36 are the pair of equivalent rational
numbers or not? We first take the rational number 3/12, and convert it into the standard form. We
observe that the HCF of 3 and 12 are 3. So we divide the numerator and the denominator of 3/12 by 3.
We get (3 ÷ 3) / (12 ÷ 3)

 = ¼. Similarly we now take 9 / 36. Taking HCF of 9 and 36, we get 9. So we divide the numerator and
the denominator by 9 and get ( 9 ÷ 9) / ( 36 ÷ 9) = ¼.

 In both the rational numbers 3/12 and 9/36, we get the standard form as ¼. Thus we conclude that the
two rational numbers are equivalent Rational Numbers. The same question can be attempted by
another method. Lets first write the two rational numbers say 3/12 and 9 / 36.

Now we cross multiply such that we get ( 3 * 36 ) and ( 9 * 12 )

                                   Or we get   108      and 108. Both the numbers we get are same, so
the given two rational numbers are equivalent.

 We can form infinite number of rational numbers from the given rational number. Thus we come
across a new rational number which is equivalent to the given rational number.

Ques: find 5 rational numbers equivalent to 2/7?

Sol: We multiply the numerator and the denominator of the given rational number by the same integer
(positive or a negative). Thus we get 4/14, 6/21, 8 / 28, 10/35, 12/42 ……. Endless rational numbers
equivalent to the given number 2/7.



                                Read More About :- Convert a Whole Number to a Fraction


    Math.Edurite.com                                                           Page : 2/3
     Thank You




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