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Example: Finding Rational Numbers Between Fractions

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Rational number


In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. (Our solved example in mathguru.com uses this concept)

Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q.

The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number.




Comparing fractions


Comparing fractions with the same denominator only requires comparing the numerators.

 because 3>2.

One way to compare fractions with different denominators is to find a common denominator. To compare  and, these are converted to  and . Then bd is a common denominator and the numerators ad and bc can be compared.

 ?  gives 

As a short cut, known as "cross multiplying", you can just compare ad and bc, without computing the denominator.


Multiply 17 by 5 and multiply 18 by 4. Since 85 is greater than 72, (Our solved example in mathguru.com uses this concept)





The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.