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Example: Finding Rational Numbers Between Fractions

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Explanation:

 

 

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.

 

http://en.wikipedia.org/wiki/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)

 

 

http://en.wikipedia.org/wiki/Fraction_(mathematics)

 

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.