Mathguru – Help – To find five rational numbers between two given fractions.

1.2 Rational Numbers between Two rational numbers > No. 5(ii)

To find five rational numbers between two given 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.

$Description: \tfrac{3}{4}>\tfrac{2}{4}$ because 3>2.

One way to compare fractions with different denominators is to find a common denominator. To compare $Description: \tfrac{a}{b}$ and $Description: \tfrac{c}{d}$ , these are converted to $Description: \tfrac{ad}{bd}$ and $Description: \tfrac{bc}{bd}$ . Then bd is a common denominator and the numerators ad and bc can be compared.

$Description: \tfrac{2}{3}$ ? $Description: \tfrac{1}{2}$ gives $Description: \tfrac{4}{6}>\tfrac{3}{6}$

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

$Description: \tfrac{5}{18}$ ? $Description: \tfrac{4}{17}$

Multiply 17 by 5 and multiply 18 by 4. Since 85 is greater than 72, $Description: \tfrac{5}{18}>\tfrac{4}{17}$ (Our solved example in mathguru.com uses this concept)

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

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