Mathguru – Help – How to compare two given fractions?

9.1 Introduction > No. 8(v)

How to compare two given fractions?

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Explanation:

Inequality (mathematics)

In mathematics, an inequality is a statement how the relative size or order of two objects, or about whether they are the same or not.

§ The notation a < b means that a is less than b.

§ The notation a > b means that a is greater than b.

§ The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

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

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)

Another method of comparing fractions is this: if two fractions have the same numerator, then the fraction with the smaller denominator is the larger fraction. The reasoning is that since, in the first fraction, fewer equal pieces are needed to make up a whole, each piece must be larger.

Also note that every negative number, including negative fractions, is less than zero, and every positive number, including positive fractions, is greater than zero, so every negative fraction is less than any positive fraction.

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.