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# Ordering Fractions

A fraction is known as a part of the whole and is written in the form of ratio of two numbers. Top one is known as numerator, while bottom one in called denominator. For example: $\frac{4}{5}$, $\frac{11}{2}$ etc.
Here, we shall discuss about ordering fractions.
Ordering Fractions
Ordering of fractions is also known as comparing of fractions. There are two methods which are frequently used for ordering fractions. These methods are:

• Cross-multiplication Method
• Lowest Common Denominator Method

Cross-multiplication Method: This method is used for comparing two fractions only. Follow given steps for ordering of two fractions:
Let us consider two fractions $\frac{3}{5}$ and $\frac{5}{6}$.
Step 1: Multiply numerator of first and denominator of second, like: 3 x 6 = 18.
Step 2: Multiply denominator of first and numerator of second. like: 5 x 5 = 25.
Step 3: Compare the results.
18 < 25
Therefore,
$\frac{3}{5}$ < $\frac{5}{6}$.

Lowest Common Denominator Method: This method is used more often because there is no limitation of applicability with this method, since it can be used for ordering any set of fractions, whether two or more.
Let us consider following fractions $\frac{1}{6}$, $\frac{2}{3}$, $\frac{7}{9}$. Following steps should be followed while ordering two or more fractions by this method.
Step 1:  Evaluate lowest common denominator. In order to do so, find LCM of all the denominators.
Here, denominators are 6, 3 and 9 whose lowest common denominator (LCD) is 18.
Step 2: Convert each fraction with denominator equivalent to LCD.
$\frac{1}{6}$ = $\frac{1 \times 3}{6 \times 3}$ = $\frac{3}{18}$

$\frac{2}{3}$ = $\frac{2 \times 6}{3 \times 6}$ = $\frac{12}{18}$

$\frac{7}{9}$ = $\frac{7 \times 2}{9 \times 2}$ = $\frac{14}{18}$
Step 3: Compare the results and order them.
$\frac{3}{18}$ < $\frac{12}{18}$ < $\frac{14}{18}$
Therefore,
$\frac{1}{6}$ < $\frac{2}{3}$ < $\frac{7}{9}$

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