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.

- 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.

Here, denominators are 6, 3 and 9 whose lowest common denominator (LCD) is 18.

$\frac{1}{6}$ = $\frac{1 \times 3}{6 \times 3}$ = $\frac{3}{18}$

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

$\frac{7}{9}$ = $\frac{7 \times 2}{9 \times 2}$ = $\frac{14}{18}$**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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