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First, rewrite [tex]\frac{5}{6}[/tex] and [tex]\frac{9}{11}[/tex] so that they have a common denominator. Then, use [tex]\ \textless \ [/tex], [tex]=[/tex], or [tex]\ \textgreater \ [/tex] to order [tex]\frac{5}{6}[/tex] and [tex]\frac{9}{11}[/tex].

[tex]\frac{5}{6} = \frac{\square}{\square} \quad ; \quad \frac{9}{11} = \frac{\square}{\square}[/tex]

[tex]\frac{5}{6} \, \square \, \frac{9}{11}[/tex]



Answer :

GinnyAnswer
To compare the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex], we first need to rewrite them so that they have a common denominator.

1. Find a common denominator:

The denominators of the given fractions are 6 and 11. The common denominator will be the product of these two denominators:
[tex]\[ \text{Common denominator} = 6 \times 11 = 66 \][/tex]

2. Rewrite the fractions with the common denominator:

- For the fraction [tex]\(\frac{5}{6}\)[/tex]:
[tex]\[ \frac{5}{6} = \frac{5 \times 11}{6 \times 11} = \frac{55}{66} \][/tex]

- For the fraction [tex]\(\frac{9}{11}\)[/tex]:
[tex]\[ \frac{9}{11} = \frac{9 \times 6}{11 \times 6} = \frac{54}{66} \][/tex]

So, the fractions [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{9}{11}\)[/tex] can be rewritten with the common denominator 66 as follows:
[tex]\[ \frac{5}{6} = \frac{55}{66} \quad ; \quad \frac{9}{11} = \frac{54}{66} \][/tex]

3. Compare the fractions:

Now, we need to compare the numerators of the two fractions with the common denominator:
[tex]\[ \frac{55}{66} \quad \text{and} \quad \frac{54}{66} \][/tex]

Since 55 is greater than 54, we have:
[tex]\[ \frac{55}{66} > \frac{54}{66} \quad \text{which means} \quad \frac{5}{6} > \frac{9}{11} \][/tex]

Thus, the final answer is:
[tex]\[ \frac{5}{6} > \frac{9}{11} \][/tex]

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