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First, rewrite [tex]\frac{19}{20}[/tex] and [tex]\frac{14}{15}[/tex] so that they have a common denominator. Then, use [tex]\ < \ [/tex], [tex]=[/tex], or [tex]\ > \ [/tex] to order [tex]\frac{19}{20}[/tex] and [tex]\frac{14}{15}[/tex].

[tex]
\[
\begin{array}{c}
\frac{19}{20} = \frac{\square}{\square} \\
\frac{14}{15} = \frac{\square}{\square} \\
\frac{19}{20} \div \frac{14}{15}
\end{array}
\]
[/tex]

Answer :

To compare the fractions [tex]\(\frac{19}{20}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], we need to rewrite them with a common denominator.

1. Finding a Common Denominator:
- The denominators are 20 and 15.
- To find the common denominator, we calculate the least common multiple (LCM) of 20 and 15.
- The LCM of 20 and 15 is 60.

2. Adjusting the Numerators:
- To convert [tex]\(\frac{19}{20}\)[/tex] to a fraction with a denominator of 60:
[tex]\[
\frac{19}{20} = \frac{19 \times 3}{20 \times 3} = \frac{57}{60}
\][/tex]
- To convert [tex]\(\frac{14}{15}\)[/tex] to a fraction with a denominator of 60:
[tex]\[
\frac{14}{15} = \frac{14 \times 4}{15 \times 4} = \frac{56}{60}
\][/tex]

3. Comparing the Fractions:
- Now we have the fractions [tex]\(\frac{57}{60}\)[/tex] and [tex]\(\frac{56}{60}\)[/tex].
- Since [tex]\(57 > 56\)[/tex], we have:
[tex]\[
\frac{57}{60} > \frac{56}{60}
\][/tex]
- Therefore:
[tex]\[
\frac{19}{20} > \frac{14}{15}
\][/tex]

4. Division of the Fractions:
- Finally, we need to divide [tex]\(\frac{19}{20}\)[/tex] by [tex]\(\frac{14}{15}\)[/tex]:
[tex]\[
\frac{19}{20} \div \frac{14}{15} = \frac{19}{20} \times \frac{15}{14} = \frac{19 \times 15}{20 \times 14} = \frac{285}{280} = 1.0178571428571428
\][/tex]

So, the steps can be summarized as:

1. [tex]\(\frac{19}{20} = \frac{57}{60}\)[/tex]
2. [tex]\(\frac{14}{15} = \frac{56}{60}\)[/tex]
3. Comparing them: [tex]\(\frac{57}{60} > \frac{56}{60}\)[/tex], or [tex]\(\frac{19}{20} > \frac{14}{15}\)[/tex]
4. Division result: [tex]\(\frac{19}{20} \div \frac{14}{15} = 1.0178571428571428\)[/tex]

Thus, the ordered fractions and the division result are as follows:
[tex]\[
\frac{19}{20} > \frac{14}{15}
\][/tex]
[tex]\[
\frac{19}{20} \div \frac{14}{15} = 1.0178571428571428
\][/tex]

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Rewritten by : Barada