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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]\frac{19}{20}=\frac{\square}{\square}[/tex]; [tex]\quad \frac{14}{15}=\frac{\square}{\square}[/tex]

[tex]\frac{19}{20} \square \frac{14}{15}[/tex]

Answer :

To find a common denominator for the fractions [tex]\(\frac{19}{20}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex], follow these steps:

1. Find the Least Common Denominator (LCD):
- The denominators of the two fractions are 20 and 15. The least common denominator is the least common multiple (LCM) of these two numbers. The LCM of 20 and 15 is 60.

2. Rewrite [tex]\(\frac{19}{20}\)[/tex] with the common denominator:
- To convert [tex]\(\frac{19}{20}\)[/tex] to a fraction with a denominator of 60, determine what number [tex]\(20\)[/tex] must be multiplied by to get [tex]\(60\)[/tex]. This number is [tex]\(60 \div 20 = 3\)[/tex].
- Multiply both the numerator and denominator of [tex]\(\frac{19}{20}\)[/tex] by this number:
[tex]\[
\frac{19 \times 3}{20 \times 3} = \frac{57}{60}
\][/tex]

3. Rewrite [tex]\(\frac{14}{15}\)[/tex] with the common denominator:
- Similarly, convert [tex]\(\frac{14}{15}\)[/tex] to a fraction with a denominator of 60. Determine what number [tex]\(15\)[/tex] must be multiplied by to get [tex]\(60\)[/tex]. This number is [tex]\(60 \div 15 = 4\)[/tex].
- Multiply both the numerator and denominator of [tex]\(\frac{14}{15}\)[/tex] by this number:
[tex]\[
\frac{14 \times 4}{15 \times 4} = \frac{56}{60}
\][/tex]

4. Compare the fractions:
- Now that both fractions have the same denominator, compare their numerators:
- [tex]\(\frac{57}{60}\)[/tex] and [tex]\(\frac{56}{60}\)[/tex]

- Since 57 is greater than 56, we have:
[tex]\[
\frac{57}{60} > \frac{56}{60}
\][/tex]
- Therefore, [tex]\(\frac{19}{20} > \frac{14}{15}\)[/tex].

Now let's fill in the answers:
- [tex]\(\frac{19}{20} = \frac{57}{60}\)[/tex];
- [tex]\(\frac{14}{15} = \frac{56}{60}\)[/tex];

The order is:
- [tex]\(\frac{19}{20} > \frac{14}{15}\)[/tex]

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