College

First, rewrite [tex]\frac{12}{25}[/tex] and [tex]\frac{9}{20}[/tex] so that they have a common denominator. Then, use [tex]\ < \ [/tex], [tex]=[/tex], or [tex]\ > \ [/tex] to order [tex]\frac{12}{25}[/tex] and [tex]\frac{9}{20}[/tex].

[tex]\frac{12}{25} = \frac{\square}{\square}; \quad \frac{9}{20} = \frac{\square}{\square}[/tex]

[tex]\frac{12}{25} \quad \square \quad \frac{9}{20}[/tex]

Answer :

To determine which of the fractions [tex]\(\frac{12}{25}\)[/tex] and [tex]\(\frac{9}{20}\)[/tex] is larger, let's first rewrite each fraction with a common denominator.

1. Find the Least Common Denominator (LCD):
The denominators of the two fractions are 25 and 20. The least common denominator of 25 and 20 is 100.

2. Rewrite [tex]\(\frac{12}{25}\)[/tex] with the common denominator of 100:
- First, figure out what you need to multiply 25 by to get 100:
[tex]\[ \frac{100}{25} = 4 \][/tex]
- Multiply both the numerator and the denominator by 4:
[tex]\[ \frac{12 \times 4}{25 \times 4} = \frac{48}{100} \][/tex]

3. Rewrite [tex]\(\frac{9}{20}\)[/tex] with the common denominator of 100:
- Determine what you need to multiply 20 by to get 100:
[tex]\[ \frac{100}{20} = 5 \][/tex]
- Multiply both the numerator and the denominator by 5:
[tex]\[ \frac{9 \times 5}{20 \times 5} = \frac{45}{100} \][/tex]

4. Compare the two fractions [tex]\(\frac{48}{100}\)[/tex] and [tex]\(\frac{45}{100}\)[/tex]:
- Since 48 is greater than 45, we can conclude that:
[tex]\[ \frac{12}{25} > \frac{9}{20} \][/tex]

Therefore, after rewriting the fractions with a common denominator and comparing them, we see that [tex]\(\frac{12}{25} > \frac{9}{20}\)[/tex].