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].
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].