Answer :
To determine which fraction is in its simplest form, we need to simplify each option and see which one cannot be simplified further.
1. Fraction: [tex]\(\frac{5}{10}\)[/tex]
- Find the greatest common divisor (GCD) of 5 and 10. The GCD is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
- Simplified form is [tex]\(\frac{1}{2}\)[/tex].
2. Fraction: [tex]\(\frac{7}{14}\)[/tex]
- Find the greatest common divisor (GCD) of 7 and 14. The GCD is 7.
- Divide both the numerator and the denominator by 7:
[tex]\[
\frac{7}{14} = \frac{7 \div 7}{14 \div 7} = \frac{1}{2}
\][/tex]
- Simplified form is [tex]\(\frac{1}{2}\)[/tex].
3. Fraction: [tex]\(\frac{10}{25}\)[/tex]
- Find the greatest common divisor (GCD) of 10 and 25. The GCD is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{10}{25} = \frac{10 \div 5}{25 \div 5} = \frac{2}{5}
\][/tex]
- Simplified form is [tex]\(\frac{2}{5}\)[/tex].
4. Fraction: [tex]\(\frac{12}{25}\)[/tex]
- Find the greatest common divisor (GCD) of 12 and 25. The GCD is 1 since 12 and 25 have no common factors other than 1.
- Since the GCD is 1, the fraction [tex]\(\frac{12}{25}\)[/tex] is already in its simplest form.
After simplifying all the fractions, we find that [tex]\(\frac{12}{25}\)[/tex] is already in its simplest form without any need for reduction. Therefore, the correct answer is [tex]\(\frac{12}{25}\)[/tex], which corresponds to option d.
1. Fraction: [tex]\(\frac{5}{10}\)[/tex]
- Find the greatest common divisor (GCD) of 5 and 10. The GCD is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
\][/tex]
- Simplified form is [tex]\(\frac{1}{2}\)[/tex].
2. Fraction: [tex]\(\frac{7}{14}\)[/tex]
- Find the greatest common divisor (GCD) of 7 and 14. The GCD is 7.
- Divide both the numerator and the denominator by 7:
[tex]\[
\frac{7}{14} = \frac{7 \div 7}{14 \div 7} = \frac{1}{2}
\][/tex]
- Simplified form is [tex]\(\frac{1}{2}\)[/tex].
3. Fraction: [tex]\(\frac{10}{25}\)[/tex]
- Find the greatest common divisor (GCD) of 10 and 25. The GCD is 5.
- Divide both the numerator and the denominator by 5:
[tex]\[
\frac{10}{25} = \frac{10 \div 5}{25 \div 5} = \frac{2}{5}
\][/tex]
- Simplified form is [tex]\(\frac{2}{5}\)[/tex].
4. Fraction: [tex]\(\frac{12}{25}\)[/tex]
- Find the greatest common divisor (GCD) of 12 and 25. The GCD is 1 since 12 and 25 have no common factors other than 1.
- Since the GCD is 1, the fraction [tex]\(\frac{12}{25}\)[/tex] is already in its simplest form.
After simplifying all the fractions, we find that [tex]\(\frac{12}{25}\)[/tex] is already in its simplest form without any need for reduction. Therefore, the correct answer is [tex]\(\frac{12}{25}\)[/tex], which corresponds to option d.