Answer :
To determine which fraction is already reduced to its lowest terms, we need to check each fraction and simplify them if possible. A fraction is in lowest terms when the greatest common divisor (GCD) of its numerator and denominator is 1.
Let's look at each fraction:
1. Fraction: [tex]\(\frac{5}{10}\)[/tex]
- The GCD of 5 and 10 is 5.
- Simplifying: [tex]\(\frac{5}{10} = \frac{5 ÷ 5}{10 ÷ 5} = \frac{1}{2}\)[/tex]
2. Fraction: [tex]\(\frac{24}{30}\)[/tex]
- The GCD of 24 and 30 is 6.
- Simplifying: [tex]\(\frac{24}{30} = \frac{24 ÷ 6}{30 ÷ 6} = \frac{4}{5}\)[/tex]
3. Fraction: [tex]\(\frac{17}{18}\)[/tex]
- The GCD of 17 and 18 is 1.
- This fraction is already in its lowest terms: [tex]\(\frac{17}{18}\)[/tex]
4. Fraction: [tex]\(\frac{6}{33}\)[/tex]
- The GCD of 6 and 33 is 3.
- Simplifying: [tex]\(\frac{6}{33} = \frac{6 ÷ 3}{33 ÷ 3} = \frac{2}{11}\)[/tex]
From this, we can see that [tex]\(\frac{17}{18}\)[/tex] has a GCD of 1 for its numerator and denominator, indicating that it is already reduced to the lowest terms.
Therefore, the fraction that is already in its lowest terms is [tex]\(\frac{17}{18}\)[/tex].
Let's look at each fraction:
1. Fraction: [tex]\(\frac{5}{10}\)[/tex]
- The GCD of 5 and 10 is 5.
- Simplifying: [tex]\(\frac{5}{10} = \frac{5 ÷ 5}{10 ÷ 5} = \frac{1}{2}\)[/tex]
2. Fraction: [tex]\(\frac{24}{30}\)[/tex]
- The GCD of 24 and 30 is 6.
- Simplifying: [tex]\(\frac{24}{30} = \frac{24 ÷ 6}{30 ÷ 6} = \frac{4}{5}\)[/tex]
3. Fraction: [tex]\(\frac{17}{18}\)[/tex]
- The GCD of 17 and 18 is 1.
- This fraction is already in its lowest terms: [tex]\(\frac{17}{18}\)[/tex]
4. Fraction: [tex]\(\frac{6}{33}\)[/tex]
- The GCD of 6 and 33 is 3.
- Simplifying: [tex]\(\frac{6}{33} = \frac{6 ÷ 3}{33 ÷ 3} = \frac{2}{11}\)[/tex]
From this, we can see that [tex]\(\frac{17}{18}\)[/tex] has a GCD of 1 for its numerator and denominator, indicating that it is already reduced to the lowest terms.
Therefore, the fraction that is already in its lowest terms is [tex]\(\frac{17}{18}\)[/tex].
