To determine which fractions are equivalent to [tex]\(\frac{5}{6}\)[/tex], let's go through each option and check if it simplifies or equals [tex]\(\frac{5}{6}\)[/tex].
1. Option A: [tex]\(\frac{11}{12}\)[/tex]
To compare [tex]\(\frac{5}{6}\)[/tex] and [tex]\(\frac{11}{12}\)[/tex], find a common denominator and see if they are equal.
[tex]\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\][/tex]
Clearly, [tex]\(\frac{11}{12}\)[/tex] is not equal to [tex]\(\frac{10}{12}\)[/tex]. Hence, [tex]\(\frac{11}{12}\)[/tex] is not equivalent to [tex]\(\frac{5}{6}\)[/tex].
2. Option B: [tex]\(\frac{1}{10}\)[/tex]
To determine the equivalence, compare [tex]\(\frac{1}{10}\)[/tex] directly with [tex]\(\frac{5}{6}\)[/tex]:
Clearly, [tex]\(\frac{1}{10}\)[/tex] is a much smaller fraction compared to [tex]\(\frac{5}{6}\)[/tex]. Therefore, [tex]\(\frac{1}{10}\)[/tex] is not equivalent to [tex]\(\frac{5}{6}\)[/tex].
3. Option C: [tex]\(\frac{15}{18}\)[/tex]
Simplify [tex]\(\frac{15}{18}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 3:
[tex]\[
\frac{15 \div 3}{18 \div 3} = \frac{5}{6}
\][/tex]
Since simplifying [tex]\(\frac{15}{18}\)[/tex] results in [tex]\(\frac{5}{6}\)[/tex], [tex]\(\frac{15}{18}\)[/tex] is equivalent to [tex]\(\frac{5}{6}\)[/tex].
4. Option D: [tex]\(\frac{10}{12}\)[/tex]
Simplify [tex]\(\frac{10}{12}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{10 \div 2}{12 \div 2} = \frac{5}{6}
\][/tex]
Since simplifying [tex]\(\frac{10}{12}\)[/tex] results in [tex]\(\frac{5}{6}\)[/tex], [tex]\(\frac{10}{12}\)[/tex] is equivalent to [tex]\(\frac{5}{6}\)[/tex].
In conclusion, the fractions that are equivalent to [tex]\(\frac{5}{6}\)[/tex] are:
- Option C: [tex]\(\frac{15}{18}\)[/tex]
- Option D: [tex]\(\frac{10}{12}\)[/tex]
Therefore, the correct answers are C and D.
