To determine which fractions among [tex]\(\frac{7}{21}\)[/tex], [tex]\(\frac{3}{12}\)[/tex], [tex]\(\frac{2}{6}\)[/tex], and [tex]\(\frac{3}{3}\)[/tex] are equivalent to [tex]\(\frac{1}{3}\)[/tex], we need to compare each given fraction against [tex]\(\frac{1}{3}\)[/tex]. Fractions are equivalent if they have the same value when reduced to their simplest form.
1. Examine [tex]\(\frac{7}{21}\)[/tex]
- Simplify [tex]\(\frac{7}{21}\)[/tex]:
[tex]\[
\frac{7}{21} = \frac{7 \div 7}{21 \div 7} = \frac{1}{3}
\][/tex]
- Since the simplified form is [tex]\(\frac{1}{3}\)[/tex], [tex]\(\frac{7}{21}\)[/tex] is equivalent to [tex]\(\frac{1}{3}\)[/tex].
2. Examine [tex]\(\frac{3}{12}\)[/tex]
- Simplify [tex]\(\frac{3}{12}\)[/tex]:
[tex]\[
\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}
\][/tex]
- The simplified form is [tex]\(\frac{1}{4}\)[/tex], which is not equal to [tex]\(\frac{1}{3}\)[/tex]. Therefore, [tex]\(\frac{3}{12}\)[/tex] is not equivalent to [tex]\(\frac{1}{3}\)[/tex].
3. Examine [tex]\(\frac{2}{6}\)[/tex]
- Simplify [tex]\(\frac{2}{6}\)[/tex]:
[tex]\[
\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\][/tex]
- Since the simplified form is [tex]\(\frac{1}{3}\)[/tex], [tex]\(\frac{2}{6}\)[/tex] is equivalent to [tex]\(\frac{1}{3}\)[/tex].
4. Examine [tex]\(\frac{3}{3}\)[/tex]
- Simplify [tex]\(\frac{3}{3}\)[/tex]:
[tex]\[
\frac{3}{3} = \frac{3 \div 3}{3 \div 3} = \frac{1}{1} = 1
\][/tex]
- The simplified form is [tex]\(1\)[/tex], which is not equal to [tex]\(\frac{1}{3}\)[/tex]. Therefore, [tex]\(\frac{3}{3}\)[/tex] is not equivalent to [tex]\(\frac{1}{3}\)[/tex].
After examining all the given fractions, we find that the fractions which are equivalent to [tex]\(\frac{1}{3}\)[/tex] are:
[tex]\[
\boxed{\frac{7}{21} \text{ and } \frac{2}{6}}
\][/tex]
