To determine which fraction is equivalent to [tex]\(\frac{2}{6}\)[/tex], we can follow a few steps to simplify the fraction and find its equivalents.
1. Simplify the fraction [tex]\(\frac{2}{6}\)[/tex]:
First, we need to simplify [tex]\(\frac{2}{6}\)[/tex] by finding the greatest common divisor (GCD) of the numerator and the denominator. The numerator is 2 and the denominator is 6. The GCD of 2 and 6 is 2.
To simplify the fraction, we divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{2}{6} = \frac{2 \div 2}{6 \div 2} = \frac{1}{3}
\][/tex]
So, [tex]\(\frac{1}{3}\)[/tex] is the simplified form of [tex]\(\frac{2}{6}\)[/tex].
2. Find equivalent fractions:
Equivalent fractions are found by multiplying both the numerator and the denominator of the simplified fraction [tex]\(\frac{1}{3}\)[/tex] by the same whole number.
Let's generate some equivalent fractions by multiplying both parts of [tex]\(\frac{1}{3}\)[/tex] by numbers from 1 to 10:
[tex]\[
\frac{1}{3} \times 1 = \frac{1}{3}
\][/tex]
[tex]\[
\frac{1}{3} \times 2 = \frac{2}{6}
\][/tex]
[tex]\[
\frac{1}{3} \times 3 = \frac{3}{9}
\][/tex]
[tex]\[
\frac{1}{3} \times 4 = \frac{4}{12}
\][/tex]
[tex]\[
\frac{1}{3} \times 5 = \frac{5}{15}
\][/tex]
[tex]\[
\frac{1}{3} \times 6 = \frac{6}{18}
\][/tex]
[tex]\[
\frac{1}{3} \times 7 = \frac{7}{21}
\][/tex]
[tex]\[
\frac{1}{3} \times 8 = \frac{8}{24}
\][/tex]
[tex]\[
\frac{1}{3} \times 9 = \frac{9}{27}
\][/tex]
[tex]\[
\frac{1}{3} \times 10 = \frac{10}{30}
\][/tex]
In summary, the fraction [tex]\(\frac{2}{6}\)[/tex] is equivalent to [tex]\(\frac{1}{3}\)[/tex]. The equivalent fractions of [tex]\(\frac{1}{3}\)[/tex] include [tex]\(\frac{1}{3}\)[/tex], [tex]\(\frac{2}{6}\)[/tex], [tex]\(\frac{3}{9}\)[/tex], [tex]\(\frac{4}{12}\)[/tex], [tex]\(\frac{5}{15}\)[/tex], [tex]\(\frac{6}{18}\)[/tex], [tex]\(\frac{7}{21}\)[/tex], [tex]\(\frac{8}{24}\)[/tex], [tex]\(\frac{9}{27}\)[/tex], and [tex]\(\frac{10}{30}\)[/tex].
