To check if the fractions are equivalent or not, we need to make the denominators the same.
So, \(\frac{1}{2}\) and \(\frac{1}{2}\)
Here, denominators are the same but numerators are different. So, \(\frac{2}{3}\) and \(\frac{3}{4}\) are not equivalent.
(b) \(\frac{3}{5}\) and \(\frac{6}{10}\)
Solution:
To check if the fractions are equivalent or not, we need to make the denominators the same.
\(\frac{3}{5}=\frac{3 \times 2}{5 \times 2}=\frac{6}{10}\), and \(\frac{6}{10}=\frac{6}{10}\)
Here, numerators and denominators of both fractions are the same. So, \(\frac{3}{5}\) and \(\frac{6}{10}\) are equivalent.
(c) \(\frac{4}{12}\) and \(\frac{2}{6}\)
Solution:
To check if fractions are equivalent or not, we need to make denominators the same.
\(\frac{4}{12}=\frac{4}{12}\) and \(\frac{2}{6}=\frac{2 \times 2}{6 \times 2}=\frac{4}{12}\)
Here, numerators and denominators of both fractions are the same.
So, \(\frac{4}{12}\) and \(\frac{2}{6}\) are equivalent.
(d) \(\frac{6}{9}\) and \(\frac{1}{3}\)
Solution:
To check if the fractions are equivalent or not, we need to make denominators the same.
\(\frac{6}{9}=\frac{6}{9}\) and \(\frac{1}{3}=\frac{1 \times 3}{3 \times 3}=\frac{3}{9}\)
Here, denominators are the same but numerators are different. So, \(\frac{6}{9}\) and \(\frac{1}{3}\) are not equivalent.