question_answer

Check whether the given fractions are equivalent:

(a) \[\frac{5}{9},\frac{30}{54}\]

(b) \[\frac{3}{10},\frac{12}{50}\]

(c) \[\frac{7}{13},\frac{5}{11}\]

Answer:

By the cross multiplication, we have

(a) From \[\frac{5}{9},\frac{30}{54}\]

\[5\times 54=270\]

and       \[30\times 9=270\]

So,       \[5\times 57=30\times 9\]

Thus \[\frac{5}{9}\] and \[\frac{30}{54}\] are equivalent fractions.

(b) From \[\frac{3}{10},\frac{12}{50}\]

\[3\times 50=150\]

and       \[10\times 12=120\]

So,       \[3\times 50\ne 10\times 12\]

Thus \[\frac{3}{10}\] and \[\frac{12}{50}\] are not equivalent fractions.

(c) From \[\frac{7}{13},\frac{5}{11}\]

\[7\times 11=77\]

and       \[13\times 5=65\]

So,       \[7\times 11\ne 13\times 5\]

Thus \[\frac{7}{13}\] and \[\frac{5}{11}\] are not equivalent fractions.