question_answer

Write the fractions. Are all these fractions equivalent?

(a)

(b)

Answer:

(a) In order, the given figures represent the fractions \[\frac{1}{2},\frac{2}{4},\frac{3}{6}\]  and \[\frac{4}{8}\]  respectively.

Now,     \[\frac{2}{4}=\frac{2\div 2}{4\div 2}=\frac{1}{2}\]

\[\frac{3}{6}=\frac{3\div 3}{6\div 3}=\frac{1}{2}\]

\[\frac{4}{8}=\frac{4\div 4}{8\div 4}=\frac{1}{2}\]

So, the fractions are equivalent

(b) In order, the given figures represent the tractions \[\frac{4}{12},\frac{3}{9},\frac{2}{6},\frac{1}{3}\] and \[\frac{6}{15}\] respectively.

Now,      \[\frac{4}{12}=\frac{2\div 2}{4\div 2}=\frac{1}{2}\]

\[\frac{3}{9}=\frac{3\div 3}{9\div 3}=\frac{1}{3}\],

\[\frac{2}{6}=\frac{2\div 2}{6\div 2}=\frac{1}{3}\],

\[\frac{6}{15}=\frac{6\div 3}{15\div 3}=\frac{2}{5}\]

So, \[\frac{4}{12},\frac{3}{9},\frac{2}{6},\frac{1}{3}\] and \[\frac{6}{15}\] are not equivalent.