Question

Each of the following sets of equivalent fractions uses all the digits from $1$ to $9$ only once.

$\frac{3}{6}=\frac{7}{14}=\frac{29}{58}$ ; $\frac{3}{6}=\frac{9}{18}=\frac{27}{54}$ ; $\frac{2}{6}=\frac{3}{9}=\frac{58}{174}$

Find another similar sets

Answer 1

Here we can chose any random value starting from $1$ to $9$

Let us consider a fraction $\frac{1}{2}$in its lowest term. Now according to the question, framing equivalent fractions of $\frac{1}{2}$, we get

$\frac{1}{2}$$=\frac{1\times 2}{2\times 2}=\frac{2}{4}$

$\frac{1}{2}$$=\frac{1\times 3}{2\times 3}=\frac{3}{6}$

$\frac{1}{2}$$=\frac{1\times 79}{2\times 79}=\frac{79}{158}$

Thus, the required set of equivalent fractions is $\frac{2}{4}=\frac{3}{6}=\frac{79}{158}$. Answer