# Question #8d885

Jun 19, 2017

$\frac{4}{9} , \frac{5}{11} , \frac{3}{5}$ (However, there are an infinite number of answers.)

#### Explanation:

$\frac{1}{3} = \overline{.3}$

$\frac{4}{9} = \overline{.4}$

$\frac{5}{11} = \overline{.45}$

$\frac{3}{5} = .6$

$\frac{2}{3} = \overline{.6}$

Jun 19, 2017

Convert to equivalent fractions with bigger denominators.

#### Explanation:

The easiest way to find fractions between given fractions is to convert to equivalent fractions with much bigger denominators,
then you can write down any number of fractions by inspection.

We have $\frac{1}{3} \mathmr{and} \frac{2}{3}$ which are equal to $\textcolor{b l u e}{\frac{10}{30} \mathmr{and} \frac{20}{30}}$

Fractions between these two have numerators from $11 \text{ to } 19$

$\textcolor{b l u e}{\frac{10}{30}} , \frac{11}{30} , \frac{12}{30} , \frac{13}{30} \ldots \ldots . \frac{17}{30} , \frac{18}{30} , \frac{19}{30} , \textcolor{b l u e}{\frac{20}{30}} \text{ } \leftarrow$ (some simplify)

$\frac{1}{3} \mathmr{and} \frac{2}{3}$ are also equal to $\textcolor{b l u e}{\frac{15}{45} \mathmr{and} \frac{30}{45}}$

Between these we have fractions with numerators from $16 \text{ to } 29$

$\textcolor{b l u e}{\frac{15}{45}} , \frac{16}{45} , \frac{17}{45} , \frac{18}{45} \ldots \ldots \ldots \frac{.27}{45} , \frac{28}{45} , \frac{29}{45} , \textcolor{b l u e}{\frac{30}{45}}$

The bigger you choose the denominator, the more choices you have:
$\frac{1}{3} \mathmr{and} \frac{2}{3}$ are equal to $\textcolor{b l u e}{\frac{100}{300} \mathmr{and} \frac{200}{300}}$

Fractions between these two have numerators from $101 \text{ to } 199$

$\textcolor{b l u e}{\frac{100}{300}} , \frac{101}{300} , \frac{102}{300} , \frac{103}{300.} \ldots \ldots \ldots . \frac{.197}{300} , \frac{198}{300} , \frac{199}{300} , \textcolor{b l u e}{\frac{200}{300}}$