Question

Order 2/3, 3/7, 7/19 From least to greatest

Answer 1

Given:

The fractions are,

$\frac{2}{3},\frac{3}{7},\frac{7}{19}$

To order: From least to greatest.

Explanation:

Since the denominator is unequal

Let us find the LCM of 3, 7, and 19.

$\begin{gathered} LCM=3\times7\times19 \\ =399 \end{gathered}$

Let us make all the denominators 399.

$\begin{gathered} \frac{2}{3}\times\frac{133}{133}=\frac{266}{399} \\ \frac{3}{7}\times\frac{57}{57}=\frac{171}{399} \\ \frac{7}{19}\times\frac{21}{21}=\frac{147}{399} \end{gathered}$

Since,

$147<171<266$

Therefore, we can write

$\frac{7}{19}\lt\frac{3}{7}\lt\frac{2}{3}$

Therefore, the numbers from least to greatest is,

$\frac{7}{19},\frac{3}{7},\frac{2}{3}$

Final answer:

$\frac{7}{19},\frac{3}{7},\frac{2}{3}$