Question

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

Answer 1

Given:

The fractions are,

`(2)/(3),(3)/(7),(7)/(19)`

To order: From least to greatest.

Step-by-step explanation:

Since the denominator is unequal

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

`\begin{gathered} LCM=3*7*19 \\ =399 \end{gathered}`

Let us make all the denominators 399.

`\begin{gathered} (2)/(3)*(133)/(133)=(266)/(399) \\ (3)/(7)*(57)/(57)=(171)/(399) \\ (7)/(19)*(21)/(21)=(147)/(399) \end{gathered}`

Since,

`147<171<266`

Therefore, we can write

`(7)/(19)\lt(3)/(7)\lt(2)/(3)`

Therefore, the numbers from least to greatest is,

`(7)/(19),(3)/(7),(2)/(3)`

Final answer:

`(7)/(19),(3)/(7),(2)/(3)`