Question

I need help to:Determine what the 3 sets of numbers have in common.1. 2/5 and 8/202. 12/28 and 21/493. 10/18 and 15/27

Answer 1

Notice that:

(1)

`(8)/(20)=(2\cdot4)/(5\cdot4)=(2)/(5)\text{.}`

Therefore:

`(8)/(20)=(2)/(5)\text{.}`

(2)

`\begin{gathered} (12)/(28)=(3\cdot4)/(7\cdot4)=(3)/(7), \\ (21)/(49)=(3\cdot7)/(7\cdot7)=(3)/(7)\text{.} \end{gathered}`

Therefore:

`(12)/(28)=(21)/(49)\text{.}`

(3)

`\begin{gathered} (10)/(18)=(5\cdot2)/(9\cdot2)=(5)/(9), \\ (15)/(27)=(5\cdot3)/(9\cdot3)=(5)/(9)\text{.} \end{gathered}`

Therefore:

`(10)/(18)=(15)/(27)\text{.}`

Answer: The 3 sets have in common that in each case both fractions represent the same number.