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)

$\frac{8}{20}=\frac{2\cdot4}{5\cdot4}=\frac{2}{5}\text{.}$

Therefore:

$\frac{8}{20}=\frac{2}{5}\text{.}$

(2)

$\begin{gathered} \frac{12}{28}=\frac{3\cdot4}{7\cdot4}=\frac{3}{7}, \\ \frac{21}{49}=\frac{3\cdot7}{7\cdot7}=\frac{3}{7}\text{.} \end{gathered}$

Therefore:

$\frac{12}{28}=\frac{21}{49}\text{.}$

(3)

$\begin{gathered} \frac{10}{18}=\frac{5\cdot2}{9\cdot2}=\frac{5}{9}, \\ \frac{15}{27}=\frac{5\cdot3}{9\cdot3}=\frac{5}{9}\text{.} \end{gathered}$

Therefore:

$\frac{10}{18}=\frac{15}{27}\text{.}$

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