Question

7) Coloque o sinal de maior (>) ou menor (<) entre cada par de frações, nas situações abaixo.
1/5 e 1/3
2/7 e 3/9
3/4 e 1/2 vale 90.000.000​

Answer 1

$\boxed{\begin{array}{l}\tt a)~\begin{array}{c|l}\sf3,5&\sf3\\\sf1,5&\sf5\\\sf1,1\end{array}\\\sf m\cdot m\cdot c(3,5)=3\cdot5=15\\\sf\dfrac{1}{5}=\dfrac{3}{15}~~~\dfrac{1}{3}=\dfrac{5}{15}\\\\\sf \dfrac{3}{15}<\dfrac{5}{15}\implies \dfrac{1}{5}<\dfrac{1}{3}\end{array}}$

$\boxed{\begin{array}{l}\tt b)~\begin{array}{c|l}\sf7,9&\sf3\\\sf7,3&\sf3\\\sf7,1&\sf7\\\sf1,1\end{array}\\\sf m\cdot m\cdot c(7,9)=3\cdot3\cdot7=63\\\sf\dfrac{2}{7}=\dfrac{18}{63}~~~\dfrac{3}{9}=\dfrac{27}{63}\\\\\sf\dfrac{18}{63}<\dfrac{27}{63}\implies\dfrac{2}{7}<\dfrac{3}{9}\end{array}}$

$\large\boxed{\begin{array}{l}\tt c)~\begin{array}{c|l}\sf4,2&\sf2\\\sf2,1&\sf2\\\sf1,1\end{array}\\\sf m\cdot m\cdot c~(4,2)=2\cdot2=4\\\sf\dfrac{1}{2}=\dfrac{2}{4}\\\\\sf\dfrac{3}{4}>\dfrac{2}{4}\implies\dfrac{3}{4}>\dfrac{1}{2}\end{array}}$