Respuesta :
The fractions are [tex]\frac{2}{3}[/tex] and [tex]\frac{1}{3}[/tex]
Solution:
Given, The difference of two fractions is [tex]\frac{1}{3}[/tex]
Let the two factions be [tex]\frac{a}{b}[/tex] and [tex]\frac{c}{d}[/tex] ,
[tex]\text { Where } \frac{a}{b}>\frac{c}{d}[/tex]
By given, difference is [tex]\frac{1}{3}[/tex] , we get
[tex]\text { Then, } \frac{a}{b}-\frac{c}{d}=\frac{1}{3} \rightarrow(1)[/tex]
The sum of these two fractions is 1
[tex]\text { Then, } \frac{a}{b}+\frac{c}{d}=1 \rightarrow(2)[/tex]
The quotient of larger fraction divided by the smaller fraction is 2.
[tex]\text { Then, } \frac{\frac{a}{b}}{\frac{c}{a}}=2 \rightarrow(3)[/tex]
We have to find what are the two fractions
[tex]\text { Now, }(3) \rightarrow \frac{a}{b}=2 \times \frac{c}{d}[/tex]
[tex]\text { So substitute } \frac{a}{b} \text { value in }(2) \text { and }(1)[/tex]
[tex](1) \rightarrow 2 \frac{c}{d}-\frac{c}{d}=\frac{1}{3} \\\\\rightarrow \frac{c}{d}=\frac{1}{3}[/tex]
So, smaller fraction is [tex]\frac{1}{3}[/tex]
[tex]\text { Then from }(3) \rightarrow \frac{a}{b}=2 \times \frac{1}{3} \rightarrow \frac{a}{b}=\frac{2}{3}[/tex]
Hence, the fractions are [tex]\frac{2}{3}[/tex] and [tex]\frac{1}{3}[/tex]
