Answer: Fraction of all eligible voters voted for Shelly is [tex]\dfrac{3}{20}[/tex] .
Morgan received the most votes .
Step-by-step explanation:
Given : The fraction of all eligible voters cast votes =[tex]\dfrac{1}{2}[/tex]
The fraction of votes received by Shelly = [tex]\dfrac{3}{10}[/tex] (1)
Now, the fraction of all eligible voters voted for Shelly is given by :_
[tex]\dfrac{3}{10}\times\dfrac{1}{2}=\dfrac{3}{20}[/tex]
Thus, the fraction of all eligible voters voted for Shelly is [tex]\dfrac{3}{20}[/tex] .
The fraction of vote received by Morgan= [tex]\dfrac{5}{8}[/tex] (2)
To compare the fractions given in (1) and (2), we need to find least common multiple of 10 and 8 .
LCM (10, 8)=40
Now, make denominator 40 (to make equivalent fraction) in (1), (2) we get
Fraction of all eligible voters voted for Shelly = [tex]\dfrac{3\times4}{10\times4}=\dfrac{12}{40}[/tex]
Fraction of all eligible voters voted for Morgan =[tex]\dfrac{5\times5}{8\times5}=\dfrac{25}{40}[/tex]
Since, [tex]\dfrac{25}{40}>\dfrac{12}{40}[/tex] [By comparing numerators]
Therefore, Morgan received the most votes .
