The correct answer between all the choices given is the first choice or letter A, which is 1/2. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.
Answer:
The answer is the option a
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
we have
[tex]\frac{6}{10}> (\ ) > \frac{1}{3}[/tex]
we know that
In order to compare fractions of different denominator, we are going to multiply each of the fractions by a unit fraction, to obtain a common denominator
Multiply [tex]\frac{6}{10}[/tex] by [tex]\frac{6}{6}[/tex]
[tex](6/6)*\frac{6}{10}=\frac{36}{60}[/tex]
Multiply [tex]\frac{1}{3}[/tex] by [tex]\frac{20}{20}[/tex]
[tex](20/20)*\frac{1}{3}=\frac{20}{60}[/tex]
Verify each case
case a) we have [tex]\frac{1}{2}[/tex]
Multiply [tex]\frac{1}{2}[/tex] by [tex]\frac{30}{30}[/tex]
[tex](30/30)*\frac{1}{2}=\frac{30}{60}[/tex]
substitute in the expression
[tex]\frac{36}{60}> \frac{30}{60} > \frac{20}{60}[/tex] ------> is true
The fraction [tex]\frac{1}{2}[/tex] is a solution
case b) we have [tex]\frac{1}{4}[/tex]
Multiply [tex]\frac{1}{4}[/tex] by [tex]\frac{15}{15}[/tex]
[tex](15/15)*\frac{1}{4}=\frac{15}{60}[/tex]
substitute in the expression
[tex]\frac{36}{60}> \frac{15}{60} > \frac{20}{60}[/tex] ------> is not true
The fraction [tex]\frac{1}{4}[/tex] is not a solution
case c) we have [tex]\frac{2}{3}[/tex]
Multiply [tex]\frac{2}{3}[/tex] by [tex]\frac{20}{20}[/tex]
[tex](20/20)*\frac{2}{3}=\frac{40}{60}[/tex]
substitute in the expression
[tex]\frac{36}{60}> \frac{40}{60} > \frac{20}{60}[/tex] ------> is not true
The fraction [tex]\frac{2}{3}[/tex] is not a solution
case d) we have [tex]\frac{3}{4}[/tex]
Multiply [tex]\frac{3}{4}[/tex] by [tex]\frac{15}{15}[/tex]
[tex](15/15)*\frac{3}{4}=\frac{45}{60}[/tex]
substitute in the expression
[tex]\frac{36}{60}> \frac{45}{60} > \frac{20}{60}[/tex] ------> is not true
The fraction [tex]\frac{3}{4}[/tex] is not a solution
