Question

Which comparison is true?

Answer 1

In order to see if the comparisons are true we need to see what each fraction is equal to

a.

`\begin{gathered} (3)/(4)=0.75 \\ (6)/(7)\cong0.86 \\ (3)/(4)>(6)/(7)\Rightarrow FALSE \end{gathered}`

According to this the statement is false, because 0.86 is greater than 0.75

b.

`(2)/(8)>(3)/(9)`

For the second one we can start by simplifying the fractions

`\begin{gathered} (2)/(8)=(1)/(4) \\ (3)/(9)=(1)/(3) \\ (1)/(4)>(1)/(3)\Rightarrow FALSE \end{gathered}`

The expression is false because because when talking about fractions as bigger the number gets on the denominator, smaller the equivalent to the fraction gets.

Meaning that 1/3 is bigger than 1/4.

c.

`(2)/(5)>(2)/(12)`

start by simplifying the fraction that can be simplified

`\begin{gathered} (2)/(5)=(2)/(5) \\ (2)/(12)=(1)/(6) \end{gathered}`

find the equivalent to the fractions

`\begin{gathered} (2)/(5)=0.4 \\ (1)/(6)\cong0.17 \end{gathered}`
`\begin{gathered} (2)/(5)>(1)/(6)\Rightarrow TRUE \\ 0.4>0.17 \end{gathered}`

The comparison is true because 0.4 is greater than 0.17

d.

`(3)/(6)>(8)/(12)`

start by simplifying the fractions

`\begin{gathered} (3)/(6)=(1)/(3) \\ (8)/(12)=(2)/(3) \end{gathered}`

rewrite the expression

`\begin{gathered} (3)/(6)>(8)/(12) \\ (1)/(3)>(2)/(3)\Rightarrow FALSE \end{gathered}`

Since both fractions have the same denominator, and 2 is greater the 1 the expression is false.