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.

$\begin{gathered} \frac{3}{4}=0.75 \\ \frac{6}{7}\cong0.86 \\ \frac{3}{4}>\frac{6}{7}\Rightarrow FALSE \end{gathered}$

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

b.

$\frac{2}{8}>\frac{3}{9}$

For the second one we can start by simplifying the fractions

$\begin{gathered} \frac{2}{8}=\frac{1}{4} \\ \frac{3}{9}=\frac{1}{3} \\ \frac{1}{4}>\frac{1}{3}\Rightarrow FALSE \end{gathered}$

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.

$\frac{2}{5}>\frac{2}{12}$

start by simplifying the fraction that can be simplified

$\begin{gathered} \frac{2}{5}=\frac{2}{5} \\ \frac{2}{12}=\frac{1}{6} \end{gathered}$

find the equivalent to the fractions

$\begin{gathered} \frac{2}{5}=0.4 \\ \frac{1}{6}\cong0.17 \end{gathered}$$\begin{gathered} \frac{2}{5}>\frac{1}{6}\Rightarrow TRUE \\ 0.4>0.17 \end{gathered}$

The comparison is true because 0.4 is greater than 0.17

d.

$\frac{3}{6}>\frac{8}{12}$

start by simplifying the fractions

$\begin{gathered} \frac{3}{6}=\frac{1}{3} \\ \frac{8}{12}=\frac{2}{3} \end{gathered}$

rewrite the expression

$\begin{gathered} \frac{3}{6}>\frac{8}{12} \\ \frac{1}{3}>\frac{2}{3}\Rightarrow FALSE \end{gathered}$

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