Question

6. Select all that apply: Which inequalities are true? O 10

Answer 1

When sorting fractions without expressing them as decimal values you have to keep in mind that the greater the denominator is, the smaller the value of the fraction.

For

`(5)/(4)>(9)/(10)`

The denominator in the first fraction is smaller than the denominator in the second one, so we know that the value of the first fraction is greater than the value of the second one.

To prove it you may express them as decimal values:

`\begin{gathered} (5)/(4)=1.25 \\ (9)/(10)=0.9 \\ 1.25>0.9 \end{gathered}`

This inequation is true.

For

`(1)/(4)<(3)/(2)`

The denominator of the first fraction is greater than the denominator of the second one → 4>2, this means that the first fraction represents a value smaller than the second one.

This inequation is true

For

`(7)/(8)>(4)/(3)`

The denominator of the first equation is greater than the denominator of the second one 8>3, this means that the value the first fraction represents is less than the value of the second fraction.

This inequality is false.

For

`(3)/(2)<(5)/(7)`

The denominator of the first fraction is less than the denominator of the second one 2<7, this means that the first fraction is greater than the second one, so this inequation is false.