Respuesta :
We have the fraction
[tex]\frac{7}{4}[/tex]We want to rewrite it as
[tex]\frac{x}{20}[/tex]Where x is a number that we don't know, but it will turn the fraction equivalent, then we can say that
[tex]\frac{7}{4}=\frac{x}{20}[/tex]We can do a cross multiplication and solve it for x
[tex]\begin{gathered} 4x=7\cdot20 \\ \\ x=\frac{7\cdot20}{4} \end{gathered}[/tex]Then in fact, to discover the new numerator we must do
[tex]\text{ new numerator = }\frac{\text{ old numerator x LCD}}{\text{ old denominator}}[/tex]Let's do it then!
[tex]\begin{gathered} \text{ new numerator =}\frac{7\cdot20}{4} \\ \\ \text{ new numerator }=35 \end{gathered}[/tex]Then
[tex]\frac{7}{4}=\frac{35}{20}[/tex]The equivalent fraction is 35/20
Now for the second question, we can use the logic
[tex]\begin{gathered} \text{ new numerator = }\frac{\text{ 9 x 20}}{10} \\ \\ \text{new numerator = {}18} \end{gathered}[/tex]The equivalent fraction is
[tex]\frac{9}{10}=\frac{18}{20}[/tex]Final answers:
[tex]\begin{gathered} \frac{7}{4}=\frac{35}{20} \\ \\ \frac{9}{10}=\frac{18}{20} \end{gathered}[/tex]