Respuesta :
To solve the exercise, first, we are going to write in numerical form the equation shown in fraction models:
[tex]\begin{gathered} \frac{4}{10}+x=\frac{88}{100} \\ \text{ Because} \\ \frac{4}{10}\Rightarrow\text{ There are 4 shaded lines out of the 10 in total} \\ \frac{88}{100}\Rightarrow\text{ There are 88 shaded squares out of the 100 in total} \end{gathered}[/tex]Now, you can solve the equation for x:
[tex]\begin{gathered} \frac{4}{10}+x=\frac{88}{100} \\ \text{ Subtract }\frac{4}{10}\text{ from both sides of the equation} \\ \frac{4}{10}+x-\frac{4}{10}=\frac{88}{100}-\frac{4}{10} \\ x=\frac{88}{100}-\frac{4}{10} \end{gathered}[/tex]To subtract these fractions, you can amplify the fraction 4/10, that is, multiply by 10 in the numerator and denominator of the fraction:
[tex]\frac{4}{10}=\frac{4\cdot10}{10\cdot10}=\frac{40}{100}[/tex]Now that both fractions have the same denominator, it is easier to subtract them, since it is enough to subtract their numerators. So, you have:
[tex]\begin{gathered} x=\frac{88}{100}-\frac{4}{10} \\ x=\frac{88}{100}-\frac{40}{100} \\ x=\frac{88-40}{100} \\ x=\frac{48}{100} \\ \end{gathered}[/tex]Therefore, the fraction that makes the equation true is
[tex]\frac{48}{100}[/tex]and the correct answer is option C.
