To find the unknown quotient that makes the equation [tex]\(1 \frac{7}{8} = \text{unknown quotient}\)[/tex] true, we need to determine what [tex]\(1 \frac{7}{8}\)[/tex] equals in decimal form.
First, let's convert the mixed number [tex]\(1 \frac{7}{8}\)[/tex] to an improper fraction:
[tex]\[ 1 \frac{7}{8} = 1 + \frac{7}{8} = \frac{8}{8} + \frac{7}{8} = \frac{15}{8} \][/tex]
Next, we convert [tex]\(\frac{15}{8}\)[/tex] to its decimal form. Dividing 15 by 8 gives:
[tex]\[ 15 \div 8 = 1.875 \][/tex]
Now we need to identify the number from the list that matches this value. The list is:
[tex]\[
\begin{array}{ll}
1.875 & 0.583 \\
1.87 \overline{5} & 0.58 \overline{3}=\frac{7}{12} \\
\hline 1 . \overline{875} & 0.5 \overline{83}
\end{array}
\][/tex]
Looking at the numbers provided, we see that [tex]\(1.875\)[/tex] matches our calculated decimal exactly.
So, the number for the unknown quotient that makes the equation true is:
[tex]\[ \boxed{1.875} \][/tex]
