To determine the order of the fractions [tex]\(\frac{3}{4}\)[/tex], [tex]\(\frac{5}{6}\)[/tex], [tex]\(\frac{16}{25}\)[/tex], and [tex]\(\frac{9}{15}\)[/tex] from smallest to largest, let’s label the fractions as given:
[tex]\[
A = \frac{3}{4}, \quad B = \frac{5}{6}, \quad C = \frac{16}{25}, \quad D = \frac{9}{15}
\][/tex]
First, let's list each fraction with its decimal equivalent to compare their sizes:
1. [tex]\(\frac{9}{15}\)[/tex] label D converts to [tex]\(0.6\)[/tex]
2. [tex]\(\frac{16}{25}\)[/tex] label C converts to [tex]\(0.64\)[/tex]
3. [tex]\(\frac{3}{4}\)[/tex] label A converts to [tex]\(0.75\)[/tex]
4. [tex]\(\frac{5}{6}\)[/tex] label B converts to [tex]\(0.833...\)[/tex]
After converting the fractions to their decimal forms, we can compare and order them:
1. The smallest is [tex]\( \frac{9}{15} \)[/tex] (0.6), so we label this D.
2. The next fraction is [tex]\( \frac{16}{25} \)[/tex] (0.64), we label this C.
3. Followed by [tex]\( \frac{3}{4} \)[/tex] (0.75), we label this A.
4. Finally, the largest is [tex]\( \frac{5}{6} \)[/tex] (0.833...), we label this B.
So, putting the labels in order from the smallest to the largest fraction, we get:
[tex]\[
D, \quad C, \quad A, \quad B
\][/tex]
Thus, the fractions in order of size from smallest to largest, using their labels, are:
[tex]\[
\boxed{D} \quad \boxed{C} \quad \boxed{A} \quad \boxed{B}
\][/tex]
