Here are four fractions labeled A, B, C, and D.

[tex]\[
\begin{array}{cccc}
\frac{3}{4} & \frac{5}{6} & \frac{16}{25} & \frac{9}{15} \\
A & B & C & D
\end{array}
\][/tex]

Using the labels A, B, C, and D, write the fractions in order of size. Start with the smallest fraction.

[tex]\[
\square \\
\square \\
\square \\
\square
\][/tex]



Answer :

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]