To determine which proportion is false, we need to verify if the given pairs of fractions are equal. We will check each one step-by-step by cross-multiplying.
### Proportion 1:
[tex]\[
\frac{30}{48}=\frac{5}{8}
\][/tex]
Cross-multiply:
[tex]\[
30 \cdot 8 \stackrel{?}{=} 48 \cdot 5
\][/tex]
Calculate both sides:
[tex]\[
240 == 240
\][/tex]
This proportion is true.
### Proportion 2:
[tex]\[
\frac{2}{5}=\frac{10}{15}
\][/tex]
Cross-multiply:
[tex]\[
2 \cdot 15 \stackrel{?}{=} 5 \cdot 10
\][/tex]
Calculate both sides:
[tex]\[
30 == 50
\][/tex]
This proportion is false.
### Proportion 3:
[tex]\[
\frac{9}{21}=\frac{3}{7}
\][/tex]
Cross-multiply:
[tex]\[
9 \cdot 7 \stackrel{?}{=} 21 \cdot 3
\][/tex]
Calculate both sides:
[tex]\[
63 == 63
\][/tex]
This proportion is true.
### Proportion 4:
[tex]\[
\frac{8}{13}=\frac{16}{26}
\][/tex]
Cross-multiply:
[tex]\[
8 \cdot 26 \stackrel{?}{=} 13 \cdot 16
\][/tex]
Calculate both sides:
[tex]\[
208 == 208
\][/tex]
This proportion is true.
Therefore, the false proportion is:
[tex]\[
\frac{2}{5} = \frac{10}{15}
\][/tex]
So, the answer is:
[tex]\[
2
\][/tex]
