To determine if the given proportion [tex]\(\frac{125 \, \text{mg}}{5 \, \text{mL}} = \frac{250 \, \text{mg}}{10 \, \text{mL}}\)[/tex] is true, let's analyze both sides of the equation step-by-step.
1. Calculate the left side of the proportion:
- The given ratio is [tex]\(\frac{125 \, \text{mg}}{5 \, \text{mL}}\)[/tex].
- To simplify, divide the numerator by the denominator:
[tex]\[
\frac{125 \, \text{mg}}{5 \, \text{mL}} = 25 \, \text{mg/mL}
\][/tex]
2. Calculate the right side of the proportion:
- The given ratio is [tex]\(\frac{250 \, \text{mg}}{10 \, \text{mL}}\)[/tex].
- To simplify, divide the numerator by the denominator:
[tex]\[
\frac{250 \, \text{mg}}{10 \, \text{mL}} = 25 \, \text{mg/mL}
\][/tex]
3. Compare the simplified ratios:
- From our calculations, both sides of the proportion simplify to [tex]\(25 \, \text{mg/mL}\)[/tex].
Since both the left side and the right side of the proportion simplify to the same value, [tex]\(\frac{125 \, \text{mg}}{5 \, \text{mL}} = \frac{250 \, \text{mg}}{10 \, \text{mL}}\)[/tex], we can conclude that the given proportion is true.
Therefore, the answer is True.
