To determine the total amount of drugs mixed together, we need to add the given fractions: [tex]\(\frac{2}{5}\)[/tex], [tex]\(\frac{5}{3}\)[/tex], and [tex]\(\frac{9}{3}\)[/tex]. Let's work through this step by step.
1. Identifying the Fractions:
- Drug A: [tex]\(\frac{2}{5}\)[/tex]
- Drug B: [tex]\(\frac{5}{3}\)[/tex]
- Drug C: [tex]\(\frac{9}{3}\)[/tex]
2. Expressing Fractions with a Common Denominator:
To add these fractions, we need a common denominator. The lowest common denominator (LCD) of the denominators 5 and 3 is 15.
3. Converting Fractions to the Common Denominator:
- Convert [tex]\(\frac{2}{5}\)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\][/tex]
- Convert [tex]\(\frac{5}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{5}{3} = \frac{5 \times 5}{3 \times 5} = \frac{25}{15}
\][/tex]
- Convert [tex]\(\frac{9}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[
\frac{9}{3} = \frac{9 \times 5}{3 \times 5} = \frac{15}{5} = 3 \quad \text{and} \quad 3 = 3 \times \frac{5}{5} = \frac{15}{5} = \frac{45}{15}
\][/tex]
4. Adding the Fractions:
Now that the fractions have a common denominator, we can add them directly:
[tex]\[
\frac{6}{15} + \frac{25}{15} + \frac{45}{15}
\][/tex]
Combine the numerators over the common denominator:
[tex]\[
\frac{6 + 25 + 45}{15} = \frac{76}{15}
\][/tex]
5. Simplified Form:
The fraction [tex]\(\frac{76}{15}\)[/tex] is already in its simplest form.
6. Conclusion:
The total amount of the mixed drugs is:
[tex]\[
\frac{2}{5} + \frac{5}{3} + \frac{9}{3} = \frac{76}{15}
\][/tex]
Thus, the total amount of drugs mixed together, in its simplest form, is [tex]\(\frac{76}{15}\)[/tex]. The lowest common denominator (LCD) we used to solve this was 15.
