Answer :
To solve this problem, we need to find the fraction of the total number of patients in the study who felt improvement within 3 days of taking the drug.
1. Understand the problem:
- We know that 9 out of 10 patients (which is [tex]\(\frac{9}{10}\)[/tex]) who took the drug found relief.
- Out of these patients who found relief, 5 out of 6 of them (which is [tex]\(\frac{5}{6}\)[/tex]) felt improvement within 3 days.
2. Calculate the overall fraction of patients who felt improvement within 3 days:
- We need to multiply the two fractions to find the fraction of the total number of patients who felt improvement within 3 days:
[tex]\[
\text{Fraction of total patients with improvement} = \frac{9}{10} \times \frac{5}{6}
\][/tex]
3. Perform the multiplication:
- Multiply the numerators: [tex]\(9 \times 5 = 45\)[/tex]
- Multiply the denominators: [tex]\(10 \times 6 = 60\)[/tex]
- So, the fraction is [tex]\(\frac{45}{60}\)[/tex].
4. Simplify the fraction:
- To simplify [tex]\(\frac{45}{60}\)[/tex], find the greatest common divisor (GCD) of 45 and 60, which is 15.
- Divide both the numerator and the denominator by 15:
[tex]\[
\frac{45 ÷ 15}{60 ÷ 15} = \frac{3}{4}
\][/tex]
Therefore, the fraction of the total number of patients in the study who felt improvement within 3 days of taking the drug is [tex]\(\frac{3}{4}\)[/tex].
The correct answer is [tex]\(\frac{3}{4}\)[/tex].
1. Understand the problem:
- We know that 9 out of 10 patients (which is [tex]\(\frac{9}{10}\)[/tex]) who took the drug found relief.
- Out of these patients who found relief, 5 out of 6 of them (which is [tex]\(\frac{5}{6}\)[/tex]) felt improvement within 3 days.
2. Calculate the overall fraction of patients who felt improvement within 3 days:
- We need to multiply the two fractions to find the fraction of the total number of patients who felt improvement within 3 days:
[tex]\[
\text{Fraction of total patients with improvement} = \frac{9}{10} \times \frac{5}{6}
\][/tex]
3. Perform the multiplication:
- Multiply the numerators: [tex]\(9 \times 5 = 45\)[/tex]
- Multiply the denominators: [tex]\(10 \times 6 = 60\)[/tex]
- So, the fraction is [tex]\(\frac{45}{60}\)[/tex].
4. Simplify the fraction:
- To simplify [tex]\(\frac{45}{60}\)[/tex], find the greatest common divisor (GCD) of 45 and 60, which is 15.
- Divide both the numerator and the denominator by 15:
[tex]\[
\frac{45 ÷ 15}{60 ÷ 15} = \frac{3}{4}
\][/tex]
Therefore, the fraction of the total number of patients in the study who felt improvement within 3 days of taking the drug is [tex]\(\frac{3}{4}\)[/tex].
The correct answer is [tex]\(\frac{3}{4}\)[/tex].
