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Answer :
Let's solve this problem step-by-step:
1. Identify the fractions given in the problem:
- The fraction of patients who felt relief after taking the drug is [tex]\(\frac{9}{10}\)[/tex].
- The fraction of those relieved patients who felt improvement within 3 days is [tex]\(\frac{5}{6}\)[/tex].
2. Calculate the fraction of the total number of patients who felt improvement within 3 days:
- To find this, multiply the two fractions together:
[tex]\[
\frac{9}{10} \times \frac{5}{6} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60}
\][/tex]
3. 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]\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4}
\][/tex]
So, 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].
1. Identify the fractions given in the problem:
- The fraction of patients who felt relief after taking the drug is [tex]\(\frac{9}{10}\)[/tex].
- The fraction of those relieved patients who felt improvement within 3 days is [tex]\(\frac{5}{6}\)[/tex].
2. Calculate the fraction of the total number of patients who felt improvement within 3 days:
- To find this, multiply the two fractions together:
[tex]\[
\frac{9}{10} \times \frac{5}{6} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60}
\][/tex]
3. 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]\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4}
\][/tex]
So, 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].
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