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Answer :
To solve this problem, we need to find out what fraction of the total number of patients felt improvement within 3 days after taking the drug.
1. Start with the given fractions:
- The fraction of patients who got relief from taking the drug is [tex]\(\frac{9}{10}\)[/tex].
- The fraction of these relieved patients who felt improvement within 3 days is [tex]\(\frac{5}{6}\)[/tex].
2. Multiply the fractions to find the total fraction of patients who felt improvement:
[tex]\[
\frac{9}{10} \times \frac{5}{6} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60}
\][/tex]
3. Simplify the fraction [tex]\(\frac{45}{60}\)[/tex]:
- Both the numerator (45) and the denominator (60) can be divided by their greatest common divisor, which is 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. Start with the given fractions:
- The fraction of patients who got relief from taking the drug is [tex]\(\frac{9}{10}\)[/tex].
- The fraction of these relieved patients who felt improvement within 3 days is [tex]\(\frac{5}{6}\)[/tex].
2. Multiply the fractions to find the total fraction of patients who felt improvement:
[tex]\[
\frac{9}{10} \times \frac{5}{6} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60}
\][/tex]
3. Simplify the fraction [tex]\(\frac{45}{60}\)[/tex]:
- Both the numerator (45) and the denominator (60) can be divided by their greatest common divisor, which is 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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