Question
14 L'hôpital se modernise ! On a décidé de numériser les dossiers papier des patients. On pourra désormais consulter les dossiers à l'ordinateur plutôt que dans les classeurs. Au cours de la première semaine, on numérise 50% des dossiers. Au cours de la 2^e semaine, on numérise (1)/(3) des dossiers restants Quelle fraction irréductible représente les dossiers quil reste encore à numériser par rapport à l'ensemble des dossiers?
Solution
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ArnoldElite · Tutor for 8 years
Answer
### The fraction of dossiers that remains to be digitized is \( \frac{1}{3} \).
Explain
## Step 1: Calculate the fraction of dossiers digitized in the first week<br />### Initially, \( 50\% \) of the dossiers are digitized. This corresponds to \( \frac{50}{100} = \frac{1}{2} \). Therefore, half of the dossiers remain after the first week.<br />## Step 2: Calculate the fraction of dossiers digitized in the second week<br />### In the second week, \( \frac{1}{3} \) of the remaining dossiers (\( \frac{1}{2} \)) are digitized. The fraction digitized is \( \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} \).<br />## Step 3: Determine the fraction of dossiers still not digitized<br />### After two weeks, the total fraction digitized is \( \frac{1}{2} + \frac{1}{6} \). To add these fractions, find a common denominator:<br />\[<br />\frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6}.<br />\]<br />Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \). Thus, \( \frac{2}{3} \) of the dossiers have been digitized, leaving \( 1 - \frac{2}{3} = \frac{1}{3} \) of the dossiers still not digitized.
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