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Selling in stages

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A fund sells $\frac{3}{8}$ of its holding on Monday, then sells $\frac{2}{5}$ of what is left on Tuesday. What fraction of the original holding remains? Give a fraction in lowest terms.

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Hint

The Tuesday sale applies to the remainder, not to the original.

Solution

After Monday the remaining fraction is $1 - \frac{3}{8} = \frac{5}{8}$ .
On Tuesday $\frac{2}{5}$ of that is sold, so $\frac{3}{5}$ is kept.
The remainder is $\frac{5}{8} \times \frac{3}{5}$ ; the $5$ cancels.
What remains is $\frac{3}{8}$ .

Answer: $\frac{3}{8}$

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