Question

a group of culinary students baked pies and sampled the results. afterward, the instructor noted what remained. he saw 1/2 of a pie filled with apples, 1/10 of a pie filled with pears, 1/5 of a pie filled with cherries, and 1/5 of a pie filled with mixed berries. how many leftover pies did the instructor see in all?

pies

Explanation:

Step1: Convert to common denominator

To add the fractions \(\frac{1}{2}\), \(\frac{1}{10}\), \(\frac{1}{5}\), and \(\frac{1}{5}\), we first find a common denominator. The least common denominator of 2, 10, and 5 is 10.

• \(\frac{1}{2}=\frac{1\times5}{2\times5}=\frac{5}{10}\)
• \(\frac{1}{10}\) remains \(\frac{1}{10}\)
• \(\frac{1}{5}=\frac{1\times2}{5\times2}=\frac{2}{10}\) (for both the cherry and mixed berry pies)

Step2: Add the fractions

Now we add the converted fractions: \(\frac{5}{10}+\frac{1}{10}+\frac{2}{10}+\frac{2}{10}\).
Adding the numerators: \(5 + 1+2 + 2=10\).
So the sum is \(\frac{10}{10}\).

Step3: Simplify the result

\(\frac{10}{10}=1\).

Answer:

1