A pie chart shows that a school library has 240 books distributed by genre. The library receives a donation of 30 biography books. What fraction of the new total number of books will be biographies? Express your answer in its simplest form.
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Worked Solution
Step 1: Find the current number of biography books.
20% of 240 = 0.20 × 240 = 48 books
Step 2: After the donation, new biography count.
48 + 30 = 78 books
Step 3: New total number of books.
240 + 30 = 270 books
Step 4: Write the fraction of biographies.
78/270
Step 5: Simplify. Find GCD of 78 and 270.
78 = 2 × 3 × 13
270 = 2 × 3³ × 5
GCD = 2 × 3 = 6
78 ÷ 6 = 13
270 ÷ 6 = 45
Simplified fraction = 13/45
Correct answer: 13/45
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