NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Real numbers

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A library in Adelaide has a collection of 75 books, of which 69 are fiction. What is the exact fraction of non-fiction books in the collection?

Express your answer in simplest form.

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Rational numbers inside the real numbers. Rational and irrational numbers are disjoint parts of the real numbers. The examples 4 and 1/2 are rational; √2 and π are irrational.Real numbersRationalIrrational4 1/2√2 π
Rational and irrational numbers are disjoint parts of the real numbers. The examples 4 and 1/2 are rational; √2 and π are irrational.

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Worked solution

  1. The library has 75 books in total, and 69 are fiction.
  2. To find the number of non-fiction books, subtract the fiction books from the total: 75 - 69 = 6.
  3. The fraction of non-fiction books is the number of non-fiction books divided by the total number of books: 6 / 75.
  4. Simplify the fraction 6/75 by finding the greatest common divisor (GCD) of 6 and 75. The GCD of 6 and 75 is 3.
  5. Divide both numerator and denominator by 3: (6 ÷ 3) / (75 ÷ 3) = 2 / 25.
  6. The fraction 2/25 is in simplest form because 2 and 25 have no common factors other than 1.
  7. Verify the result: 2/25 = 0.08, and 0.08 × 75 = 6, which matches the number of non-fiction books.
  8. The exact fraction of non-fiction books is 2/25.

Reference answer: 2/25

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