NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Adding and subtracting integers

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A library in Brisbane has 64 books in the fiction section and 93 books in the non-fiction section. During a stock update, 27 fiction books were removed due to damage, and 15 non-fiction books were added after a donation.

What is the new total number of books in both sections combined? Provide the exact integer value.

Concept illustrations

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Adding five to negative three. Start at −3. Move five units right to reach 2.-5-4-3-2-1012345+5
Start at −3. Move five units right to reach 2.
Multiplication before addition. In 2 + 3 × 4, multiply 3 × 4 before adding 2. The answer is 14, not 20.2 + 3 × 4Original→2 + 12Multiply first→14Then add
In 2 + 3 × 4, multiply 3 × 4 before adding 2. The answer is 14, not 20.

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The library initially has 64 fiction books and 93 non-fiction books. The total number of books before any changes is 64 + 93.
  2. Calculate the initial total: 64 + 93 = 157 books.
  3. 27 fiction books are removed due to damage. This is a subtraction: 64 - 27.
  4. Perform the subtraction: 64 - 27 = 37 fiction books remaining.
  5. 15 non-fiction books are added after a donation. This is an addition: 93 + 15.
  6. Perform the addition: 93 + 15 = 108 non-fiction books now.
  7. The new total number of books is the sum of the updated fiction and non-fiction sections: 37 + 108.
  8. Perform the final addition: 37 + 108 = 145.
  9. Verify the result using a number line: start at 157, subtract 27 (move left 27 units) to 130, then add 15 (move right 15 units) to 145.
  10. Check the arithmetic: 64 - 27 = 37 (correct), 93 + 15 = 108 (correct), 37 + 108 = 145 (correct).
  11. The new total number of books in both sections combined is 145.
  12. The result is an integer and matches the expected format. No rounding or conversion is needed.

Reference answer: 145

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