Integers

3

Step 1: We must solve from left to right since division is not associative. Step 2: First solve the bracket: (-36) ÷ 4. Negative ÷ positive = negative. So (-36) ÷ 4 = -9. Step 3: Now divide the result by (-3): (-9) ÷ (-3). Negative ÷ negative = positive. Step 4: (-9) ÷ (-3) = 3. Final Answer: 3. A common mistake is to ignore the brackets and divide in the wrong order.

24

Step 1: Total questions = 15, Correct = 9, so Wrong = 15 - 9 = 6. Step 2: Marks for correct answers = 9 × 4 = 36. Step 3: Marks for wrong answers = 6 × (-2) = -12. Step 4: Total score = 36 + (-12) = 36 - 12 = 24. Final Answer: 24 marks. Students often forget to subtract the wrong answer penalty or miscalculate the number of wrong answers.

-19

Step 1: First simplify -(-19). The negative of a negative number is positive, so -(-19) = +19. Step 2: The additive inverse of any integer 'a' is '-a', because a + (-a) = 0. Step 3: The additive inverse of 19 is -19, because 19 + (-19) = 0. Step 4: Verify: 19 + (-19) = 0. Yes, that is correct. Final Answer: -19. Students often confuse additive inverse with multiplicative inverse (which would be 1/19).

-1

Step 1: We are multiplying (-1) five times. Step 2: (-1) × (-1) = +1 (two negatives = positive). Step 3: 1 × (-1) = -1 (three negatives total so far, product is negative). Step 4: (-1) × (-1) = +1 (four negatives = positive); then +1 × (-1) = -1 (five negatives = negative). Key Rule: (-1)^n = -1 if n is odd, and +1 if n is even. Here n = 5 (odd), so answer = -1. Final Answer: -1. Always count the number of negative signs to determine the sign of the product.