Topic Review — Integers and Rational Numbers

Review Questions

1. Adding and subtracting integers. Fluency

   1. 8 + (−3)
   2. −5 + (−7)
   3. 4 − (−6)
   4. −12 − (−5)
   5. −9 + 14
   6. (−3) + (−8) − (−2)
   7. The temperature is −4°C and rises by 11°C. What is the new temperature?
   8. Place in ascending order: −7, 3, −1, −10, 0, 5

2. Multiplying and dividing integers. Fluency

   1. (−4) × 7
   2. (−6) × (−5)
   3. 36 ÷ (−9)
   4. (−48) ÷ (−8)
   5. (−3) × (−4) × 2
   6. (−72) ÷ 9
   7. State the sign of: (−2)⁵
   8. State the sign of: (−3)⁴

3. Operations with rational numbers. Understanding

   1. ½ + ¼
   2. ¾ − ⅙
   3. 2⅓ + 1¾
   4. ⅗ × ⅖
   5. 1½ × 2⅔
   6. ⅞ ÷ ¾
   7. −½ + ¾
   8. −1¼ − (−¾)

4. Order of operations. Understanding

   1. 3 + 4 × 2
   2. (3 + 4) × 2
   3. 20 − 8 ÷ 4 + 3
   4. 4 × (7 − 3)²
   5. 18 ÷ (2 + 4) × 3 − 5
   6. (3 + −2) × (4 − −1)
   7. 2² + 3 × (10 − 4) ÷ 2
   8. (−5)² − 4 × 3 + 10 ÷ 2

5. Mixed integers, rational numbers and order of operations. Problem Solving

   1. A diver is at −12 m. She ascends 7 m, then descends 4 m. What is her final depth?
   2. A company loses $350 per week for 6 weeks, then makes a profit of $800. Write and evaluate an expression to find the overall result.
   3. Evaluate: ½ × (3 + −1)² − ¾
   4. Find the missing number: (−3) × ☐ = −48
   5. Use order of operations to evaluate: 5 × 3² − (12 − 7) + 24 ÷ 8
   6. A recipe uses ⅔ cup of sugar per batch. How many cups are needed for 4½ batches?