Topic Review — Integers

Review Questions

1. Order integers from smallest to largest: Fluency

   1. −3, 5, −7, 2, −1, 0
   2. −10, 4, −4, 7, −2
   3. Which is larger: −3 or −7?
   4. Which is smaller: 0 or −5?

2. Add and subtract using a number line: Fluency

   1. −4 + 7
   2. 5 − 9
   3. −3 − 5
   4. −8 + 8
   5. 2 − 10
   6. −6 + 4
   7. −1 − 6
   8. −7 + 12

3. Simplify by removing double signs: Fluency

   1. 3 + (−5)
   2. −4 − (−7)
   3. −2 + (−6)
   4. 8 − (−3)
   5. 0 − (−9)
   6. −5 + (−5)
   7. 10 − (−4)
   8. −3 − (−3)

4. Integer reasoning: Understanding

   1. Which of these calculations cross zero (change sign)? −3 + 2  |  −3 + 5  |  4 − 6  |  −1 + (−4)
   2. True or False: adding a negative number always makes the result smaller.
   3. True or False: subtracting a negative is the same as adding a positive.
   4. Without calculating, is −4 − 8 positive or negative?

5. Integer problem solving: Problem Solving

   1. The temperature is −6°C. It rises by 11°C. What is the new temperature?
   2. A submarine is at −40 m. It rises 25 m. What is its new depth?
   3. A bank account has a balance of −$35. A deposit of $100 is made. What is the new balance?
   4. Find x: x + 9 = 4
   5. Find n: −3 + n = 5

6. Multiply and divide integers: Fluency

   1. (−4) × 7
   2. (−6) × (−5)
   3. 9 × (−3)
   4. (−28) ÷ 4
   5. (−36) ÷ (−6)
   6. 50 ÷ (−10)
   7. (−8) × (−8)
   8. (−3)³

7. Integer multiplication reasoning: Understanding

   1. True or False: (−5)² = −25
   2. Without calculating, is (−2) × (−3) × (−4) positive or negative?
   3. Find the missing number: (−7) × __ = 42
   4. Find the missing number: __ ÷ (−4) = −9

8. Integer multiplication in context: Problem Solving

   1. A business loses $200 per day for 5 days. Express the total loss as an integer.
   2. The temperature drops 4°C per hour for 6 hours. What is the total temperature change?
   3. A lift descends 3 floors per second. After 7 seconds, what is the change in floor level?

9. Order of operations with integers: Understanding

   1. (−3) × 4 − (−6)
   2. (−2)² − 5
   3. 10 − (−3) × 2
   4. −4 × (−2) + (−3) × 3

10. Integer reasoning in context: Problem Solving

    1. The highest point in a valley is 45 m above sea level and the lowest point is 12 m below sea level. What is the difference in height between the two points?
    2. In a quiz, correct answers score +3 and wrong answers score −2. Sam gets 7 correct and 3 wrong. What is Sam’s total score?
    3. The temperature at noon was 6°C. It dropped by 3°C each hour for 4 hours. What was the temperature after 4 hours?