maddyhelps

Math 7

Math 7 · Worksheets

Integers

Ten questions of mixed difficulty, covering Integers. Print it, or work through it on screen — the answer key starts on its own page.

All worksheets

Integers

Math 7 · maddyhelps.com

Name
Date
Score
/ 10

Circle the best answer for each question. Show your work in the space provided.

  1. Which expression has the same value as −9 − (−3)?

    1. a) 9 + 3
    2. b) −9 + 3
    3. c) −9 − 3
    4. d) −9 + (−3)

  2. −8 + (−5) + 9 equals

    1. a) 6
    2. b) −4
    3. c) 4
    4. d) −22

  3. Yellow tiles are +1 and red tiles are −1. What integer do 5 red tiles and 3 yellow tiles show?

    1. a) −8
    2. b) 8
    3. c) −2
    4. d) 2

  4. A submarine is 150 m below sea level, at −150 m. It rises 60 m. What is its new position?

    1. a) −90 m
    2. b) −210 m
    3. c) 210 m
    4. d) 90 m

  5. A diver is 18 m under the water, at −18 m. A gull is flying 25 m above the water, directly over her. How many metres higher than the diver is the gull?

    1. a) 7 m
    2. b) 43 m
    3. c) −43 m
    4. d) −7 m

  6. −7 + 4 equals

    1. a) −3
    2. b) −11
    3. c) 11
    4. d) 3

  7. At midnight in Red Deer it was −4 °C. The temperature fell 9 degrees by 6 a.m., then rose 15 degrees by 2 p.m. What was the temperature at 2 p.m.?

    1. a) −13 °C
    2. b) 2 °C
    3. c) −28 °C
    4. d) −2 °C

  8. −4 − 6 equals

    1. a) 2
    2. b) −2
    3. c) −10
    4. d) 10

  9. The sum of two integers is −3. One of them is 8. What is the other?

    1. a) −11
    2. b) 11
    3. c) −5
    4. d) 5

  10. At 7 a.m. in Calgary it was −12 °C. By 3 p.m. it was 5 °C. By how many degrees did the temperature rise?

    1. a) −17 °C
    2. b) 17 °C
    3. c) −7 °C
    4. d) 7 °C

Answer key · Integers

Math 7 · maddyhelps.com

  1. b) −9 + 3 — Subtracting a number is the same as adding its opposite, and the opposite of −3 is 3: −9 − (−3) = −9 + 3 = −6. With tiles, taking 3 red tiles away from 9 red tiles leaves 6 red. −9 + (−3) switches the subtraction to addition but forgets to switch the sign of the 3.
  2. b) −4 — −8 + (−5) = −13, and adding 9 moves 9 to the right, to −4. Treating the (−5) as +5 gives 6, and −22 subtracts the 9 instead of adding it.
  3. c) −2 — Each red and yellow pair is a zero pair, worth 0. Three pairs cancel, which leaves 2 red tiles: −2. Answering 2 gets the size right but the sign wrong — there were more red tiles than yellow — and −8 or 8 counts all the tiles instead of pairing them.
  4. a) −90 m — Rising means adding: −150 + 60 = −90 m, which is still 90 m below the surface. Answering −210 m goes down instead of up, and 90 m drops the sign — the submarine has not reached the surface, so it cannot be above it.
  5. b) 43 m — Subtract the lower position from the higher one: 25 − (−18) = 25 + 18 = 43 m — 18 m up to the surface and 25 m more to the gull. Answering 7 m subtracts 18 from 25 as if the diver were above the water too, and −43 m subtracts in the wrong order.
  6. a) −3 — The 4 positives cancel 4 of the 7 negatives as zero pairs, which leaves −3. On a number line, start at −7 and move 4 to the right. Answering −11 moves left instead, as if the 4 were negative.
  7. b) 2 °C — Falling 9 degrees from −4 takes it to −13 °C, and rising 15 degrees from there passes 0 and ends at 2 °C: −4 − 9 + 15 = 2. Answering −2 keeps the sign of −13, but 15 degrees up is more than the 13 needed to reach 0. −13 °C was the temperature at 6 a.m.
  8. c) −10 — Start at −4 and move 6 more to the left: −10. Answering 2 or −2 finds the gap between 4 and 6, but taking a positive number away from a negative one takes you further below zero.
  9. a) −11 — You need 8 + ? = −3: from 8 it takes −8 to get down to 0 and another −3 to reach −3, so the other number is −11, and 8 + (−11) = −3 ✓. −5 comes from 8 − 3 with a minus sign stuck on, but 8 + (−5) = 3, not −3.
  10. b) 17 °C — The rise is the final temperature minus the starting one: 5 − (−12) = 5 + 12 = 17. On a thermometer it climbs 12 degrees to reach 0, then 5 more. Answering 7 takes 5 from 12 as if both temperatures were on the same side of zero.