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Math 9

Math 9 · Worksheets

Rational numbers

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

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Rational numbers

Math 9 · maddyhelps.com

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

  1. −2.4 − (−3.1) × 2 equals

    1. a) 3.8
    2. b) 1.4
    3. c) −11.0
    4. d) −8.6

  2. Which number lies between −1/2 and −1/4?

    1. a) 0.3
    2. b) −0.6
    3. c) −0.2
    4. d) −0.3

  3. −3/4 + 1/2 equals

    1. a) −5/4
    2. b) 1/4
    3. c) −2/6
    4. d) −1/4

  4. −2/3 ÷ 4/9 equals

    1. a) −3/2
    2. b) 3/2
    3. c) −8/27
    4. d) −2/3

  5. (−1.5) × (−4) equals

    1. a) −6
    2. b) 0.6
    3. c) 6
    4. d) −5.5

  6. Which of these rational numbers is greatest?

    1. a) −0.5
    2. b) −2/3
    3. c) −3/4
    4. d) −0.45

  7. A pond's water level dropped 3/8 m each week for 6 weeks. Then a storm raised it 3/4 m. What was the overall change in the water level?

    1. a) 1½ m
    2. b) −1½ m
    3. c) −3 m
    4. d) 3/8 m

  8. Four days' low temperatures in Grande Prairie were −8.5 °C, −3.0 °C, 2.5 °C and −6.0 °C. What was the mean low temperature?

    1. a) −3.75 °C
    2. b) 3.75 °C
    3. c) −5.0 °C
    4. d) −15.0 °C

  9. Which list is in order from least to greatest?

    1. a) −1.2, −3/4, −0.7, 0.5
    2. b) −0.7, −3/4, −1.2, 0.5
    3. c) −1.2, −0.7, −3/4, 0.5
    4. d) 0.5, −0.7, −3/4, −1.2

  10. A diver starts at the surface and descends 2.4 m every minute. What is her position relative to the surface after 3.5 minutes?

    1. a) −8.4 m
    2. b) −0.84 m
    3. c) 8.4 m
    4. d) −5.9 m

Answer key · Rational numbers

Math 9 · maddyhelps.com

  1. a) 3.8 — Multiply first: (−3.1) × 2 = −6.2. Then −2.4 − (−6.2) = −2.4 + 6.2 = 3.8. Working left to right gives (−2.4 + 3.1) × 2 = 1.4, and subtracting 6.2 instead of adding it gives −8.6.
  2. d) −0.3 — −1/2 = −0.5 and −1/4 = −0.25, so the number must be between −0.5 and −0.25, and −0.3 is. −0.2 is closer to zero than −0.25, so it is greater than both, and −0.6 is less than both.
  3. d) −1/4 — Use a common denominator: −3/4 + 2/4 = −1/4. The answer is negative because the negative part is bigger. Adding tops and bottoms separately gives −2/6, which is never how fractions add.
  4. a) −3/2 — Multiply by the reciprocal of the divisor: −2/3 × 9/4 = −18/12 = −3/2. Multiplying without flipping gives −8/27, and flipping the first fraction instead of the second gives −2/3. The signs differ, so the answer is negative.
  5. c) 6 — A negative times a negative is positive, and 1.5 × 4 = 6. Adding instead of multiplying gives −5.5, and −6 forgets the sign rule.
  6. d) −0.45 — Negative numbers get smaller the further they are from zero, and −0.45 is the closest to zero, so it is the greatest. −3/4 = −0.75 is actually the least; choosing it because 3/4 is the biggest fraction ignores the sign.
  7. b) −1½ m — Six drops of 3/8 m is 6 × (−3/8) = −18/8 = −2¼ m. Adding the rise gives −2¼ + ¾ = −1½ m, so the pond ended 1½ m lower. Forgetting to multiply by 6 gives 3/8, and treating the rise as another drop gives −3.
  8. a) −3.75 °C — Add with the signs: −8.5 + (−3.0) + 2.5 + (−6.0) = −15.0, then divide by 4 to get −3.75 °C. Treating 2.5 as −2.5 gives −20.0 ÷ 4 = −5.0 °C; the one day above zero pulls the mean up.
  9. a) −1.2, −3/4, −0.7, 0.5 — As decimals the numbers are −1.2, −0.75, −0.7 and 0.5. The most negative is furthest left on a number line, so −1.2 comes first, and −0.75 comes before −0.7. Ordering by size without the signs gives −0.7, −3/4, −1.2, which is backwards.
  10. a) −8.4 m — Going down is negative: 3.5 × (−2.4) = −8.4 m, which is 8.4 m below the surface. Adding −2.4 and −3.5 gives −5.9, and −0.84 misplaces the decimal — 2.4 × 3.5 must be more than 2 × 3 = 6.