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Divisibility and decimals

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

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Divisibility and decimals

Math 7 · maddyhelps.com

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

  1. Which number is divisible by 9?

    1. a) 5832
    2. b) 1239
    3. c) 9091
    4. d) 3199

  2. 3.6 + 0.45 equals

    1. a) 0.81
    2. b) 3.05
    3. c) 4.05
    4. d) 3.51

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

    1. a) 0.6, 0.65, 2/3, 5/8
    2. b) 2/3, 0.65, 5/8, 0.6
    3. c) 5/8, 0.6, 0.65, 2/3
    4. d) 0.6, 5/8, 0.65, 2/3

  4. Which number is divisible by 8?

    1. a) 5128
    2. b) 2468
    3. c) 3148
    4. d) 7612

  5. Which number is divisible by 6?

    1. a) 2361
    2. b) 4610
    3. c) 7314
    4. d) 5216

  6. 5.6 + 2.4 ÷ 0.8 equals

    1. a) 5.9
    2. b) 8.6
    3. c) 35.6
    4. d) 10

  7. The divisibility rule for 4 says to look only at the last two digits. Why does that work?

    1. a) The last two digits of an even number always divide evenly by 4.
    2. b) 4 is 2 × 2, so the rule needs two digits, one for each 2 in the number 4.
    3. c) Every multiple of 100 divides evenly by 4, so only the last two digits can leave a remainder.
    4. d) Every multiple of 10 divides evenly by 4, so only the last two digits can leave a remainder.

  8. Which number is greatest?

    1. a) 0.7
    2. b) 0.65
    3. c) 0.099
    4. d) 0.625

  9. Which fraction lies between 0.6 and 0.7?

    1. a) 3/4
    2. b) 6/7
    3. c) 2/3
    4. d) 4/7

  10. What is 8 ÷ 0?

    1. a) It equals 8, because dividing by 0 changes nothing.
    2. b) It cannot be done, because no number times 0 equals 8.
    3. c) It equals 0, because any number divided by 0 is 0.
    4. d) It cannot be done, because 0 is not a whole number.

Answer key · Divisibility and decimals

Math 7 · maddyhelps.com

  1. a) 5832 — A number is divisible by 9 when its digits add up to a multiple of 9: 5 + 8 + 3 + 2 = 18, so 5832 is (5832 ÷ 9 = 648). Having a 9 in it does not help — 1239's digits add up to 15, which is a multiple of 3 but not of 9.
  2. c) 4.05 — Line up the decimal points and write 3.6 as 3.60: 3.60 + 0.45 = 4.05. 3.51 adds the parts after the decimal point as if they were whole numbers (6 + 45), and 0.81 lines the numbers up at the right-hand end instead of at the decimal point.
  3. d) 0.6, 5/8, 0.65, 2/3 — As decimals, 5/8 = 0.625 and 2/3 = 0.666…, so the order is 0.6, 0.625, 0.65, 0.666…. Putting 5/8 last treats a bigger denominator as a bigger fraction, but eighths are smaller pieces than thirds, and putting it first reads 5/8 as 0.58.
  4. a) 5128 — For 8, test the last three digits, because 1000 = 8 × 125: 128 ÷ 8 = 16, so 5128 is divisible by 8. 3148 ends in 48, which 8 does divide, but looking at two digits is the rule for 4 — 148 ÷ 8 = 18.5, so 3148 is not.
  5. c) 7314 — A number is divisible by 6 when it passes both the test for 2 and the test for 3: 7314 is even, and its digits add up to 15. 2361 passes the test for 3 but is odd, and 5216 ends in 6 but its digits add up to 14 — ending in 6 is not the test.
  6. b) 8.6 — Divide before you add: 2.4 ÷ 0.8 = 3, because 0.8 × 3 = 2.4, so the answer is 5.6 + 3 = 8.6. Working left to right gives 8 ÷ 0.8 = 10. 5.9 comes from 2.4 ÷ 0.8 = 0.3, but dividing by a number less than 1 makes the answer bigger, not smaller.
  7. c) Every multiple of 100 divides evenly by 4, so only the last two digits can leave a remainder. — Split a number into hundreds and the rest: 5716 = 5700 + 16. Since 100 = 4 × 25, any number of hundreds divides evenly by 4, so only the 16 can leave a remainder. 10 is not a multiple of 4, which is why the last digit alone is not enough — 14 is even but not divisible by 4.
  8. a) 0.7 — Compare the tenths first: 0.7 has 7 tenths, and 0.65 and 0.625 have only 6. More digits after the decimal point does not make a number bigger — that thinking picks 0.625, which is 625 thousandths against 0.7's 700 thousandths.
  9. c) 2/3 — 2 ÷ 3 = 0.666…, which is between 0.6 and 0.7. 6/7 looks right because it is built from a 6 and a 7, but 6 ÷ 7 ≈ 0.857. 4/7 ≈ 0.571 is just below 0.6, and 3/4 = 0.75 is just above 0.7.
  10. b) It cannot be done, because no number times 0 equals 8. — Division undoes multiplication, so 8 ÷ 0 would need a number that makes 8 when you multiply it by 0 — and every number times 0 is 0. Answering 0 fails that check, since 0 × 0 is 0, not 8. And 0 is a whole number, so that is not the reason.