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Math 7

Math 7 · Worksheets

Mixed review · Numbers, integers and fractions

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

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Mixed review · Numbers, integers and fractions

Math 7 · maddyhelps.com

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

  1. To find −2 − 4 with tiles, you start with 2 red tiles (−1 each). You must take away 4 yellow tiles (+1 each), but there are none. How many zero pairs do you need to add, and what is the answer?

    1. a) Add 2 zero pairs; the answer is 2
    2. b) Add 2 zero pairs; the answer is −6
    3. c) Add 4 zero pairs; the answer is −6
    4. d) Add 4 zero pairs; the answer is −2

  2. Which decimal is exactly equal to 2/3?

    1. a) 1.5
    2. b) 0.6
    3. c) 0.67
    4. d) 0.666…

  3. 3 − (−5) equals

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

  4. 5.6 + 2.4 ÷ 0.8 equals

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

  5. 0.4 × 0.3 equals

    1. a) 0.7
    2. b) 1.2
    3. c) 0.12
    4. d) 0.012

  6. A school has 400 students. 35% of them take the bus and 25% get a ride in a car. The rest walk or bike. How many students walk or bike?

    1. a) 40
    2. b) 160
    3. c) 260
    4. d) 300

  7. A $40 jacket is on sale for 15% off. What is the sale price?

    1. a) $46
    2. b) $34
    3. c) $25
    4. d) $6

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

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

  9. −8 + (−5) + 9 equals

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

  10. 3.6 + 0.45 equals

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

Answer key · Mixed review · Numbers, integers and fractions

Math 7 · maddyhelps.com

  1. c) Add 4 zero pairs; the answer is −6 — Adding 4 zero pairs (4 yellow and 4 red) does not change the value, and it gives you 4 yellow tiles to take away. That leaves 6 red tiles: −2 − 4 = −6. Answering −2 takes away the whole zero pairs, red tiles too, which just puts you back where you started.
  2. d) 0.666… — 2 ÷ 3 = 0.6666…, and the 6 repeats forever, so the exact value is 0.666…. 0.67 is that decimal rounded to hundredths — close, but not equal — and 1.5 is 3 ÷ 2.
  3. b) 8 — Subtracting −5 is the same as adding 5, so 3 − (−5) = 3 + 5 = 8. On a number line, the distance from −5 up to 3 is 8. Answering −2 works out 3 − 5 and drops the second negative sign.
  4. 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.
  5. c) 0.12 — 4 × 3 = 12, and the two factors have one decimal place each, so the answer has two: 0.12. It is smaller than both factors, as it must be when you multiply two numbers less than 1. 1.2 counts only one decimal place, and 0.7 adds instead of multiplying.
  6. b) 160 — 35% + 25% = 60% ride, so 100% − 60% = 40% walk or bike, and 40% of 400 is 0.40 × 400 = 160. 40 is the percent, not the number of students the question asks for, and 260 or 300 takes away only one of the two groups that ride.
  7. b) $34 — 10% of $40 is $4, and 5% is half of that, $2, so 15% is $6. The sale price is $40 − $6 = $34. $6 is the discount, not the price, and $25 takes off 15 dollars instead of 15 percent.
  8. b) 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.
  9. 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.
  10. a) 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.