Grade 7 The Number System Practice

Question 1 of 33Score 0/0Medium

Question 1 of 33: What is 5/6 โˆ’ 3/4?

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Keep going: Read the lesson: Operations with Rational Numbers Number Line Plotter Fraction Simplifier
Answer key for parents & teachers (33 questions)
  1. What is 5/6 โˆ’ 3/4? โ€” 1/12. LCD = 12. 5/6 = 10/12, 3/4 = 9/12. 10/12 โˆ’ 9/12 = 1/12.
  2. What is (โˆ’2/5) ร— (โˆ’3/4)? โ€” 6/20. Negative ร— Negative = Positive. (2/5) ร— (3/4) = 6/20 = 3/10, which is positive.
  3. Calculate: (โˆ’1/2) รท (3/4) โ€” โˆ’2/3. (โˆ’1/2) ร— (4/3) = โˆ’4/6 = โˆ’2/3. The result is negative because the signs differ.
  4. What is the sign of the product of three negative numbers? โ€” Negative. Neg ร— Neg = Pos, then Pos ร— Neg = Neg. An odd number of negatives always gives a negative product.
  5. What is 3.2 + (โˆ’7.5)? โ€” โˆ’4.3. Different signs: subtract absolute values (7.5 โˆ’ 3.2 = 4.3) and keep the sign of the larger absolute value (negative). Answer: โˆ’4.3.
  6. What is (โˆ’5) ร— (3) ร— (โˆ’2)? โ€” 30. (โˆ’5) ร— 3 = โˆ’15, then โˆ’15 ร— (โˆ’2) = +30. Even number of negatives โ†’ positive.
  7. A bank account has $โˆ’200. The owner deposits $350. What is the new balance? โ€” $150. โˆ’200 + 350 = 150. The account now has $150.
  8. What is the result of (โˆ’7/8) + (3/8)? โ€” โˆ’4/8. Same denominators: โˆ’7/8 + 3/8 = (โˆ’7 + 3)/8 = โˆ’4/8 = โˆ’1/2.
  9. What is 1/3 + (โˆ’5/6)? โ€” โˆ’1/2. LCD = 6. 1/3 = 2/6. 2/6 + (โˆ’5/6) = โˆ’3/6 = โˆ’1/2.
  10. A football team loses 8 yards on a play, then loses another 3 yards. Express and calculate the total yardage change. โ€” โˆ’11 yards. โˆ’8 + (โˆ’3) = โˆ’11 yards. Both losses are negative; the total is โˆ’11 yards (11 yard loss).
  11. Which expression has a POSITIVE result? โ€” (โˆ’6) รท (โˆ’3). (โˆ’6) รท (โˆ’3) = +2. Same signs give a positive result in division.
  12. What is 7/8 as a decimal? โ€” 0.875. 7 รท 8 = 0.875. Calculate: 7.000 รท 8 step by step.
  13. Convert 0.ฬ„6 (0.6666โ€ฆ) to a fraction. โ€” 2/3. Let x = 0.6ฬ„. Then 10x = 6.6ฬ„. 10x โˆ’ x = 6, so 9x = 6, x = 6/9 = 2/3.
  14. What is 5/6 as a decimal? โ€” 0.833โ€ฆ. 5 รท 6 = 0.8333โ€ฆ The digit 3 repeats. Written as 0.8ฬ„3.
  15. Is 0.121121112โ€ฆ (non-repeating) a rational number? โ€” No, because it does not repeat โ€” it is irrational. Rational numbers have terminating or REPEATING decimals. A non-repeating infinite decimal is irrational.
  16. Which of these fractions has a repeating decimal? โ€” 1/6. 1/6 = 0.1666โ€ฆ The 6 repeats. The others (1/2 = 0.5, 1/4 = 0.25, 1/5 = 0.2) all terminate.
  17. Convert 0.4ฬ„ (0.4444โ€ฆ) to a fraction. โ€” 4/9. Let x = 0.4ฬ„. 10x = 4.4ฬ„. 9x = 4. x = 4/9.
  18. What decimal does 7/9 equal? โ€” 0.7ฬ„. 7 รท 9 = 0.777โ€ฆ = 0.7ฬ„.
  19. What fraction equals 0.125? โ€” 1/8. 0.125 = 125/1000 = 1/8. Alternatively, recall that 1/8 = 0.125.
  20. Convert 0.ฬ„5 (0.5555โ€ฆ) to a fraction. โ€” 5/9. Let x = 0.5ฬ„. 10x = 5.5ฬ„. 9x = 5. x = 5/9.
  21. Order from least to greatest: 2/3, 0.6, 5/8 โ€” 0.6, 5/8, 2/3. 2/3 โ‰ˆ 0.667, 0.6 = 0.6, 5/8 = 0.625. Order: 0.6 < 0.625 < 0.667, so 0.6, 5/8, 2/3.
  22. What is 13/20 as a decimal? โ€” 0.65. 13 รท 20 = 0.65. Also: 20 = 4 ร— 5 = 2ยฒ ร— 5, so it terminates.
  23. Which of the following is the correct definition of |x|? โ€” |x| = x if x โ‰ฅ 0; |x| = โˆ’x if x < 0. Absolute value equals x when x is non-negative, and equals โˆ’x (which is positive) when x is negative.
  24. Which is greater: โˆ’1/2 or โˆ’3/4? โ€” โˆ’1/2. โˆ’1/2 > โˆ’3/4 because โˆ’1/2 is closer to 0 on the number line (less negative).
  25. City A is at โˆ’15ยฐC and City B is at 8ยฐC. What is the temperature difference? โ€” 23ยฐC. |โˆ’15 โˆ’ 8| = |โˆ’23| = 23ยฐC difference.
  26. A scuba diver is at โˆ’25 feet and swims up to โˆ’10 feet. What distance did she travel? โ€” 15 feet. |โˆ’25 โˆ’ (โˆ’10)| = |โˆ’25 + 10| = |โˆ’15| = 15 feet traveled.
  27. Which statement about negative numbers is TRUE? โ€” A number with greater absolute value can be a SMALLER negative number. โˆ’100 < โˆ’1 even though |โˆ’100| > |โˆ’1|. For negatives, greater absolute value means the number is more negative (smaller).
  28. Evaluate: |โˆ’2| ร— |3| โˆ’ |โˆ’5| โ€” 1. |โˆ’2| = 2, |3| = 3, |โˆ’5| = 5. So: 2 ร— 3 โˆ’ 5 = 6 โˆ’ 5 = 1.
  29. A stock changed by โˆ’$4.50 on Monday and +$2.30 on Tuesday. What was the total absolute change over both days? โ€” $6.80. Total absolute change = |โˆ’4.50| + |2.30| = 4.50 + 2.30 = $6.80.
  30. What does |a โˆ’ b| represent geometrically? โ€” The distance between a and b on the number line. |a โˆ’ b| gives the distance between points a and b on the number line.
  31. If |x| = 4, what are the possible values of x? โ€” 4 or โˆ’4. Absolute value equations have two solutions: x = 4 or x = โˆ’4, because both are 4 units from 0.
  32. Which inequality is correct? โ€” |โˆ’8| = |8|. |โˆ’8| = 8 and |8| = 8. They are equal, so |โˆ’8| = |8|.
  33. What is โˆ’|โˆ’9|? โ€” โˆ’9. |โˆ’9| = 9, then the negative sign outside makes it โˆ’9. Always work inside the bars first.