Grade 6 The Number System Practice — Hard

Question 1 of 16Score 0/0Hard

Question 1 of 16: What is 7/12 Ãˇ 7/8?

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Keep going: Read the lesson: Dividing Fractions by Fractions Number Line Plotter Factors, GCF & LCM
Answer key for parents & teachers (16 questions)
  1. What is 7/12 Ãˇ 7/8? — 2/3. 7/12 Ãˇ 7/8 = 7/12 × 8/7 = 56/84 = 2/3.
  2. A ribbon of length 5/6 yard is cut into pieces of 5/18 yard each. How many complete pieces are there? — 3. 5/6 Ãˇ 5/18 = 5/6 × 18/5 = 90/30 = 3 pieces.
  3. Evaluate: (2/3 Ãˇ 4/5) Ãˇ (1/2) — 5/3. First: 2/3 Ãˇ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Then: 5/6 Ãˇ 1/2 = 5/6 × 2/1 = 10/6 = 5/3.
  4. A recipe uses 3/4 cup of oil. You only want to make 2/3 of the recipe. How much oil do you need? — 1/2 cup. This is multiplication: 3/4 × 2/3 = 6/12 = 1/2 cup. (Note: this is multiplication, not division — careful with the context.)
  5. What is 11/12 Ãˇ 11/18? — 3/2. 11/12 Ãˇ 11/18 = 11/12 × 18/11 = 198/132 = 3/2.
  6. A baker has 7/8 lb of flour. Each loaf needs 7/32 lb. How many loaves can be made? — 4. 7/8 Ãˇ 7/32 = 7/8 × 32/7 = 224/56 = 4 loaves.
  7. The GCF of two numbers is 7 and their LCM is 84. One number is 28. What is the other? — 21. a × b = GCF × LCM = 7 × 84 = 588. Other number = 588 Ãˇ 28 = 21.
  8. What is the GCF of 48, 72, and 120? — 24. 48=2⁴×3, 72=2Âŗ×3², 120=2Âŗ×3×5. GCF = 2Âŗ×3 = 24.
  9. Trains depart from a station every 8 minutes and 12 minutes respectively. If both depart at 9:00 AM, when do they next depart together? — 9:24 AM. LCM(8, 12) = 24 minutes. Next joint departure = 9:00 AM + 24 min = 9:24 AM.
  10. Find GCF(132, 198) using prime factorization. — 66. 132 = 2Â˛Ã—3×11. 198 = 2×3Â˛Ã—11. GCF = 2×3×11 = 66.
  11. Two pieces of rope measure 84 cm and 60 cm. What is the longest piece you can cut both ropes into (no waste)? — 12 cm. GCF(84, 60) = 12. Cut both into 12 cm pieces: 84Ãˇ12=7 pieces, 60Ãˇ12=5 pieces. No waste.
  12. A company's profit/loss over 4 days: −$200, $350, −$100, $180. What is the total? — $230. −200 + 350 − 100 + 180 = (350 + 180) − (200 + 100) = 530 − 300 = $230 profit.
  13. Plot the points (2, 3), (−2, 3), (−2, −3), (2, −3) and connect them. What shape do you get? — A rectangle. These four points form a rectangle (actually a square-like shape). The shape is a rectangle in the coordinate plane.
  14. What is the absolute value of the sum of −8 and −5? — 13. −8 + (−5) = −13. |−13| = 13.
  15. If |x| = 7, what are all possible values of x? — x = 7 or x = −7. The absolute value equation |x| = 7 has two solutions: x = 7 and x = −7, since both are 7 units from zero.
  16. Point P is at (−3, −4). What is its distance from the origin? — 5. Distance = √(x² + y²) = √(9 + 16) = √25 = 5.