Grade 6 The Number System Practice — Medium

Question 1 of 33Score 0/0Medium

Question 1 of 33: What is 3/8 Ãˇ 3/4?

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Keep going: Read the lesson: Dividing Fractions by Fractions Number Line Plotter Factors, GCF & LCM
Answer key for parents & teachers (33 questions)
  1. What is 3/8 Ãˇ 3/4? — 1/2. 3/8 Ãˇ 3/4 = 3/8 × 4/3 = 12/24 = 1/2.
  2. A rope is 5/6 of a meter long. You cut it into pieces each 1/12 of a meter. How many pieces do you get? — 10. 5/6 Ãˇ 1/12 = 5/6 × 12/1 = 60/6 = 10 pieces.
  3. What is 7/8 Ãˇ 7/16? — 2. 7/8 Ãˇ 7/16 = 7/8 × 16/7 = 112/56 = 2.
  4. A container holds 3/4 gallon. Each cup holds 1/8 gallon. How many cups can be filled? — 6. 3/4 Ãˇ 1/8 = 3/4 × 8/1 = 24/4 = 6 cups.
  5. What is 2/3 Ãˇ 4/9? — 3/2. 2/3 Ãˇ 4/9 = 2/3 × 9/4 = 18/12 = 3/2.
  6. Simplify: 5/12 Ãˇ 5/6 — 1/2. 5/12 Ãˇ 5/6 = 5/12 × 6/5 = 30/60 = 1/2.
  7. You have 2/3 of a pie. Each person gets 1/6 of a pie. How many people can be served? — 4. 2/3 Ãˇ 1/6 = 2/3 × 6/1 = 12/3 = 4 people.
  8. What is 9/10 Ãˇ 3/5? — 3/2. 9/10 Ãˇ 3/5 = 9/10 × 5/3 = 45/30 = 3/2.
  9. A wall is 5/3 meters wide. Tiles are 5/12 meters each. How many tiles fit across? — 4. 5/3 Ãˇ 5/12 = 5/3 × 12/5 = 60/15 = 4 tiles.
  10. What is 1 Ãˇ 3/4? — 4/3. 1 Ãˇ 3/4 = 1 × 4/3 = 4/3.
  11. What is 3/5 Ãˇ 9/10? — 2/3. 3/5 Ãˇ 9/10 = 3/5 × 10/9 = 30/45 = 2/3.
  12. What is the GCF of 24 and 36? — 12. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 36: 1,2,3,4,6,9,12,18,36. GCF = 12.
  13. What is the LCM of 6 and 10? — 30. Prime factors: 6 = 2×3, 10 = 2×5. LCM = 2×3×5 = 30.
  14. Use GCF to simplify 18/24. — 3/4. GCF(18, 24) = 6. 18Ãˇ6 = 3, 24Ãˇ6 = 4. Simplified: 3/4.
  15. You have 18 red and 24 blue balloons to make identical bunches using all balloons. How many bunches can you make? — 6. GCF(18, 24) = 6. You can make 6 identical bunches (3 red + 4 blue each).
  16. A neon sign blinks every 4 seconds; another blinks every 6 seconds. How often do they blink together? — Every 12 seconds. LCM(4, 6) = 12. They blink together every 12 seconds.
  17. What is the GCF of 45 and 60? — 15. 45 = 3Â˛Ã—5. 60 = 2Â˛Ã—3×5. GCF = product of shared primes (lowest powers) = 3×5 = 15.
  18. What is the LCM of 4, 6, and 10? — 60. 4=2², 6=2×3, 10=2×5. LCM = 2Â˛Ã—3×5 = 60.
  19. If GCF(a, b) = 5 and LCM(a, b) = 60, what is a × b? — 300. GCF × LCM = a × b. So 5 × 60 = 300.
  20. What relationship holds between GCF and LCM of two numbers? — GCF × LCM = product of the two numbers. For any two numbers a and b: GCF(a,b) × LCM(a,b) = a × b.
  21. What is the GCF of two consecutive integers (like 7 and 8)? — 1. Consecutive integers share no common factors except 1. GCF of any two consecutive integers is always 1.
  22. What is the LCM of 7 and 11 (both prime)? — 77. When two numbers are both prime (and different), their GCF = 1 and LCM = their product: 7 × 11 = 77.
  23. A submarine is at −450 feet. It ascends 200 feet. What is its new elevation? — −250 feet. −450 + 200 = −250 feet. It is now 250 feet below sea level.
  24. What is the distance between −4 and 6 on a number line? — 10. Distance = |6 − (−4)| = |6 + 4| = |10| = 10 units.
  25. Which point is NOT in Quadrant III? — (−2, 3). Quadrant III has both x and y negative. (−2, 3) has a positive y, so it is in Quadrant II, not III.
  26. If you reflect point (3, −5) across the x-axis, what are the new coordinates? — (3, 5). Reflecting across the x-axis flips the y-coordinate sign. (3, −5) → (3, 5).
  27. A temperature is −12°F. It rises 20°F. What is the new temperature? — 8°F. −12 + 20 = 8°F.
  28. Compare: |−15| vs. |9|. Which is greater? — |−15| (since 15 > 9). |−15| = 15 and |9| = 9. Since 15 > 9, |−15| is greater.
  29. Point A is at (−2, 4) and point B is at (−2, −3). What is the vertical distance between them? — 7. Both points have the same x-coordinate. Vertical distance = |4 − (−3)| = |7| = 7.
  30. In which quadrant does the point (−100, −0.01) lie? — Quadrant III. Both x and y are negative, so the point is in Quadrant III.
  31. The high temperature was 3°C and the low was −11°C. What was the temperature range? — 14°C. Range = high − low = 3 − (−11) = 3 + 11 = 14°C.
  32. What is the reflection of (5, −2) across the y-axis? — (−5, −2). Reflecting across the y-axis flips the x-coordinate sign. (5, −2) → (−5, −2).
  33. Which number has the greatest absolute value: −20, 15, −18, 12? — −20. |−20| = 20, |15| = 15, |−18| = 18, |12| = 12. The greatest absolute value is 20, belonging to −20.