Grade 5 Operations & Algebraic Thinking Practice ā€” Medium

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Question 1 of 32: Which expression matches "add 7 to the product of 2 and 5"?

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Answer key for parents & teachers (32 questions)
  1. Which expression matches "add 7 to the product of 2 and 5"? ā€” 2 Ɨ 5 + 7. "Product of 2 and 5" = 2 Ɨ 5. Adding 7 gives 2 Ɨ 5 + 7. Multiplication already has priority, so no parentheses needed.
  2. Evaluate { [ (6 āˆ’ 2) Ɨ 3 ] + 5 } ā€” 17. (6āˆ’2)=4. [4Ɨ3]=12. {12+5}=17.
  3. Which expression represents "divide the sum of 10 and 2 by 4"? ā€” (10 + 2) Ć· 4. "Sum of 10 and 2" requires parentheses: (10 + 2). Then divide by 4.
  4. What is the difference between (4 + 2) Ɨ 3 and 4 + 2 Ɨ 3? ā€” 6. (4+2)Ɨ3 = 6Ɨ3 = 18. 4+2Ɨ3 = 4+6 = 10. Difference: 18āˆ’10 = 8. Wait ā€” recalculating: 18āˆ’10 = 8. The correct answer is 8.
  5. Evaluate: [ (9 āˆ’ 4) + 3 ] Ɨ 2 ā€” 16. Innermost: (9āˆ’4)=5. Next: [5+3]=8. Finally: 8Ɨ2=16.
  6. Translate to an expression: "3 times the difference of 10 and 4" ā€” 3 Ɨ (10 āˆ’ 4). "Difference of 10 and 4" = (10 āˆ’ 4). Multiply by 3 gives 3 Ɨ (10 āˆ’ 4).
  7. What is the value of { [ 2 Ɨ (3 + 4) ] āˆ’ 6 }? ā€” 8. (3+4)=7. [2Ɨ7]=14. {14āˆ’6}=8.
  8. Which expression represents "the quotient of 20 and the sum of 3 and 2"? ā€” 20 Ć· (3 + 2). "Sum of 3 and 2" = (3+2). "Quotient of 20 and that sum" = 20 Ć· (3+2).
  9. The expression 5 Ɨ [ 3 + (8 Ć· 2) ] equals: ā€” 35. (8Ć·2)=4. [3+4]=7. 5Ɨ7=35.
  10. Which expression has a value of 20? ā€” (2 + 3) Ɨ 4. (2+3)Ɨ4 = 5Ɨ4 = 20. Others give 14, 14, or 9.
  11. Jake has (4 + 6) stickers and doubles them. Which expression shows total stickers? ā€” (4 + 6) Ɨ 2. First find the total: (4+6). Then double it: Ɨ 2. So (4+6)Ɨ2 = 20.
  12. Evaluate: 10 āˆ’ [ (3 + 2) Ɨ 1 ] ā€” 5. (3+2)=5. [5Ɨ1]=5. 10āˆ’5=5.
  13. Evaluate: 5 + 4Ā² āˆ’ 3 ā€” 18. 4Ā²=16. Then left to right: 5+16=21, 21āˆ’3=18.
  14. Evaluate: 15 āˆ’ 3 Ɨ 2 + 1 ā€” 10. Multiply first: 3Ɨ2=6. Then Lā†’R: 15āˆ’6=9, 9+1=10.
  15. Evaluate: 8 Ć· 4 + 6 Ɨ 2 ā€” 14. Divide: 8Ć·4=2. Multiply: 6Ɨ2=12. Then add: 2+12=14.
  16. Evaluate: (10 āˆ’ 4) Ć· 2 Ɨ 3 ā€” 9. Parentheses: (10āˆ’4)=6. Then Lā†’R: 6Ć·2=3, 3Ɨ3=9.
  17. Evaluate: 12 Ć· (6 āˆ’ 2) Ɨ 3 ā€” 9. Parentheses: (6āˆ’2)=4. Lā†’R: 12Ć·4=3, 3Ɨ3=9.
  18. Evaluate: 3 Ɨ [ 2 + (8 Ć· 4) ] ā€” 12. Innermost: (8Ć·4)=2. Brackets: [2+2]=4. Then: 3Ɨ4=12.
  19. Sam calculates 4 + 8 Ć· 2 and gets 6. Is he correct? ā€” No, the answer is 8. PEMDAS: divide first 8Ć·2=4, then add 4+4=8. Sam forgot to divide before adding.
  20. Which is the correct first step for: 5 Ɨ 3 āˆ’ (4 + 2) Ć· 2? ā€” Evaluate (4 + 2). Parentheses are first in PEMDAS, so evaluate (4+2)=6 first.
  21. Evaluate: (7 + 3) Ć· (8 āˆ’ 3) ā€” 2. Both parentheses: (7+3)=10, (8āˆ’3)=5. Then: 10Ć·5=2.
  22. If you see 18 Ć· 9 Ɨ 2, what do you do first? ā€” 18 Ć· 9 (work left to right). Multiplication and division are equal priority; work left to right. So 18Ć·9=2 first, then 2Ɨ2=4.
  23. Which expression equals 30? ā€” (4 + 1) Ɨ 6. (4+1)Ɨ6 = 5Ɨ6 = 30. Others give 10, 10, or 10.
  24. If two number patterns have a consistent relationship, their plotted points form: ā€” A straight line. When two patterns have a constant relationship (like y = 2x), their ordered pairs fall along a straight line.
  25. Pattern X: 0, 3, 6, 9. Pattern Y: 0, 1, 2, 3. What is the relationship between X and Y? ā€” X is always 3 times Y. 0=3Ɨ0, 3=3Ɨ1, 6=3Ɨ2, 9=3Ɨ3. X is always 3 times Y.
  26. How do you check if a number sequence is arithmetic (has a constant difference)? ā€” Subtract consecutive terms ā€” the difference should be the same. An arithmetic pattern has a constant difference between consecutive terms. Subtract consecutive terms to check.
  27. Pattern A: 0, 4, 8, 12. Pattern B: 0, 2, 4, 6. What ordered pair corresponds to the 4th terms? ā€” (12, 6). 4th term of A = 12, 4th term of B = 6. The ordered pair is (A, B) = (12, 6).
  28. A pattern rule says "multiply by 3." If x = 4, what is y? ā€” 12. y = 3 Ɨ x = 3 Ɨ 4 = 12.
  29. Two patterns: x adds 5 each step (starting at 0), y adds 10 each step (starting at 0). Which ordered pair is NOT on this pattern? ā€” (10, 15). y should always be 2Ɨ x. (10, 15): 15 ā‰  2Ɨ10=20. So (10,15) does not fit.
  30. What is the next ordered pair in the sequence (0,0), (1,3), (2,6), (3,9)? ā€” (4, 12). Pattern: y = 3x. Next x = 4, so y = 12. Ordered pair: (4, 12).
  31. On a coordinate grid, the point (0, 5) is located: ā€” On the y-axis, 5 units up. When x=0, the point is ON the y-axis. Since y=5, it is 5 units above the origin.
  32. What does it mean when two patterns are graphed and the points form a straight line? ā€” There is a consistent relationship between the patterns. A straight-line graph indicates a constant ratio or constant difference relationship between the two patterns.