Grade 5 Operations & Algebraic Thinking Practice ā€” Hard

Question 1 of 18Score 0/0Hard

Question 1 of 18: Maria earns $6 each day for (3 + 2) days. Which expression gives her total?

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Answer key for parents & teachers (18 questions)
  1. Maria earns $6 each day for (3 + 2) days. Which expression gives her total? ā€” 6 Ɨ (3 + 2). Total days = (3+2). Earnings per day = $6. Total = 6 Ɨ (3+2) = 6Ɨ5 = $30.
  2. Which pair of expressions has the same value? ā€” (4 + 2) Ɨ 3 and 3 Ɨ (2 + 4). Multiplication is commutative: (4+2)Ɨ3 = 6Ɨ3 = 18, and 3Ɨ(2+4) = 3Ɨ6 = 18. They are equal.
  3. Write an expression for: "Subtract 5 from the product of 3 and the sum of 4 and 2" ā€” 3 Ɨ (4 + 2) āˆ’ 5. "Sum of 4 and 2" = (4+2). "Product of 3 and that sum" = 3Ɨ(4+2). "Subtract 5" gives 3Ɨ(4+2)āˆ’5 = 18āˆ’5 = 13.
  4. Evaluate: 3 + 6 Ɨ (5 + 4) Ć· 3 āˆ’ 7 ā€” 14. Parentheses: (5+4)=9. Multiply/Divide Lā†’R: 6Ɨ9=54, 54Ć·3=18. Add/Subtract Lā†’R: 3+18=21, 21āˆ’7=14.
  5. Which expression has the greatest value: A) 2Ɨ3+4, B) 2+3Ɨ4, C) (2+3)Ɨ4, D) 2Ɨ(3+4)? ā€” C ā€” (2+3)Ɨ4. A=10, B=14, C=20, D=14. C has the greatest value.
  6. What is 6Ā² āˆ’ 4 Ɨ 5 + 2? ā€” 18. Exponent: 6Ā²=36. Multiply: 4Ɨ5=20. Lā†’R: 36āˆ’20=16, 16+2=18.
  7. Evaluate: 5 Ɨ 3 āˆ’ (4 + 2) Ć· 2 ā€” 12. Parentheses: (4+2)=6. Multiply: 5Ɨ3=15. Divide: 6Ć·2=3. Subtract: 15āˆ’3=12.
  8. Evaluate: 20 Ć· 4 + 3Ā² Ɨ 2 ā€” 23. Exponent: 3Ā²=9. Divide: 20Ć·4=5. Multiply: 9Ɨ2=18. Add: 5+18=23.
  9. Evaluate: 2 Ɨ 3Ā² + 1 ā€” 19. Exponent: 3Ā²=9. Multiply: 2Ɨ9=18. Add: 18+1=19.
  10. What value makes this true: ā–” + 4 Ɨ 3 = 20? ā€” 8. Multiplication first: 4Ɨ3=12. So ā–”+12=20, meaning ā–”=8.
  11. Evaluate: 40 āˆ’ 5 Ɨ (2 + 4) + 1 ā€” 11. Parentheses: (2+4)=6. Multiply: 5Ɨ6=30. Lā†’R: 40āˆ’30=10, 10+1=11.
  12. Pattern P: 0, 2, 4, 6, 8. Pattern Q: 0, 6, 12, 18, 24. What is the rule linking Q to P? ā€” Q = 3 Ɨ P. 6/2=3, 12/4=3, 18/6=3, 24/8=3. Q is always 3 times P.
  13. If the points (0,0), (2,5), (4,10) all lie on a pattern, what is the rule? ā€” y = 2.5 Ɨ x. 5/2=2.5, 10/4=2.5. So y = 2.5 Ɨ x.
  14. Maria counts tiles: row 1 has 3 tiles, row 2 has 6, row 3 has 9. If row number = x and tile count = y, what is y when x = 7? ā€” 21. Rule: y = 3x. When x = 7, y = 3 Ɨ 7 = 21.
  15. Which table of values shows the relationship y = x + 4? ā€” x: 1,2,3,4 ā†’ y: 5,6,7,8. y = x + 4: (1+4)=5, (2+4)=6, (3+4)=7, (4+4)=8. First table matches.
  16. Pattern A: 0, 5, 10, 15. Pattern B: 0, 5, 10, 15. What do you expect when plotted? ā€” A straight diagonal line through (0,0). Since A and B are identical, y = x. All points lie on the diagonal line y = x.
  17. Pattern x: add 3. Pattern y: add 6. Starting from 0, what is the ordered pair at step 4? ā€” (9, 18). Step 4: x = 3Ɨ3=9 (3 steps of +3 from 0 gives step 1ā†’3, step 2ā†’6, step 3ā†’9, step 4... wait: step 0=0, step 1=3, step 2=6, step 3=9, step 4=12). At step 4: x=12, y=24. The correct answer is (12, 24).
  18. A coordinate grid pattern starts at (0,0) and each step increases x by 1 and y by 4. What is the ordered pair at step 6? ā€” (6, 24). After 6 steps: x = 6, y = 4Ɨ6 = 24. Ordered pair: (6, 24).