Evaluate Expressions With Grouping Symbols - 5th Grade Math

1. What is the value of $[15 - (6 + 2)] + 9$?

   $16$. Work inside out: $6+2=8$, $15-8=7$, then $7+9=16$.

2. What is the value of $6 \times (4 - 1)$?

   $18$. First: $(4-1)=3$, then $6 \times 3=18$.

3. Which option correctly rewrites $8 - (3 - 2)$ without parentheses?

   $8 - 3 + 2$. Subtracting a difference changes the sign of the second term.

4. What is the value of $24 \times \frac{1}{3} + (2 \times 3)$?

   $14$. Calculate $24 \times \frac{1}{3}=8$ and $(2 \times 3)=6$, then $8+6=14$.

5. What is the value of $15 - [3 \times (2 + 1)]$?

   $6$. First: $(2+1)=3$, then $3 \times 3=9$, finally $15-9=6$.

6. What is the value of $7 + [12 - 5]$?

   $14$. First evaluate brackets: $12-5=7$, then add: $7+7=14$.

7. What is the value of $\frac{1}{2} \times (8 + 4)$?

   $6$. First add in parentheses: $8+4=12$, then multiply: $\frac{1}{2} \times 12=6$.

8. Identify the correct evaluation: Is $12-3\times(2+1)$ equal to $27$ or $3$?

   $3$. $(2+1)=3$, $3\times^3=9$, then $12-9=3$ (not $27$).

9. Identify the missing grouping symbol to make $8 \times \boxed{\phantom{()}} 3 + 2$ equal $40$.

   Use parentheses: $8 \times (3 + 2)$. Without parentheses: $8 \times 3+2=26$; with them: $8 \times 5=40$.

10. What is the value of $3 \times (4 + 2)$?

    $18$. First add inside parentheses: $4+2=6$, then multiply: $3 \times 6=18$.

11. Identify the first operation to perform in $6 + 2 \times (5 - 3)$.

    Compute $(5 - 3)$. Parentheses are evaluated before any other operations.

12. What is the correct order for evaluating grouping symbols: parentheses, brackets, or braces?

    Evaluate the innermost grouping first, then work outward. This prevents errors when multiple groupings are nested.

13. What is the value of $5 \times [2 + (3 \times 4)]$?

    $70$. Work inside out: $3 \times 4=12$, then $2+12=14$, finally $5 \times 14=70$.

14. What is the order of operations used in Grade $5$ when evaluating expressions?

    Grouping symbols, then multiply/divide, then add/subtract (left to right). This follows the standard order of operations.

15. What is the value of $4 \times \{3 + [8 - (6)]\}$?

    $20$. Work inside out: $8-6=2$, $3+2=5$, $4 \times 5=20$.

16. What is the value of $3 \times (4 + 2)$?

    $18$. First add inside parentheses: $4+2=6$, then multiply: $3 \times 6=18$.

17. What is the value of $(12 - 5) + 6$?

    $13$. First subtract inside parentheses: $12-5=7$, then add: $7+6=13$.

18. What is the value of $36 \times [\frac{1}{2} + \frac{1}{4}]$?

    $27$. Add fractions inside brackets: $\frac{1}{2}+\frac{1}{4}=\frac{3}{4}$, then $36 \times \frac{3}{4}=27$.

19. Identify the grouping symbols used in numerical expressions at this grade level.

    Parentheses $()$, brackets $[]$, and braces $\{\}$. These are the three types of grouping symbols.

20. What does it mean to evaluate a numerical expression that includes grouping symbols?

    Find the value by following the order of operations and grouping symbols. This process ensures we calculate expressions correctly.

21. What is the value of $24 \times \frac{1}{3} + 2$?

    $10$. First multiply: $24 \times \frac{1}{3}=8$, then add: $8+2=10$.

22. Which option shows the correct first step for $10 - [6 - (2 + 1)]$?

    First find $(2 + 1)$. Start with the innermost parentheses.

23. What is the value of ${12 + [18 - (6 \times 2)]}$?

    $18$. Work inside out: $(6 \times 2)=12$, $[18-12]=6$, then ${12+6}=18$.

24. What is the correct order for evaluating grouping symbols in a numerical expression?

    Evaluate inside parentheses $()$, then brackets $[]$, then braces ${}$. Work from innermost to outermost grouping symbols.

25. What is the value of $40 - (12 + 8)$?

    $20$. First add in parentheses: $12+8=20$, then subtract: $40-20=20$.

26. What is the value of $(5 + \frac{1}{2}) \times 8$?

    $44$. Add inside parentheses: $5+\frac{1}{2}=5.5$, then multiply: $5.5 \times 8=44$.

27. What is the value of $\frac{1}{2} \times (14 + 6)$?

    $10$. Add inside parentheses: $14+6=20$, then multiply: $\frac{1}{2} \times 20=10$.

28. What is the value of $\{2 + [3 + (4 + 1)]\}$?

    $10$. Work from innermost: $4+1=5$, $3+5=8$, then $2+8=10$.

29. What is the value of $9 \times [2 + (3 - 1)]$?

    $36$. First: $(3-1)=2$, then $2+2=4$, finally $9 \times 4=36$.

30. What is the value of $5 + \frac{1}{2} \times 8$?

    $9$. Order of operations: multiply first $\frac{1}{2} \times 8=4$, then add $5+4=9$.

31. What is the value of $60 \times \frac{1}{5} \times (3 - 1)$?

    $24$. Evaluate parentheses: $ (3-1)=2 $, then multiply left to right: $60 \times \frac{1}{5} \times 2=24$.

32. What is the value of $(18 - 6) \times 2$?

    $24$. First subtract in parentheses: $18-6=12$, then multiply: $12 \times 2=24$.

33. What is the value of $2 \times [9 - (4 + 1)]$?

    $8$. Work inside out: $4+1=5$, $9-5=4$, then $2 \times 4=8$.

34. What is the value of $\{20 - [6 + 4]\} \times 3$?

    $30$. Work inside out: $6+4=10$, $20-10=10$, then $10 \times 3=30$.

35. What is the correct order for grouping symbols in $\{[\,(\ )\,]\}$ when evaluating?

    Evaluate inside $()$ first, then $[]$, then $\{\}$. Work from innermost to outermost grouping symbols.

36. What is the value of $\frac{1}{2} \times [16 - (4 \times 2)]$?

    $4$. Work inside out: $(4 \times 2)=8$, $[16-8]=8$, then $\frac{1}{2} \times 8=4$.

37. What is the order of operations when an expression has grouping symbols?

    Evaluate inside grouping symbols first, then follow order of operations. Grouping symbols override normal order of operations.

38. What is the value of $[4 \times (3 + 1)] - (10 - 2)$?

    $8$. Evaluate each group: $3+1=4$, $4 \times 4=16$, $10-2=8$, then $16-8=8$.

39. What is the order of operations for $+$, $-$, $\times$, and $\div$ in an expression?

    After grouping: do $\times$ and $\div$ left to right, then $+$ and $-$ left to right. PEMDAS: Parentheses, Exponents, MD left-to-right, AS left-to-right.

40. What is the value of $18 \/ [3 \times (2 + 1)]$?

    $2$. Work inside out: $2+1=3$, $3 \times 3=9$, then $18 \div 9=2$.

41. Find the value of $7 + \frac{1}{4} \times (20 - 4)$.

    $11$. First subtract in parentheses: $(20-4)=16$, then $\frac{1}{4} \times 16=4$, finally $7+4=11$.

42. What is the value of $\{30 \/ [5 \times (2 + 1)]\} + 4$?

    $6$. Work inside out: $2+1=3$, $5 \times 3=15$, $30 \div 15=2$, then $2+4=6$.

43. What is the value of $9 + (16 \/ 4) \times 2$?

    $17$. Follow order: parentheses first, then division, multiplication, addition.

44. What is the value of $\{20 - [6 \times (2 + 1)]\}$?

    $2$. Work inside out: $(2+1)=3$, $6 \times 3=18$, $20-18=2$.

45. What is the value of $[12 - (5 + 1)] \times 2$?

    $12$. First: $(5+1)=6$, then $12-6=6$, finally $6 \times 2=12$.

46. What is the value of $\{25 - [10 + (3 \times 2)]\}$?

    $9$. Work inside out: $3 \times 2=6$, $10+6=16$, $25-16=9$.

47. What is the value of $20 \times [3 - (1 + 1)]$?

    $20$. Work inside out: $(1+1)=2$, $[3-2]=1$, then $20 \times 1=20$.

48. What does it mean to evaluate a numerical expression with grouping symbols?

    Compute the value by doing operations inside grouping symbols first. Follow order of operations, starting with grouped expressions.

49. What is the value of $24 \/ (3 + 5)$?

    $3$. First add in parentheses: $3+5=8$, then divide: $24 \div 8=3$.

50. What is the value of $8 - (3 + 2)$?

    $3$. First: $(3+2)=5$, then $8-5=3$.

51. What does it mean to evaluate a numerical expression?

    Find the value by doing the operations in the correct order. It means calculating the final result step by step.

52. Which option correctly rewrites $8 - (3 + 2)$ without parentheses?

    $8 - 3 - 2$. Subtracting a sum means subtracting each term: $8-3-2$.

53. What is the value of $[18 \times 2] - 10$?

    $26$. First multiply inside brackets: $18 \times 2=36$, then subtract: $36-10=26$.

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