Evaluate Expressions With Variables - 6th Grade Math

1. What is the value of $2x^2$ when $x=-3$?

   $18$. $2(-3)^2 = 2(9) = 18$

2. What is the value of $\frac{n - 1}{3}$ when $n = 10$?

   $3$. Substitute $n = 10$: $\frac{10 - 1}{3} = \frac{9}{3} = 3$.

3. What is the value of $7+3(x-4)$ when $x=4$?

   $7$. $7+3(4-4) = 7+3(0) = 7+0 = 7$

4. What is the value of $\frac{1}{2}bh$ when $b = 8$ and $h = 5$?

   $20$. This is the area formula for a triangle: $\frac{1}{2} \times 8 \times 5 = 20$.

5. What is the value of $5(a - 2)$ when $a = 9$?

   $35$. Substitute $a = 9$: $5(9 - 2) = 5(7) = 35$.

6. What is the value of $4y - 3(y - 2)$ when $y = 5$?

   $11$. Substitute $y = 5$: $4(5) - 3(5 - 2) = 20 - 3(3) = 20 - 9 = 11$.

7. What is the value of $3x + 5$ when $x = 4$?

   $17$. Replace $x$ with $4$: $3(4) + 5 = 12 + 5 = 17$.

8. What is the value of $7 - (2t - 5)$ when $t = 6$?

   $0$. Substitute $t = 6$: $7 - (2(6) - 5) = 7 - (12 - 5) = 7 - 7 = 0$.

9. What does it mean to evaluate an expression such as $3x+2$ when $x=5$?

   Substitute $x=5$ and simplify to get a number. Replace the variable with its given value and calculate.

10. What is the value of $a^2-b$ when $a=5$ and $b=12$?

    $13$. $5^2-12 = 25-12 = 13$

11. What is the value of $3^2 + x$ when $x = 4$?

    $13$. Substitute $x = 4$: $3^2 + 4 = 9 + 4 = 13$.

12. What is the value of $\frac{x+5}{2}$ when $x=7$?

    $6$. $\frac{7+5}{2} = \frac{12}{2} = 6$

13. What is the value of $3x+2$ when $x=5$?

    $17$. $3(5)+2 = 15+2 = 17$

14. What does it mean to evaluate an expression at $x = 4$?

    Substitute $4$ for $x$ and compute the value. Replace the variable with the given number in the expression.

15. What is the distance $d = 60h$ miles when $h = 2.5$ hours?

    $150$. Substitute $h = 2.5$: $d = 60(2.5) = 150$ miles.

16. What is the total cost $C = 2.5t + 4$ dollars when $t = 6$?

    $19$. Substitute $t = 6$: $C = 2.5(6) + 4 = 15 + 4 = 19$ dollars.

17. What is the value of $2(x + 4) - x$ when $x = 7$?

    $15$. Substitute $x = 7$: $2(7 + 4) - 7 = 2(11) - 7 = 22 - 7 = 15$.

18. What is the value of $2(3x + 1)$ when $x = 2$?

    $14$. Substitute $x = 2$: $2(3(2) + 1) = 2(6 + 1) = 2(7) = 14$.

19. What is the value of $2x + 3x$ when $x = 6$?

    $30$. Substitute $x = 6$: $2(6) + 3(6) = 12 + 18 = 30$.

20. What is the value of $3(x + 4) - 2$ when $x = 1$?

    $13$. First add: $1 + 4 = 5$, multiply by $3$ to get $15$, then subtract $2$.

21. What is the value of $12(x-1)$ when $x=4$?

    $36$. $12(4-1) = 12(3) = 36$

22. What is the value of $\frac{x}{3} + 2$ when $x = 9$?

    $5$. Calculate $\frac{9}{3} = 3$, then add $2$ to get $5$.

23. What is the value of $2p+3q$ when $p=4$ and $q=1$?

    $11$. $2(4)+3(1) = 8+3 = 11$

24. What is the value of $(x + 1)^2$ when $x = 3$?

    $16$. First add: $3 + 1 = 4$, then square to get $16$.

25. What is the value of $\frac{3}{4}k$ when $k = 8$?

    $6$. Substitute $k = 8$: $\frac{3}{4}(8) = \frac{24}{4} = 6$.

26. What is the value of $\frac{3}{4}n$ when $n=20$?

    $15$. $\frac{3}{4}(20) = \frac{60}{4} = 15$

27. What is the value of $-3x + 2$ when $x = 4$?

    $-10$. Multiply first: $-3(4) = -12$, then add $2$ to get $-10$.

28. What is the value of $-3a + 4$ when $a = 5$?

    $-11$. Substitute $a = 5$: $-3(5) + 4 = -15 + 4 = -11$.

29. What is the value of $6 - (2x + 1)$ when $x = 2$?

    $1$. Calculate inside parentheses first: $2(2) + 1 = 5$, then $6 - 5 = 1$.

30. What is the correct order of operations used when evaluating expressions?

    Parentheses, exponents, multiply/divide, add/subtract. Remember PEMDAS: operations are performed in this specific sequence.

31. What order of operations should you use to evaluate an expression with variables?

    Parentheses, exponents, multiplication/division, addition/subtraction. PEMDAS ensures consistent evaluation of expressions.

32. What is the value of $18 \div (n + 2)$ when $n = 4$?

    $3$. Substitute $n = 4$: $18 \div (4 + 2) = 18 \div 6 = 3$.

33. What is the value of $2a + 3b$ when $a = 1$ and $b = 4$?

    $14$. Substitute both values: $2(1) + 3(4) = 2 + 12 = 14$.

34. What is the value of $6-2(1-k)$ when $k=-2$?

    $0$. $6-2(1-(-2)) = 6-2(3) = 6-6 = 0$

35. What is the value of $5(a - 2)$ when $a = 7$?

    $25$. First find $a - 2 = 7 - 2 = 5$, then multiply by $5$.

36. What is the distance $d = 60t$ traveled in $t = 2.5$ hours?

    $150$. Use distance formula: speed times time equals $60 \times 2.5 = 150$.

37. What is the value of $2p^2$ when $p = 3$?

    $18$. Substitute $p = 3$: $2(3)^2 = 2(9) = 18$.

38. What is the value of $12 - 2y$ when $y = 3$?

    $6$. Replace $y$ with $3$: $12 - 2(3) = 12 - 6 = 6$.

39. What is the value of $2(a+3)$ when $a=4$?

    $14$. $2(4+3) = 2(7) = 14$

40. What is the value of $x^2 - 1$ when $x = 6$?

    $35$. Square $6$ to get $36$, then subtract $1$.

41. What is the value of $5x - 2$ when $x = 0$?

    $-2$. Substitute $x = 0$: $5(0) - 2 = 0 - 2 = -2$.

42. What is the value of $2^n$ when $n = 5$?

    $32$. Calculate $2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$.

43. What is the value of $3(m-2)+5$ when $m=2$?

    $5$. $3(2-2)+5 = 3(0)+5 = 0+5 = 5$

44. What is the value of $12 - 2n$ when $n = 7$?

    $-2$. Substitute $n = 7$: $12 - 2(7) = 12 - 14 = -2$.

45. What is the value of $2q(1 + q)$ when $q = 3$?

    $24$. Substitute $q = 3$: $2(3)(1 + 3) = 2(3)(4) = 24$.

46. What is the total cost $C=2.50n$ when $n=6$ items are purchased?

    $15$. $C = 2.50(6) = 15$ dollars for 6 items.

47. What is the value of $4-(2t-1)$ when $t=3$?

    $-1$. $4-(2(3)-1) = 4-(6-1) = 4-5 = -1$

48. What is the value of $2(x - 3)^2$ when $x = 5$?

    $8$. First find $5 - 3 = 2$, square to get $4$, then multiply by $2$.

49. What is the value of $5-y^2$ when $y=3$?

    $-4$. $5-3^2 = 5-9 = -4$

50. What is the value of $\frac{2}{3}x+4$ when $x=9$?

    $10$. $\frac{2}{3}(9)+4 = 6+4 = 10$

51. What is the value of $6 + \, \frac{m}{2}$ when $m = 10$?

    $11$. Substitute $m = 10$: $6 + \frac{10}{2} = 6 + 5 = 11$.

52. What is the distance $d=60t$ after $t=\frac{1}{2}$ hour at $60$ miles per hour?

    $30$. $d = 60(\frac{1}{2}) = 30$ miles traveled in half an hour.

53. What is the total cost $C = 2.50n$ for $n = 6$ items?

    $15$. Multiply unit price by quantity: $2.50 \times 6 = 15$.

54. What is the value of $4 + 3x^2$ when $x = 2$?

    $16$. First square $2$ to get $4$, multiply by $3$, then add $4$.

Study these flashcards