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Practice Questions for Order of Operations in Elementary Education

written by: Kayla Griffin • edited by: Noreen Gunnell • updated: 2/17/2012

After you've gone through order of operations in your class, try some of these practice questions on your own to really understand the material. This worksheet includes problems with step-by-step solutions.

  • slide 1 of 5

    To complete this worksheet, you already need an introductory knowledge of the order of operations. If this is too difficult, or there are things you don’t understand, check the remainder of the series for an introduction to the order of operations.

  • slide 2 of 5

    Directions

    Solve each problem by applying the order of operation rules. For the first few problems, write down each step and which operation you used. Every problem is worked through at the end, but try to solve them as best you can before looking. Good Luck.

  • slide 3 of 5

    Problems

    Problems:

    1) (6+(-7)-1) x 8

    2) (-6)-((-2)-5)^2

    3) (6-1)((-3)-4)

    4) 20 / (3 x 2 – 4)

    5) 4-3+8+3

    6) 7 – (10-(-8))-3

    7) (28-8) / ((-9)-(-5))

    8) ((-10)+3) / ((-8) +7)

    9) 2 + (-1)^2 – 7

    10) ((-6) / (-3))x((-30) / (-3))

    11) (21-6-3) / (8-2)

    12) 8^2 / (3+5)

    13) (26+1) / (3(4-3))

    14) 3 / (8-6+6-5)

    15) 4+9-(7-6) -10

    16) 6 / (8-2) + 4 + 3

    17) 6 x (23 + 4 – 7) / 10

    18) 3^2 / (6+5-2)

    19) (9-4x1^2) x 6

    20) 6 + 8 – 8 + 8^2

  • slide 4 of 5

    Order of Operations Worksheet Solutions

    Each problem is solved step-by-step. Only one operation occurs in each line. The solutions are designed to show you exactly how to think about the problem. If you don’t understand an answer, go back and solve it slowly, comparing each step to the solution. The answers are in BOLD type.

  • slide 5 of 5

    Problem Solutions

    1) (6+(-7)-1) x 8

    = (-1-1)x 8

    = -2 x 8

    = -16

    2) (-6)-((-2)-5)^2

    = -6 – (-7)^2

    = -6 – 49

    = -55

    3) (6-1)((-3)-4)

    =(5)(-3-4)

    =(5)(-7)

    = -35

    4) 20 / (3 x 2 – 4)

    = 20 / (6-4)

    = 20 / 2

    = 10

    5) 4-3+8+3

    = 1 + 8 + 3

    =9 + 3

    = 12

    6) 7 – (10-(-8))-3

    =7 – (10+8)-3

    =7 – 18 – 3

    = -11 – 3

    = -14

    7) (28-8) / ((-9)-(-5))

    =20 / ((-9)-(-5))

    = 20 / (-9+5)

    =20/(-4)

    = -5

    8) ((-10)+3) / ((-8) +7)

    = -7 / ((-8)+7)

    = -7 / -1

    = 7

    9) 2 + (-1)^2 – 7

    = 2+1-7

    =3-7

    = -4

    10) ((-6) / (-3))((-30) / (-3))

    = (2)((-30)/(-3))

    =(2)(3)

    = 6

    11) (21-6-3) / (8-2)

    = (15-3) / (8-2)

    =12 / (8-2)

    =12/6

    =2

    12) 8^2 / (3+5)

    = 8^2 / 8

    =64 / 8

    =8

    13) (26+1) / (3(4-3))

    =27/(3(1))

    =27/3

    =9

    14) 3 / (8-6+6-5)

    =3/(2+6-5)

    =3/(8-5)

    =3/(3)

    =1

    15) 4+9-(7-6) -10

    = 4+9-1-10

    =13-1-10

    =12-10

    =2

    16) 6 / (8-2) + 4 + 3

    = 6 / 6 + 4 + 3

    =1+ 4 + 3

    =5 + 3

    = 8

    17) 6 x (23 + 4 – 7) / 10

    = 6 x (27-7)/10

    = 6 x 20/10

    =120/10

    =12

    18) 3^2 / (6+5-2)

    =3^2 / (11-2)

    =3^2 / 9

    =9/9

    =1

    19) (9-4x1^2) x 6

    = (9 – 4 x 1) x 6

    =(9-4) x 6

    =5 x 6

    = 30

    20) 6 + 8 – 8 + 8^2

    = 6 + 8 – 8 + 64

    = 14 – 8 + 64

    = 6 + 64

    =70

Order of Operations

Order of operations explanations, quizzes and homework help for kindergarten through middle school students.
  1. Solve Equations with Order of Operations
  2. A Quiz for Order of Operations
  3. Practice Questions for Order of Operations in Elementary Education