# Practice Questions for Order of Operations in Elementary Education

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.

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.

## 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.

## 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

## 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.

## 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**