Order of operations worksheet with BODMAS rule problems.

Here are the step-by-step solutions for each problem using the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction).

1) $6 \times 2 + (4 + 21 \times 7) \times 2$
* Brackets: Inside the bracket, do multiplication first: $21 \times 7 = 147$. Then add: $4 + 147 = 151$.
* Equation becomes: $6 \times 2 + 151 \times 2$
* Multiplication: $6 \times 2 = 12$ and $151 \times 2 = 302$.
* Equation becomes: $12 + 302$
* Addition: $12 + 302 = 314$.

2) $4 \times 10 \div 5 \times (3 \times 7) \div 21$
* Brackets: $3 \times 7 = 21$.
* Equation becomes: $4 \times 10 \div 5 \times 21 \div 21$
* Multiplication/Division (Left to Right):
* $4 \times 10 = 40$
* $40 \div 5 = 8$
* $8 \times 21 = 168$
* $168 \div 21 = 8$

3) $10 \times 2 \div 4 + (32 \times 10) - 26$
* Brackets: $32 \times 10 = 320$.
* Equation becomes: $10 \times 2 \div 4 + 320 - 26$
* Multiplication/Division (Left to Right):
* $10 \times 2 = 20$
* $20 \div 4 = 5$
* Equation becomes: $5 + 320 - 26$
* Addition/Subtraction (Left to Right):
* $5 + 320 = 325$
* $325 - 26 = 299$

4) $30 - 20 + (35 \times 5 - 22) \times 7$
* Brackets: Inside, do multiplication first: $35 \times 5 = 175$. Then subtract: $175 - 22 = 153$.
* Equation becomes: $30 - 20 + 153 \times 7$
* Multiplication: $153 \times 7 = 1071$.
* Equation becomes: $30 - 20 + 1071$
* Addition/Subtraction (Left to Right):
* $30 - 20 = 10$
* $10 + 1071 = 1081$

5) $5 \times 9 + 40 + 24 \div (6 + 18)$
* Brackets: $6 + 18 = 24$.
* Equation becomes: $5 \times 9 + 40 + 24 \div 24$
* Multiplication/Division:
* $5 \times 9 = 45$
* $24 \div 24 = 1$
* Equation becomes: $45 + 40 + 1$
* Addition: $45 + 40 = 85$, then $85 + 1 = 86$.

6) $18 + 8 + 19 + (29 + 19) - 9$
* Brackets: $29 + 19 = 48$.
* Equation becomes: $18 + 8 + 19 + 48 - 9$
* Addition/Subtraction (Left to Right):
* $18 + 8 = 26$
* $26 + 19 = 45$
* $45 + 48 = 93$
* $93 - 9 = 84$

7) $(9 - 9) \div 56 \div 47 \div 81 \div 67$
* Brackets: $9 - 9 = 0$.
* Equation becomes: $0 \div 56 \div 47 \div 81 \div 67$
* Division: Zero divided by any number is always 0.
* Answer is 0.

8) $30 + 17 - 3 - (30 \div 2) + 6$
* Brackets: $30 \div 2 = 15$.
* Equation becomes: $30 + 17 - 3 - 15 + 6$
* Addition/Subtraction (Left to Right):
* $30 + 17 = 47$
* $47 - 3 = 44$
* $44 - 15 = 29$
* $29 + 6 = 35$

9) $10 \times 3 - 7 - (4 \times 5 \div 4)$
* Brackets: Inside, do multiplication/division left to right. $4 \times 5 = 20$, then $20 \div 4 = 5$.
* Equation becomes: $10 \times 3 - 7 - 5$
* Multiplication: $10 \times 3 = 30$.
* Equation becomes: $30 - 7 - 5$
* Subtraction (Left to Right):
* $30 - 7 = 23$
* $23 - 5 = 18$

10) $2 + 39 \times (10 + 23) + 37 - 13$
* Brackets: $10 + 23 = 33$.
* Equation becomes: $2 + 39 \times 33 + 37 - 13$
* Multiplication: $39 \times 33 = 1287$.
* Equation becomes: $2 + 1287 + 37 - 13$
* Addition/Subtraction (Left to Right):
* $2 + 1287 = 1289$
* $1289 + 37 = 1326$
* $1326 - 13 = 1313$

11) $(40 - 4 \times 1 \times 8 + 5) \times 3$
* Brackets: Inside, do multiplication first: $4 \times 1 \times 8 = 32$.
* Bracket becomes: $(40 - 32 + 5)$
* Solve inside bracket left to right: $40 - 32 = 8$, then $8 + 5 = 13$.
* Equation becomes: $13 \times 3$
* Multiplication: $13 \times 3 = 39$.

12) $30 + 26 + 27 \times 2 - 39 \div 13$
* Multiplication/Division:
* $27 \times 2 = 54$
* $39 \div 13 = 3$
* Equation becomes: $30 + 26 + 54 - 3$
* Addition/Subtraction (Left to Right):
* $30 + 26 = 56$
* $56 + 54 = 110$
* $110 - 3 = 107$

Final Answer:
1) 314
2) 8
3) 299
4) 1081
5) 86
6) 84
7) 0
8) 35
9) 18
10) 1313
11) 39
12) 107