Absolutely! Let’s solve each problem step-by-step using the
Order of Operations (PEMDAS/BODMAS):
>
Parentheses /
Brackets
>
Exponents /
Orders (powers, roots)
>
Multiplication and
Division (left to right)
>
Addition and
Subtraction (left to right)
---
① 18 - (21 - 5) ÷ (22 - 18)
- Parentheses first:
- (21 - 5) =
16
- (22 - 18) =
4
- Now: 18 - 16 ÷ 4
- Division next: 16 ÷ 4 =
4
- Then subtraction: 18 - 4 =
14
✔ Answer: 14
---
② 24 ÷ 6 + 4 × (3 + 6)
- Parentheses: (3 + 6) =
9
- Now: 24 ÷ 6 + 4 × 9
- Division and multiplication left to right:
- 24 ÷ 6 =
4
- 4 × 9 =
36
- Addition: 4 + 36 =
40
✔ Answer: 40
---
③ 5 + 10 × (3 - 2)²
- Parentheses: (3 - 2) =
1
- Exponent: 1² =
1
- Multiplication: 10 × 1 =
10
- Addition: 5 + 10 =
15
✔ Answer: 15
---
④ (-7) + 2³ × 3 - 8
- Exponent: 2³ =
8
- Multiplication: 8 × 3 =
24
- Now: -7 + 24 - 8
- Left to right:
- -7 + 24 =
17
- 17 - 8 =
9
✔ Answer: 9
---
⑤ 8 ÷ [(-8) - (-2) + 5]³
- Inside brackets: (-8) - (-2) = -8 + 2 =
-6
- Then: -6 + 5 =
-1
- Exponent: (-1)³ =
-1
- Division: 8 ÷ (-1) =
-8
✔ Answer: -8
---
⑥ 36 ÷ 3 × [(7 - 2 - 4) × 2]
- Inner parentheses: 7 - 2 - 4 =
1
- Multiply by 2: 1 × 2 =
2
- Now: 36 ÷ 3 × 2
- Left to right:
- 36 ÷ 3 =
12
- 12 × 2 =
24
✔ Answer: 24
---
⑦ 7 × (4² + 2 - 8)
- Exponent: 4² =
16
- Inside parentheses: 16 + 2 - 8 =
10
- Multiply: 7 × 10 =
70
✔ Answer: 70
---
⑧ [8 - (-4) + (-8)]² × 4
- Inside brackets: 8 - (-4) = 8 + 4 =
12
- Then: 12 + (-8) =
4
- Exponent: 4² =
16
- Multiply: 16 × 4 =
64
✔ Answer: 64
---
⑨ (81 ÷ 9) + 25 - 17 × 2
- Parentheses: 81 ÷ 9 =
9
- Multiplication: 17 × 2 =
34
- Now: 9 + 25 - 34
- Left to right:
- 9 + 25 =
34
- 34 - 34 =
0
✔ Answer: 0
---
⑩ (-2)² ÷ 4 - 9 × 8
- Exponent: (-2)² =
4 (Note: negative squared is positive)
- Division: 4 ÷ 4 =
1
- Multiplication: 9 × 8 =
72
- Subtraction: 1 - 72 =
-71
✔ Answer: -71
---
##
✔ Final Answers:
1.
14
2.
40
3.
15
4.
9
5.
-8
6.
24
7.
70
8.
64
9.
0
10.
-71
Let me know if you’d like a printable version or more practice problems! 📚
Parent Tip: Review the logic above to help your child master the concept of orders of operation worksheet.
