Let’s solve each problem step by step using the
order of operations (PEMDAS):
>
Parentheses
>
Exponents
>
Multiplication and
Division (left to right)
>
Addition and
Subtraction (left to right)
---
Problem 1:
10 + (12 - 3)
→ First, do inside parentheses: 12 - 3 = 9
→ Then: 10 + 9 =
19
---
Problem 2:
(12 + 4) x 7 + 2
→ Parentheses first: 12 + 4 = 16
→ Multiply: 16 x 7 = 112
→ Add: 112 + 2 =
114
---
Problem 3:
(15 - 11) x 3 - 2
→ Parentheses: 15 - 11 = 4
→ Multiply: 4 x 3 = 12
→ Subtract: 12 - 2 =
10
---
Problem 4:
12 x 3 - 7 + 2
→ Multiplication first: 12 x 3 = 36
→ Then left to right: 36 - 7 = 29; 29 + 2 =
31
---
Problem 5:
8² + (15 - 7)
→ Exponent first: 8² = 64
→ Parentheses: 15 - 7 = 8
→ Add: 64 + 8 =
72
---
Problem 6:
3³ - (4 + 7)
→ Exponent: 3³ = 27
→ Parentheses: 4 + 7 = 11
→ Subtract: 27 - 11 =
16
---
Problem 7:
(4 x 3) - 3²
→ Parentheses: 4 x 3 = 12
→ Exponent: 3² = 9
→ Subtract: 12 - 9 =
3
---
Problem 8:
6 x 3 ÷ 9
→ Left to right for multiplication/division:
6 x 3 = 18
18 ÷ 9 =
2
---
Problem 9:
(3 x 5²) + (12 - 7)
→ Inside first parentheses: 5² = 25 → 3 x 25 = 75
→ Second parentheses: 12 - 7 = 5
→ Add: 75 + 5 =
80
---
Problem 10:
11² + 81
→ Exponent: 11² = 121
→ Add: 121 + 81 =
202
---
Problem 11:
6 + 4 + 11
→ Just add left to right: 6 + 4 = 10; 10 + 11 =
21
---
Problem 12:
(10 + 23) - 3 + 2
→ Parentheses: 10 + 23 = 33
→ Left to right: 33 - 3 = 30; 30 + 2 =
32
---
Final Answer:
19, 114, 10, 31, 72, 16, 3, 2, 80, 202, 21, 32
Parent Tip: Review the logic above to help your child master the concept of math worksheet middle school.
