Answer :
Alright, let's walk through each of these expressions step-by-step to reach the final answers. We'll follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. [tex]\(12 + 9 \div 3\)[/tex]:
- Division first: [tex]\(9 \div 3 = 3\)[/tex]
- Addition next: [tex]\(12 + 3 = 15\)[/tex]
2. [tex]\(32 \div 8 + 4 \times 6 - 2\)[/tex]:
- Division first: [tex]\(32 \div 8 = 4\)[/tex]
- Multiplication next: [tex]\(4 \times 6 = 24\)[/tex]
- Addition next: [tex]\(4 + 24 = 28\)[/tex]
- Subtraction last: [tex]\(28 - 2 = 26\)[/tex]
3. [tex]\(8 \times 6 + 24 \div 6 - 18\)[/tex]:
- Multiplication first: [tex]\(8 \times 6 = 48\)[/tex]
- Division next: [tex]\(24 \div 6 = 4\)[/tex]
- Addition next: [tex]\(48 + 4 = 52\)[/tex]
- Subtraction last: [tex]\(52 - 18 = 34\)[/tex]
4. [tex]\(198 - 42 \times 15 \div 5 + 6\)[/tex]:
- Multiplication first: [tex]\(42 \times 15 = 630\)[/tex]
- Division next: [tex]\(630 \div 5 = 126\)[/tex]
- Subtraction next: [tex]\(198 - 126 = 72\)[/tex]
- Addition last: [tex]\(72 + 6 = 78\)[/tex]
5. [tex]\(16 \times 8 \div 4\)[/tex]:
- Multiplication first: [tex]\(16 \times 8 = 128\)[/tex]
- Division next: [tex]\(128 \div 4 = 32\)[/tex]
6. [tex]\(23 - 8 \times 2\)[/tex]:
- Multiplication first: [tex]\(8 \times 2 = 16\)[/tex]
- Subtraction next: [tex]\(23 - 16 = 7\)[/tex]
7. [tex]\(100 - 72 \div 8 + 4 \times 3\)[/tex]:
- Division first: [tex]\(72 \div 8 = 9\)[/tex]
- Multiplication next: [tex]\(4 \times 3 = 12\)[/tex]
- Subtraction next: [tex]\(100 - 9 = 91\)[/tex]
- Addition last: [tex]\(91 + 12 = 103\)[/tex]
8. [tex]\(30 + 75 \div 15 \times 4 - 18\)[/tex]:
- Division first: [tex]\(75 \div 15 = 5\)[/tex]
- Multiplication next: [tex]\(5 \times 4 = 20\)[/tex]
- Addition next: [tex]\(30 + 20 = 50\)[/tex]
- Subtraction last: [tex]\(50 - 18 = 32\)[/tex]
9. [tex]\(56 - 36 \div 4 \times 2 + 7\)[/tex]:
- Division first: [tex]\(36 \div 4 = 9\)[/tex]
- Multiplication next: [tex]\(9 \times 2 = 18\)[/tex]
- Subtraction next: [tex]\(56 - 18 = 38\)[/tex]
- Addition last: [tex]\(38 + 7 = 45\)[/tex]
10. [tex]\(56 \div 14 \times 3 - 10 \div 5 + 1\)[/tex]:
- Division first: [tex]\(56 \div 14 = 4\)[/tex]
- Division next: [tex]\(10 \div 5 = 2\)[/tex]
- Multiplication next: [tex]\(4 \times 3 = 12\)[/tex]
- Subtraction next: [tex]\(12 - 2 = 10\)[/tex]
- Addition last: [tex]\(10 + 1 = 11\)[/tex]
11. [tex]\(105 \times 14 \div 7 + 6 - 1\)[/tex]:
- Multiplication first: [tex]\(105 \times 14 = 1470\)[/tex]
- Division next: [tex]\(1470 \div 7 = 210\)[/tex]
- Addition next: [tex]\(210 + 6 = 216\)[/tex]
- Subtraction last: [tex]\(216 - 1 = 215\)[/tex]
12. [tex]\(17 + 34 \div 17 \times 5 - 20\)[/tex]:
- Division first: [tex]\(34 \div 17 = 2\)[/tex]
- Multiplication next: [tex]\(2 \times 5 = 10\)[/tex]
- Addition next: [tex]\(17 + 10 = 27\)[/tex]
- Subtraction last: [tex]\(27 - 20 = 7\)[/tex]
Summarizing, the results for the expressions are as follows:
[tex]\[ \begin{align*} 1. & \quad 15 \\ 2. & \quad 26 \\ 3. & \quad 34 \\ 4. & \quad 78 \\ 5. & \quad 32 \\ 6. & \quad 7 \\ 7. & \quad 103 \\ 8. & \quad 32 \\ 9. & \quad 45 \\ 10. & \quad 11 \\ 11. & \quad 215 \\ 12. & \quad 7 \end{align*} \][/tex]
1. [tex]\(12 + 9 \div 3\)[/tex]:
- Division first: [tex]\(9 \div 3 = 3\)[/tex]
- Addition next: [tex]\(12 + 3 = 15\)[/tex]
2. [tex]\(32 \div 8 + 4 \times 6 - 2\)[/tex]:
- Division first: [tex]\(32 \div 8 = 4\)[/tex]
- Multiplication next: [tex]\(4 \times 6 = 24\)[/tex]
- Addition next: [tex]\(4 + 24 = 28\)[/tex]
- Subtraction last: [tex]\(28 - 2 = 26\)[/tex]
3. [tex]\(8 \times 6 + 24 \div 6 - 18\)[/tex]:
- Multiplication first: [tex]\(8 \times 6 = 48\)[/tex]
- Division next: [tex]\(24 \div 6 = 4\)[/tex]
- Addition next: [tex]\(48 + 4 = 52\)[/tex]
- Subtraction last: [tex]\(52 - 18 = 34\)[/tex]
4. [tex]\(198 - 42 \times 15 \div 5 + 6\)[/tex]:
- Multiplication first: [tex]\(42 \times 15 = 630\)[/tex]
- Division next: [tex]\(630 \div 5 = 126\)[/tex]
- Subtraction next: [tex]\(198 - 126 = 72\)[/tex]
- Addition last: [tex]\(72 + 6 = 78\)[/tex]
5. [tex]\(16 \times 8 \div 4\)[/tex]:
- Multiplication first: [tex]\(16 \times 8 = 128\)[/tex]
- Division next: [tex]\(128 \div 4 = 32\)[/tex]
6. [tex]\(23 - 8 \times 2\)[/tex]:
- Multiplication first: [tex]\(8 \times 2 = 16\)[/tex]
- Subtraction next: [tex]\(23 - 16 = 7\)[/tex]
7. [tex]\(100 - 72 \div 8 + 4 \times 3\)[/tex]:
- Division first: [tex]\(72 \div 8 = 9\)[/tex]
- Multiplication next: [tex]\(4 \times 3 = 12\)[/tex]
- Subtraction next: [tex]\(100 - 9 = 91\)[/tex]
- Addition last: [tex]\(91 + 12 = 103\)[/tex]
8. [tex]\(30 + 75 \div 15 \times 4 - 18\)[/tex]:
- Division first: [tex]\(75 \div 15 = 5\)[/tex]
- Multiplication next: [tex]\(5 \times 4 = 20\)[/tex]
- Addition next: [tex]\(30 + 20 = 50\)[/tex]
- Subtraction last: [tex]\(50 - 18 = 32\)[/tex]
9. [tex]\(56 - 36 \div 4 \times 2 + 7\)[/tex]:
- Division first: [tex]\(36 \div 4 = 9\)[/tex]
- Multiplication next: [tex]\(9 \times 2 = 18\)[/tex]
- Subtraction next: [tex]\(56 - 18 = 38\)[/tex]
- Addition last: [tex]\(38 + 7 = 45\)[/tex]
10. [tex]\(56 \div 14 \times 3 - 10 \div 5 + 1\)[/tex]:
- Division first: [tex]\(56 \div 14 = 4\)[/tex]
- Division next: [tex]\(10 \div 5 = 2\)[/tex]
- Multiplication next: [tex]\(4 \times 3 = 12\)[/tex]
- Subtraction next: [tex]\(12 - 2 = 10\)[/tex]
- Addition last: [tex]\(10 + 1 = 11\)[/tex]
11. [tex]\(105 \times 14 \div 7 + 6 - 1\)[/tex]:
- Multiplication first: [tex]\(105 \times 14 = 1470\)[/tex]
- Division next: [tex]\(1470 \div 7 = 210\)[/tex]
- Addition next: [tex]\(210 + 6 = 216\)[/tex]
- Subtraction last: [tex]\(216 - 1 = 215\)[/tex]
12. [tex]\(17 + 34 \div 17 \times 5 - 20\)[/tex]:
- Division first: [tex]\(34 \div 17 = 2\)[/tex]
- Multiplication next: [tex]\(2 \times 5 = 10\)[/tex]
- Addition next: [tex]\(17 + 10 = 27\)[/tex]
- Subtraction last: [tex]\(27 - 20 = 7\)[/tex]
Summarizing, the results for the expressions are as follows:
[tex]\[ \begin{align*} 1. & \quad 15 \\ 2. & \quad 26 \\ 3. & \quad 34 \\ 4. & \quad 78 \\ 5. & \quad 32 \\ 6. & \quad 7 \\ 7. & \quad 103 \\ 8. & \quad 32 \\ 9. & \quad 45 \\ 10. & \quad 11 \\ 11. & \quad 215 \\ 12. & \quad 7 \end{align*} \][/tex]
