Answer :
Let's go through each mathematical expression step-by-step:
40. [tex]\((8 - 2 \cdot 3) - 9\)[/tex]
First, we need to follow the order of operations (PEMDAS/BODMAS):
- Parentheses/Brackets first.
- Exponents/Orders (none in this question).
- Multiplication and Division from left to right.
- Addition and Subtraction from left to right.
1. Calculate inside the parentheses: [tex]\(8 - 2 \cdot 3\)[/tex].
2. [tex]\(2 \cdot 3 = 6\)[/tex].
3. [tex]\(8 - 6 = 2\)[/tex].
4. Now, subtract 9: [tex]\(2 - 9 = -7\)[/tex].
So, the result is: [tex]\(-7\)[/tex].
41. [tex]\((8 - 2)(3 - 9)\)[/tex]
1. Solve inside the parentheses: [tex]\(8 - 2\)[/tex] and [tex]\(3 - 9\)[/tex].
2. [tex]\(8 - 2 = 6\)[/tex].
3. [tex]\(3 - 9 = -6\)[/tex].
4. Now, multiply the results: [tex]\(6 \cdot (-6) = -36\)[/tex].
So, the result is: [tex]\(-36\)[/tex].
42. [tex]\([4(6 + 8)] \div (4 + 3)\)[/tex]
1. Solve inside the parentheses and brackets: [tex]\(6 + 8\)[/tex] and [tex]\(4 + 3\)[/tex].
2. [tex]\(6 + 8 = 14\)[/tex].
3. [tex]\(4 + 3 = 7\)[/tex].
4. Multiply and then divide: [tex]\(4 \cdot 14 = 56\)[/tex].
5. [tex]\(56 \div 7 = 8\)[/tex].
So, the result is: [tex]\(8.0\)[/tex].
43. [tex]\(4(5) - 2(6) + 4\)[/tex]
1. Multiply first: [tex]\(4 \cdot 5\)[/tex] and [tex]\(2 \cdot 6\)[/tex].
2. [tex]\(4 \cdot 5 = 20\)[/tex].
3. [tex]\(2 \cdot 6 = 12\)[/tex].
4. Now, subtract and add: [tex]\(20 - 12 + 4\)[/tex].
5. [tex]\(20 - 12 = 8\)[/tex].
6. [tex]\(8 + 4 = 12\)[/tex].
So, the result is: [tex]\(12\)[/tex].
44. [tex]\(8(-7) + 6(-5)\)[/tex]
1. Multiply first: [tex]\(8 \cdot (-7)\)[/tex] and [tex]\(6 \cdot (-5)\)[/tex].
2. [tex]\(8 \cdot (-7) = -56\)[/tex].
3. [tex]\(6 \cdot (-5) = -30\)[/tex].
4. Now, add the results: [tex]\(-56 + (-30) = -86\)[/tex].
So, the result is: [tex]\(-86\)[/tex].
45. [tex]\(10(-5) + 1(-1)\)[/tex]
1. Multiply first: [tex]\(10 \cdot (-5)\)[/tex] and [tex]\(1 \cdot (-1)\)[/tex].
2. [tex]\(10 \cdot (-5) = -50\)[/tex].
3. [tex]\(1 \cdot (-1) = -1\)[/tex].
4. Now, add the results: [tex]\(-50 + (-1) = -51\)[/tex].
So, the result is: [tex]\(-51\)[/tex].
46. [tex]\(19 - 5(-3) + 3\)[/tex]
1. Multiply first: [tex]\(5 \cdot (-3)\)[/tex].
2. [tex]\(5 \cdot (-3) = -15\)[/tex].
3. Now, subtract and add: [tex]\(19 - (-15) + 3\)[/tex].
4. [tex]\(19 - (-15) = 19 + 15 = 34\)[/tex].
5. [tex]\(34 + 3 = 37\)[/tex].
So, the result is: [tex]\(37\)[/tex].
47. [tex]\(14 - 2(-6) + 7\)[/tex]
1. Multiply first: [tex]\(2 \cdot (-6)\)[/tex].
2. [tex]\(2 \cdot (-6) = -12\)[/tex].
3. Now, subtract and add: [tex]\(14 - (-12) + 7\)[/tex].
4. [tex]\(14 - (-12) = 14 + 12 = 26\)[/tex].
5. [tex]\(26 + 7 = 33\)[/tex].
So, the result is: [tex]\(33\)[/tex].
48. [tex]\(9 \div (-3) + 16 \div 8\)[/tex]
1. Divide first: [tex]\(9 \div (-3)\)[/tex] and [tex]\(16 \div 8\)[/tex].
2. [tex]\(9 \div (-3) = -3\)[/tex].
3. [tex]\(16 \div 8 = 2\)[/tex].
4. Now, add the results: [tex]\(-3 + 2 = -1\)[/tex].
So, the result is: [tex]\(-1.0\)[/tex].
49. [tex]\(-32 - 8 \div 4 - (-2)\)[/tex]
1. Divide first: [tex]\(8 \div 4\)[/tex].
2. [tex]\(8 \div 4 = 2\)[/tex].
3. Now, substitute back into the expression and simplify: [tex]\(-32 - 2 - (-2)\)[/tex].
4. Simplify: [tex]\(-32 - 2 + 2\)[/tex].
5. [tex]\(-32 - 2 = -34\)[/tex].
6. [tex]\(-34 + 2 = -32\)[/tex].
So, the result is: [tex]\(-32.0\)[/tex].
50. [tex]\(6[9 - (3 - 4)]\)[/tex]
1. Solve inside the innermost parentheses: [tex]\(3 - 4\)[/tex].
2. [tex]\(3 - 4 = -1\)[/tex].
3. Now, substitute back and solve inside the brackets: [tex]\(9 - (-1)\)[/tex].
4. [tex]\(9 - (-1) = 9 + 1 = 10\)[/tex].
5. Finally, multiply: [tex]\(6 \cdot 10 = 60\)[/tex].
So, the result is: [tex]\(60\)[/tex].
51. [tex]\(8 - (7 - 9)\)[/tex]
1. Solve inside the parentheses: [tex]\(7 - 9\)[/tex].
2. [tex]\(7 - 9 = -2\)[/tex].
3. Now, substitute back and subtract: [tex]\(8 - (-2)\)[/tex].
4. [tex]\(8 - (-2) = 8 + 2 = 10\)[/tex].
So, the result is: [tex]\(10\)[/tex].
Therefore, the results for the expressions are:
[tex]\[ \begin{align*} 40. & \quad -7 \\ 41. & \quad -36 \\ 42. & \quad 8.0 \\ 43. & \quad 12 \\ 44. & \quad -86 \\ 45. & \quad -51 \\ 46. & \quad 37 \\ 47. & \quad 33 \\ 48. & \quad -1.0 \\ 49. & \quad -32.0 \\ 50. & \quad 60 \\ 51. & \quad 10 \\ \end{align*} \][/tex]
40. [tex]\((8 - 2 \cdot 3) - 9\)[/tex]
First, we need to follow the order of operations (PEMDAS/BODMAS):
- Parentheses/Brackets first.
- Exponents/Orders (none in this question).
- Multiplication and Division from left to right.
- Addition and Subtraction from left to right.
1. Calculate inside the parentheses: [tex]\(8 - 2 \cdot 3\)[/tex].
2. [tex]\(2 \cdot 3 = 6\)[/tex].
3. [tex]\(8 - 6 = 2\)[/tex].
4. Now, subtract 9: [tex]\(2 - 9 = -7\)[/tex].
So, the result is: [tex]\(-7\)[/tex].
41. [tex]\((8 - 2)(3 - 9)\)[/tex]
1. Solve inside the parentheses: [tex]\(8 - 2\)[/tex] and [tex]\(3 - 9\)[/tex].
2. [tex]\(8 - 2 = 6\)[/tex].
3. [tex]\(3 - 9 = -6\)[/tex].
4. Now, multiply the results: [tex]\(6 \cdot (-6) = -36\)[/tex].
So, the result is: [tex]\(-36\)[/tex].
42. [tex]\([4(6 + 8)] \div (4 + 3)\)[/tex]
1. Solve inside the parentheses and brackets: [tex]\(6 + 8\)[/tex] and [tex]\(4 + 3\)[/tex].
2. [tex]\(6 + 8 = 14\)[/tex].
3. [tex]\(4 + 3 = 7\)[/tex].
4. Multiply and then divide: [tex]\(4 \cdot 14 = 56\)[/tex].
5. [tex]\(56 \div 7 = 8\)[/tex].
So, the result is: [tex]\(8.0\)[/tex].
43. [tex]\(4(5) - 2(6) + 4\)[/tex]
1. Multiply first: [tex]\(4 \cdot 5\)[/tex] and [tex]\(2 \cdot 6\)[/tex].
2. [tex]\(4 \cdot 5 = 20\)[/tex].
3. [tex]\(2 \cdot 6 = 12\)[/tex].
4. Now, subtract and add: [tex]\(20 - 12 + 4\)[/tex].
5. [tex]\(20 - 12 = 8\)[/tex].
6. [tex]\(8 + 4 = 12\)[/tex].
So, the result is: [tex]\(12\)[/tex].
44. [tex]\(8(-7) + 6(-5)\)[/tex]
1. Multiply first: [tex]\(8 \cdot (-7)\)[/tex] and [tex]\(6 \cdot (-5)\)[/tex].
2. [tex]\(8 \cdot (-7) = -56\)[/tex].
3. [tex]\(6 \cdot (-5) = -30\)[/tex].
4. Now, add the results: [tex]\(-56 + (-30) = -86\)[/tex].
So, the result is: [tex]\(-86\)[/tex].
45. [tex]\(10(-5) + 1(-1)\)[/tex]
1. Multiply first: [tex]\(10 \cdot (-5)\)[/tex] and [tex]\(1 \cdot (-1)\)[/tex].
2. [tex]\(10 \cdot (-5) = -50\)[/tex].
3. [tex]\(1 \cdot (-1) = -1\)[/tex].
4. Now, add the results: [tex]\(-50 + (-1) = -51\)[/tex].
So, the result is: [tex]\(-51\)[/tex].
46. [tex]\(19 - 5(-3) + 3\)[/tex]
1. Multiply first: [tex]\(5 \cdot (-3)\)[/tex].
2. [tex]\(5 \cdot (-3) = -15\)[/tex].
3. Now, subtract and add: [tex]\(19 - (-15) + 3\)[/tex].
4. [tex]\(19 - (-15) = 19 + 15 = 34\)[/tex].
5. [tex]\(34 + 3 = 37\)[/tex].
So, the result is: [tex]\(37\)[/tex].
47. [tex]\(14 - 2(-6) + 7\)[/tex]
1. Multiply first: [tex]\(2 \cdot (-6)\)[/tex].
2. [tex]\(2 \cdot (-6) = -12\)[/tex].
3. Now, subtract and add: [tex]\(14 - (-12) + 7\)[/tex].
4. [tex]\(14 - (-12) = 14 + 12 = 26\)[/tex].
5. [tex]\(26 + 7 = 33\)[/tex].
So, the result is: [tex]\(33\)[/tex].
48. [tex]\(9 \div (-3) + 16 \div 8\)[/tex]
1. Divide first: [tex]\(9 \div (-3)\)[/tex] and [tex]\(16 \div 8\)[/tex].
2. [tex]\(9 \div (-3) = -3\)[/tex].
3. [tex]\(16 \div 8 = 2\)[/tex].
4. Now, add the results: [tex]\(-3 + 2 = -1\)[/tex].
So, the result is: [tex]\(-1.0\)[/tex].
49. [tex]\(-32 - 8 \div 4 - (-2)\)[/tex]
1. Divide first: [tex]\(8 \div 4\)[/tex].
2. [tex]\(8 \div 4 = 2\)[/tex].
3. Now, substitute back into the expression and simplify: [tex]\(-32 - 2 - (-2)\)[/tex].
4. Simplify: [tex]\(-32 - 2 + 2\)[/tex].
5. [tex]\(-32 - 2 = -34\)[/tex].
6. [tex]\(-34 + 2 = -32\)[/tex].
So, the result is: [tex]\(-32.0\)[/tex].
50. [tex]\(6[9 - (3 - 4)]\)[/tex]
1. Solve inside the innermost parentheses: [tex]\(3 - 4\)[/tex].
2. [tex]\(3 - 4 = -1\)[/tex].
3. Now, substitute back and solve inside the brackets: [tex]\(9 - (-1)\)[/tex].
4. [tex]\(9 - (-1) = 9 + 1 = 10\)[/tex].
5. Finally, multiply: [tex]\(6 \cdot 10 = 60\)[/tex].
So, the result is: [tex]\(60\)[/tex].
51. [tex]\(8 - (7 - 9)\)[/tex]
1. Solve inside the parentheses: [tex]\(7 - 9\)[/tex].
2. [tex]\(7 - 9 = -2\)[/tex].
3. Now, substitute back and subtract: [tex]\(8 - (-2)\)[/tex].
4. [tex]\(8 - (-2) = 8 + 2 = 10\)[/tex].
So, the result is: [tex]\(10\)[/tex].
Therefore, the results for the expressions are:
[tex]\[ \begin{align*} 40. & \quad -7 \\ 41. & \quad -36 \\ 42. & \quad 8.0 \\ 43. & \quad 12 \\ 44. & \quad -86 \\ 45. & \quad -51 \\ 46. & \quad 37 \\ 47. & \quad 33 \\ 48. & \quad -1.0 \\ 49. & \quad -32.0 \\ 50. & \quad 60 \\ 51. & \quad 10 \\ \end{align*} \][/tex]
