Let's break down each of the expressions step by step, following the order of operations, which is parenthesis, exponents, multiplication and division (left to right), and addition and subtraction (left to right).
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A. [tex]\(6 + 2 5\)[/tex]
1. According to the order of operations, we multiply before we add.
2. First, calculate [tex]\(2 5 = 10\)[/tex].
3. Next, add 6 to the result: [tex]\(6 + 10 = 16\)[/tex].
So, the result is [tex]\(16\)[/tex].
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B. [tex]\(-8 \div 2 - 5\)[/tex]
1. Divide before you subtract.
2. First, perform the division: [tex]\(-8 \div 2 = -4\)[/tex].
3. Then, subtract 5 from the result: [tex]\(-4 - 5 = -9\)[/tex].
So, the result is [tex]\(-9\)[/tex].
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C. [tex]\(5 3 + (6 + 1)\)[/tex]
1. Solve the parenthesis first: [tex]\(6 + 1 = 7\)[/tex].
2. Next, multiply: [tex]\(5 3 = 15\)[/tex].
3. Finally, add the results: [tex]\(15 + 7 = 22\)[/tex].
So, the result is [tex]\(22\)[/tex].
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D. [tex]\(2 - [-(7-2) + 1] - 2\)[/tex]
1. Solve the inner parenthesis first: [tex]\(7 - 2 = 5\)[/tex].
2. Then handle the negation: [tex]\(-(5) = -5\)[/tex].
3. Add 1: [tex]\(-5 + 1 = -4\)[/tex].
4. Subtract this result from 2: [tex]\(2 - (-4) = 2 + 4 = 6\)[/tex].
5. Finally, subtract 2: [tex]\(6 - 2 = 4\)[/tex].
So, the result is [tex]\(4\)[/tex].
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E. [tex]\(-5 \times [(-3 2) \div (-3) + 1]\)[/tex]
1. Solve the innermost parenthesis (multiplication): [tex]\(-3 2 = -6\)[/tex].
2. Then divide: [tex]\(-6 \div -3 = 2\)[/tex].
3. Add 1 to the result: [tex]\(2 + 1 = 3\)[/tex].
4. Finally, multiply by [tex]\(-5\)[/tex]: [tex]\(-5 \times 3 = -15\)[/tex].
So, the result is [tex]\(-15\)[/tex].
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F. [tex]\(14 - (8 + 7) - [4 + 2 - 3 - (4 - (-4 + 5))]\)[/tex]
1. Solve the innermost parenthesis first: [tex]\(-4 + 5 = 1\)[/tex].
2. Substitute back and solve the inner parenthesis: [tex]\(4 - 1 = 3\)[/tex].
3. Then solve the next set of parenthesis inside the brackets: [tex]\(4 + 2 - 3 = 3\)[/tex].
4. Combine these results within the brackets: [tex]\(3 - 3 = 0\)[/tex].
5. Now go back to the outer parenthesis: [tex]\(14 - (8 + 7) = 14 - 15 = -1\)[/tex].
6. Finally, subtract the bracket result from [tex]\(-1\)[/tex]: [tex]\(-1 - 0 = -1\)[/tex].
So, the result is [tex]\(-1\)[/tex].
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After performing the detailed step-by-step calculations, the results are:
A. 16
B. -9
C. 22
D. 4
E. -15
F. -1
