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Simplify the expression 82+9(12÷3⋅2)−7.
Explain each of your steps.
(5 points)
To simplify the expression 82 + 9(12 ÷ 3 ⋅ 2) − 7, we first need to evaluate the parentheses.
Inside the parentheses, we have 12 ÷ 3 ⋅ 2. To solve this, we perform the division first: 12 ÷ 3 = 4.
Now we have 4 ⋅ 2 = 8.
Substituting this back into the expression, we have 82 + 9(8) − 7.
Next, we need to perform the multiplication: 9(8) = 72.
Substituting this back into the expression, we have 82 + 72 − 7.
Finally, we can add and subtract: 82 + 72 = 154.
Substituting this back into the expression, we have 154 − 7.
Therefore, the simplified expression is 147.
To simplify the expression 82 + 9(12 ÷ 3 ⋅ 2) − 7, follow the order of operations (PEMDAS/BODMAS):
Step 1: Start with the innermost set of parentheses or brackets, which is (12 ÷ 3).
12 ÷ 3 = 4
Step 2: Next, multiply the result from Step 1 (4) by 2.
4 × 2 = 8
Step 3: Substitute the result from Step 2 (8) into the original expression and simplify the multiplication.
9(8) = 72
Step 4: Substitute the result from Step 3 (72) into the original expression and simplify the addition and subtraction.
82 + 72 - 7
Step 5: Perform the addition: 82 + 72 = 154
Step 6: Subtract 7 from the result in Step 5: 154 - 7 = 147
Therefore, the simplified expression is 147.