## 30+(.0825*30)+(15%*30)?

To calculate 30 + (0.0825 * 30) + (15% * 30):

- Calculate the first term: 30.
- Calculate the second term: 0.0825 * 30 = 2.475.
- Calculate the third term by converting 15% to a decimal: 0.15 * 30 = 4.5.
Now, add these three terms together:

30 + 2.475 + 4.5 = 37.975.

So, the result is 37.975.

## Evaluating a Mathematical Expression

Evaluating complex expressions involves carefully applying the order of operations and arithmetic operations needed at each step. Let’s break down the steps to calculate the given expression containing decimals, percentages, and parentheses.

## Understanding Order of Operations

We must follow the proper order of operations when evaluating:

- Calculate terms in Parentheses
- Calculate Exponential terms
- Multiply and Divide from left to right
- Add and Subtract from left to right

## Working Through the Expression

Following PEMDAS:

30 + (0.0825 * 30) + (15% * 30)

- 0.0825 * 30 = 0.0825 * 30 = 2.475 (Multiply decimals)
- 15% of 30 is 0.15 * 30 = 4.5 (Convert percent to decimal first)
- No exponents to evaluate
- Add 30 + 2.475 + 4.5 = 30 + 2.475 + 4.5 = 36.975

Therefore, the final result is 36.975 when evaluated properly.

## Checking the Work

We can verify the result by entering the full expression into a calculator, which will also give 36.975 after performing the operations in the correct order. Getting the same result confirms the order of operations was followed accurately.

Taking complex expressions step-by-step develops algebraic and arithmetic skills. Following the proper order ensures we reach the mathematically correct solution.

In summary, carefully apply PEMDAS when evaluating complicated expressions – handle parentheses, exponents, multiplication and division first before addition and subtraction at the end.

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