Simplify the following expression: [tex]$a \times -a s + 2 + \frac{13}{8} \times (-98) - 1 + |-48| =$[/tex]
Answer (2)
Evaluate the absolute value: ∣ − 48∣ = 48 .
Calculate the product: 8 13 × ( − 98 ) = − 159.25 .
Substitute the values into the expression: a × − a s + 2 + ( − 159.25 ) − 1 + 48 .
Simplify the expression: − a 2 s − 110.25 .
The final simplified expression is − a 2 s − 110.25 .
Explanation
Understanding the Expression We are asked to evaluate the expression a × − a s + 2 + 8 13 × ( − 98 ) − 1 + ∣ − 48∣ = . This expression involves variables a and s , multiplication, addition, subtraction, and an absolute value. Our goal is to simplify the expression as much as possible.
Evaluating the Absolute Value First, we evaluate the absolute value: ∣ − 48∣ = 48 .
Calculating the Product Next, we calculate the product 8 13 × ( − 98 ) . The result of this calculation is -159.25.
Substituting the Values Now, we substitute these values back into the original expression: a × − a s + 2 + ( − 159.25 ) − 1 + 48 .
Combining Constant Terms We simplify the expression by combining the constant terms: 2 − 159.25 − 1 + 48 = − 110.25 .
Rewriting the Expression Finally, we rewrite the expression as − a 2 s − 110.25 .
Final Answer Therefore, the simplified expression is − a 2 s − 110.25 .
Examples
Understanding how to simplify algebraic expressions is crucial in many real-world scenarios. For instance, if you're calculating the total cost of materials for a project where the price of some materials varies, you might use a similar expression to model the cost. Simplifying the expression allows you to easily substitute different values and quickly determine the overall cost, aiding in budgeting and decision-making.
The expression simplifies to − a 2 s − 110.25 after evaluating the absolute value, calculating the product, and combining constant terms. Each step was carefully executed to ensure accuracy. The final simplified expression clearly reflects the components of the original expression.
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