Solving the Expression: f(5) = −14/3(125) + 33(25) − 211/3(5) + 45

Calculating complex algebraic expressions step-by-step can be challenging, but simplifying f(5) = −14/3(125) + 33(25) − 211/3(5) + 45 step by step not only reveals the correct value but also strengthens your understanding of arithmetic and algebra. In this article, we break down the expression f(5) together and solve it precisely.

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Understanding the Expression

The function defined as f(5) = −14/3(125) + 33(25) − 211/3(5) + 45 involves multiple multiplicative and additive terms. To evaluate this correctly, we follow proper order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).

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Step-by-Step Evaluation

Step 1: Evaluate the multiplicative terms involving fractions.

First, compute each fraction multiplied by the numbers:

• −14/3 × 125 = −(14 × 125)/3 = −1750/3
• 33 × 25 = 825
• −211/3 × 5 = −(211 × 5)/3 = −1055/3

So, the expression becomes:

f(5) = −1750/3 + 825 − 1055/3 + 45

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Step 2: Combine the fractional terms.

Since both −1750/3 and −1055/3 share the same denominator, add them:

−1750/3 − 1055/3 = (−1750 − 1055)/3 = −2805/3

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Step 3: Combine constant terms.

825 + 45 = 870

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Step 4: Rewrite the expression with combined terms:

f(5) = −2805/3 + 870

Now, express 870 as a fraction over 3:

870 = 870 × 3/3 = 2610/3

So,

f(5) = −2805/3 + 2610/3 = (−2805 + 2610)/3 = −195/3

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Step 5: Simplify the result.

−195/3 = −65

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Final Answer

f(5) = −65

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Why This Calculation Matters

Solving expressions like f(5) helps reinforce skills in:

• Breaking down complex algebraic statements
• Performing accurate arithmetic with fractions and whole numbers
• Combining like terms effectively

Understanding this process makes it easier to analyze functions, evaluate models, and solve real-world problems in science, engineering, finance, and computer science.

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Summary

We evaluated:

f(5) = −14/3(125) + 33(25) − 211/3(5) + 45

Step by step:

• Computed each term with fractions
• Combined like terms step-wise
• Simplified to get f(5) = −65

This method ensures both accuracy and clarity—essential traits for mastering algebra and advanced mathematics.

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Key Takeaway: Always simplify fractions and combine terms carefully when solving expressions like f(5)—this approach avoids sign errors and calculation mistakes.

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If you're looking to improve your algebra skills or verify tricky calculations, mastering expression evaluation is a powerful foundation. Practice step-by-step breakdowns, and soon such problems will become second nature!