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.

Understanding the Context

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).

Step-by-Step Evaluation

$f(5) = -\frac{14}{3}(125) + 33(25) - \frac{211}{3}(5) + 45 = -\frac{1750}{3} + 825 - \frac{1055}{3} + 45$

Key Insights

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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Final Thoughts

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

Step 3: Combine constant terms.

825 + 45 = 870

Step 4: Rewrite the expression with combined terms:

f(5) = −2805/3 + 870

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