Math Problem Statement

Simplify the given mathematical expression and compute the result.

Solution

The equation in the uploaded image is:

(19)2+(25)2+(242150)228(252×19)19×25\frac{(19)^2 + (25)^2 + \frac{(242 - 150)^2}{28 - (25 - 2 \times 19)}}{19 \times 25}

Step-by-step Solution:

  1. Square the numbers:

    • 192=36119^2 = 361
    • 252=62525^2 = 625
  2. Simplify the numerator:

    • Calculate 242150=92242 - 150 = 92, then square it: 922=846492^2 = 8464.

    • For the denominator inside the fraction, first evaluate 252×1925 - 2 \times 19: 252×19=2538=13.25 - 2 \times 19 = 25 - 38 = -13. Then calculate: 28(13)=28+13=41.28 - (-13) = 28 + 13 = 41. So, the fraction is: 846441.\frac{8464}{41}.

      Dividing: 846441=206.\frac{8464}{41} = 206.

      Therefore, the numerator becomes: 361+625+206=1192.361 + 625 + 206 = 1192.

  3. Simplify the denominator:

    • 19×25=47519 \times 25 = 475.
  4. Final computation:

    • The overall fraction is: 1192475.\frac{1192}{475}.

      Simplifying this fraction: 11924752.51(rounded to two decimal places).\frac{1192}{475} \approx 2.51 \, (\text{rounded to two decimal places}).

Final Answer:

2.51\boxed{2.51}

Would you like a deeper explanation of any of the steps?


Related Questions:

  1. How do you simplify fractions with large numbers like 846441\frac{8464}{41}?
  2. What is the process for handling negative values in denominators?
  3. Can this equation be rewritten in a different format for clarity?
  4. How do we calculate squares of numbers faster without a calculator?
  5. What are some practical applications of such expressions in mathematics?

Tip:

When working with nested fractions, simplify the inner terms first to avoid confusion!

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Math Problem Analysis

Mathematical Concepts

Algebra
Arithmetic Operations
Nested Fractions

Formulas

a^2 (Square of a number)
Simplification of fractions
Order of operations (PEMDAS/BODMAS)

Theorems

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Suitable Grade Level

Grades 8-10