Simplify Expression using BODMAS

This solution details the simplification of the mathematical expression $\frac{4}{11} \times \frac{121}{16} \times 24 (75^2 - 55^2) \times \frac{1}{100}$ using the BODMAS rule.

BODMAS Rule Application

The BODMAS hierarchy ensures correct calculation order:

• Brackets
• Orders (powers, roots)
• Division
• Multiplication
• Addition
• Subtraction

We follow this sequence precisely.

Bracket Simplification $(75^2 - 55^2)$

The first step involves the bracket $(75^2 - 55^2)$. Using the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$:

Let $a = 75, b = 55$.

$(75^2 - 55^2) = (75 - 55)(75 + 55)$

$(75^2 - 55^2) = (20)(130)$

$(75^2 - 55^2) = 2600$

Expression Substitution and Multiplication

Substitute the bracket value back into the expression:

$\frac{4}{11} \times \frac{121}{16} \times 24 \times 2600 \times \frac{1}{100}$

Simplify the initial fractions:

$\frac{4}{11} \times \frac{121}{16} = \frac{4}{11} \times \frac{11 \times 11}{4 \times 4}$

Cancel out common factors:

$= \frac{11}{4}$

The expression becomes:

$\frac{11}{4} \times 24 \times 2600 \times \frac{1}{100}$

Perform multiplication from left to right:

$(\frac{11}{4} \times 24) = 11 \times (\frac{24}{4}) = 11 \times 6 = 66$

The expression is now:

$66 \times 2600 \times \frac{1}{100}$

Fraction Division and Final Product

Continue the calculation by simplifying the division by 100:

$66 \times (\frac{2600}{100}) = 66 \times 26$

Calculate the final product:

$66 \times 26 = 1716$

The simplified value is 1716.