Solving the Math Expression: Step-by-Step

We need to solve the given mathematical expression using the correct order of operations (PEMDAS/BODMAS). The expression is:

$$ \frac{6}{2} \times \frac{10}{2} \div \frac{6}{2} \times 6^2 + 5 \times 4 = ? $$

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). BODMAS stands for Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

Step 1: Simplify Fractions and Exponents

First, we simplify the fractions and calculate the exponent term:

• Simplify \(\frac{6}{2}\): $$ \frac{6}{2} = 3 $$
• Simplify \(\frac{10}{2}\): $$ \frac{10}{2} = 5 $$
• Calculate the exponent term \(6^2\): $$ 6^2 = 6 \times 6 = 36 $$

Substituting these back into the expression, we get:

$$ 3 \times 5 \div 3 \times 36 + 5 \times 4 $$

Step 2: Perform Multiplication and Division (Left to Right)

Next, we perform multiplication and division operations as they appear from left to right.

• First multiplication: \(3 \times 5\) $$ 3 \times 5 = 15 $$ The expression becomes: \(15 \div 3 \times 36 + 5 \times 4\)
• Next, division: \(15 \div 3\) $$ 15 \div 3 = 5 $$ The expression becomes: \(5 \times 36 + 5 \times 4\)
• Next multiplication: \(5 \times 36\) $$ 5 \times 36 = 180 $$ The expression becomes: \(180 + 5 \times 4\)
• Last multiplication: \(5 \times 4\) $$ 5 \times 4 = 20 $$ The expression becomes: \(180 + 20\)

Step 3: Perform Addition

Finally, we perform the addition operation:

$$ 180 + 20 = 200 $$

Conclusion

Following the order of operations (PEMDAS/BODMAS), the calculation yields 200. This matches the 4th option provided.