Problem 120 - Algebra and Trigonometry

Question

Use the order of operations to simplify each expression. $$\frac{12 \div 3 \cdot 5\left|2^{2}+3^{2}\right|}{7+3-6^{2}}$$

Step-by-Step Solution

Answer

The simplified expression is -10.

Step 1: Simplify Inside Absolute Values and Parentheses

The first step according to BODMAS/BIDMAS principles is to simplify the expression inside the absolute value which also acts as parentheses or brackets. It includes powers or indices and addition. So we simplify \(2^{2}+3^{2}\) to get \(4 + 9 = 13\). And our expression becomes \(\frac{12 \div 3 \cdot 5\left|13\right|}{7+3-6^{2}}\)

Step 2: Operate Upon Absolute Value

As our expression inside the absolute value is already a positive number, simply remove absolute value notation. So, the expression becomes \(\frac{12 \div 3 \cdot 5\cdot13}{7+3-6^{2}}\)

Step 3: Simplify Division and Multiplication of Numerator

Following BODMAS/BIDMAS principles, first perform division, then multiplication in the numerator. Thus, \(\frac{12 \div 3 \cdot 5\cdot13}{7+3-6^{2}}\) simplifies to \(\frac{4 \cdot 5\cdot13}{7+3-6^{2}}\) and further to \(\frac{20\cdot13}{7+3-6^{2}}\) and finally we get \(\frac{260}{7+3-6^{2}}\)

Step 4: Simplify Addition and Subtraction of Denominator

According to BODMAS/BIDMAS principles, perform addition first, then subtraction in the denominator. Thus, \(\frac{260}{7+3-6^{2}}\) simplifies to \(\frac{260}{10-6^{2}}\), then to \(\frac{260}{10-36}\) and finally we get \(\frac{260}{-26}\)

Step 5: Divide Numerator by Denominator

Perform the division of numerator by denominator, therefore \(\frac{260}{-26} = -10\).