Problem 90 - Elementary Algebra

Question

\(15+6^{2} \cdot 2 \div 3+9\)

Step-by-Step Solution

Answer

48

Step 1: Identify the order of operations (PEMDAS/BODMAS)

First, understand that you need to follow the order of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), Addition and Subtraction (left to right).

Step 2: Evaluate the exponent

Calculate the exponent first: ex. evaluate the exponent ex. 6^2 = 36

Step 3: Perform multiplication

Next, multiply the result of the exponent by 2: 36 times 2 equals 72

Step 4: Perform division

Take the previous result and divide it by 3: 72 divided by 3 equals 24.

Step 5: Perform addition

Add the result from the division to the remaining numbers: 15 + 24 + 9 equals 48.

Key Concepts

PEMDAS

To solve any mathematical expression correctly, you need to follow a specific order. This order is remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Following PEMDAS helps you avoid mistakes. For example, in our exercise, starting with an expression like 15 + 6^2 * 2 ÷ 3 + 9, you first look at anything inside Parentheses (there are none here).

Next, you handle any Exponents. Then, move on to Multiplication and Division before finally doing Addition and Subtraction last. By following this sequence, each step is clear, and you won’t miss crucial operations.

Exponents

Exponents are used to represent repeated multiplication of a number by itself. For example, 6^2 means 6 multiplied by 6, which equals 36.

In our original exercise, the exponent is the first operation you handle after checking for parentheses. So, 6^2 is calculated before you do any multiplication or division. This is a critical step because ignoring exponents can change the entire result of your calculation.

Always remember to resolve any exponentiation before moving forward.

Multiplication and Division

After evaluating exponents, the next steps are Multiplication and Division. These operations are handled from left to right as they appear in the expression.

Once we've calculated 6^2 to get 36, we then multiply this by 2:

36 * 2 = 72.

Then, we divide the result by 3:

72 ÷ 3 = 24.

If you perform these steps in any other order, the result will be incorrect. Always remember: left to right!

Addition

The final step in our order of operations is Addition. After handling any parentheses, exponents, multiplication, and division, you add the remaining numbers.

In our case, we have 15 + 24 + 9 left. Adding these together gives us:

15 + 24 = 39

and then, 39 + 9 = 48.

Addition is usually the last step in the process, allowing you to combine all remaining numbers into one final result. Simple but crucial!