Problem 22 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ 4+6(3+6) $$

Step-by-Step Solution

Answer

58

Step 1: Simplify Inside the Parentheses

First, solve the expression inside the parentheses. Here, add the numbers inside the parentheses:

Step 2: Perform the Multiplication

Next, multiply the result of the parentheses by 6.

Step 3: Add the Results

Finally, add the result of the multiplication to the number 4.

Key Concepts

order of operations

Understanding the order of operations is crucial when simplifying algebraic expressions. The standard order can be remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This rule ensures that everyone interprets the expression the same way and gets the same result.
For example, in the expression given:
\( 4 + 6(3 + 6) \)
Following PEMDAS:

• First, solve expressions inside parentheses: \( (3+6) \).
• Next, handle any multiplication or division. Here, it's \( 6 \times 9 \).
• Finally, perform addition and subtraction. Add the 4 to the result of the multiplication: \( 4 + 54 \).

This systematic approach helps to avoid errors and confusion.

parentheses in math

Parentheses are used in math to indicate what should be calculated first. For example, in our exercise:
\( 4 + 6(3+6) \)
The expression inside the parentheses, \( (3+6) \), must be calculated before anything outside. Without solving what's inside the parentheses first, the rest of the calculation wouldn't make sense. It's like following instructions step by step to build something correctly.
Once you solve what's inside the parentheses, the expression becomes:
\( 4 + 6 \times 9 \)
This reduces the complexity of the original problem and makes it easier to follow through with the next steps of the calculation.

basic arithmetic operations

There are four fundamental arithmetic operations: addition, subtraction, multiplication, and division. In our example, each of these operations plays a role.
Starting with the expression:
\( 4 + 6(3+6) \)

• Addition: Adding within the parentheses: \( 3 + 6 \). This equals 9.
• Multiplication: Multiplying 6 by the result from the parentheses: \( 6 \times 9 \).
• Addition: Finally, adding 4 to the product obtained: \( 4 + 54 \).

Using these simple arithmetic operations effectively allows for breaking down complex expressions into manageable steps, making solving them straightforward and less prone to mistakes.