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Chapter 1: Problem 114

In the following exercises, simplify using the order of operations. $$ 4+6(3+6) $$

Short Answer

Expert verified
58

Step by step solution

01

Simplify inside the Parentheses

First, simplify the expression inside the parentheses: \(3 + 6\). This results in 9.
02

Multiply

Next, multiply the result from the parentheses by 6: \(6 \times 9\). This results in 54.
03

Addition

Finally, add the result from the multiplication to 4: \(4 + 54\). This results in 58.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions
Simplifying expressions means making them easier to work with. To do this, we follow the order of operations: parentheses first, then exponents, multiplication and division, and finally addition and subtraction. This is often remembered by the acronym **PEMDAS**.

By following these steps, we ensure that everyone simplifies expressions the same way.
Parentheses
Parentheses are used to group parts of an expression that should be simplified first. They tell us which operations to perform before others.

In the given exercise, we have the expression: \(4+6(3+6)\). The first thing to do is simplify what's inside the parentheses: \(3 + 6\).

This results in 9. Parentheses help remove ambiguity and make it clear what should be calculated first.
Multiplication
After handling parentheses, the next step is multiplication. Multiplication is a way of adding a number to itself a specific number of times.

In our example, after simplifying inside the parentheses, we get 9. Next, we multiply this by 6: \(6 \times 9\). This results in 54.

Since multiplication is done before addition, it's crucial to get this step right.
Addition
Finally, we perform the addition operation. Addition is combining numbers to get a total or sum.

Referring to our example, we now add the result of our multiplication to 4: \(4 + 54\). This gives us 58.

Addition is often the final step when simplifying expressions, as per the order of operations.

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