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Chapter 5: Problem 78

For Exercises \(71-82,\) simplify by using the order of operations. $$6.84+(3.6)(9)$$

Short Answer

Expert verified
39.24

Step by step solution

01

Identify the operations

The expression contains addition and multiplication: \(6.84+(3.6)(9)\)
02

Perform the multiplication

According to the order of operations, perform the multiplication first: \((3.6)(9) = 32.4\)
03

Perform the addition

Now, add the result of the multiplication to 6.84: \(6.84 + 32.4 = 39.24\)

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Key Concepts

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

Simplification
Simplification is a key step in solving problems which involve multiple mathematical operations. It means breaking down a complex mathematical expression into simpler components that are easier to work with.
In this exercise, we simplify the expression \(6.84 + (3.6)(9)\) by first understanding each part of it. Here, simplification helps us manage operations efficiently by following a systematic approach.
For example, recognizing that multiplication needs to be done before addition according to the order of operations. By simplifying step-by-step, we avoid mistakes and ensure accurate results.
Addition
Addition is one of the basic arithmetic operations and involves combining two or more numbers to get a total sum. In the context of our exercise, addition is performed after the multiplication.
Once we've calculated \(3.6 \times 9 = 32.4\), we then add this to \(6.84\). This results in \(6.84 + 32.4 = 39.24\).
It's important to ensure all preliminary operations (like multiplication) are done first to avoid errors in the final addition.
By following the order of operations correctly, we can be confident the sum we reach is accurate.
Multiplication
Multiplication is another fundamental arithmetic operation and involves combining groups of equal sizes. In our original expression, multiplication must be completed before addition.
The expression has \(3.6 \times 9\), which we solve first to get \(32.4\).
This step is crucial as performing the multiplication out of order would lead to an incorrect result. Since multiplication has precedence over addition in order of operations, we handle it first.
This systematic approach helps in breaking down complex problems and ensures each step is handled correctly to achieve the right answer.

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