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Chapter 1: Problem 58

Perform each indicated operation. $$ 5+3(6-4) $$

Short Answer

Expert verified
11

Step by step solution

01

Identify the components inside the parentheses

Look at the expression inside the parentheses first: \(6 - 4\)
02

Perform the operation inside the parentheses

Calculate the value inside the parentheses:\(6 - 4 = 2\)
03

Substitute the value back into the expression

Replace the parentheses with the calculated value:\(5 + 3 \times 2\)
04

Apply the order of operations

Follow the order of operations (PEMDAS/BODMAS). First, perform the multiplication: \(3 \times 2 = 6\)
05

Complete the addition

Now, add the result to 5: \(5 + 6 = 11\)

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Key Concepts

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

PEMDAS
In mathematics, the order of operations is crucial to solving expressions correctly. One common mnemonic to remember this order is PEMDAS:
  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction

This means that when solving an expression, you should handle operations inside parentheses first, then exponents, followed by multiplication and division (from left to right), and finally, addition and subtraction (from left to right). Understanding PEMDAS helps ensure that you solve expressions in the correct sequence, yielding the right answers.
Parentheses
The first step in the order of operations is to deal with anything inside parentheses. Parentheses are used to group parts of an expression that should be evaluated first.
For example, in the expression \(5+3(6-4)\), parentheses dictate that you must first solve the subtraction inside them: \(6-4=2\).
Ignoring parentheses can lead to incorrect answers, so always start inside them before moving on.
Multiplication
After handling the parentheses, the next step is to perform any multiplication or division from left to right. In our example, the expression simplifies to \(5 + 3 \times 2\).
Here, multiplication comes before addition, so you first calculate \(3 \times 2 = 6\).
Once all multiplications are completed, you can proceed to addition or subtraction.
Addition
The final step in our example involves addition. After simplifying the multiplication, the expression is reduced to \(5 + 6\).
Now, you simply add these two numbers together to get the final result: \(5 + 6 = 11\).
Following all the steps of PEMDAS ensures that you arrive at the correct answer without confusion or errors.

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Most popular questions from this chapter

Nadine Blackwood enjoys playing Triominoes every Wednesday night. Last Wednesday, on four successive turns, her scores were \(-19,28,-5,\) and \(13 .\) What was her final score for the four turns?

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