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Chapter 1: Problem 69

Evaluate the given expression. Remember to follow the order of operations. $$6+4(3+2)$$

Short Answer

Expert verified
The expression evaluates to 26.

Step by step solution

01

- Evaluate the Parentheses

First, solve the operation inside the parentheses. In this case, add 3 and 2.\(3 + 2 = 5\)
02

- Substitute the Result

Replace the parentheses with the result obtained.The expression now is: \(6 + 4 \times 5\)
03

- Perform Multiplication

Next, according to the order of operations (PEMDAS/BODMAS), perform the multiplication before addition.\(4 \times 5 = 20\)
04

- Perform Addition

Finally, add the result of the multiplication to 6.\(6 + 20 = 26\)

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Key Concepts

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

Parentheses
Parentheses are the first step in the order of operations. When you see an expression with parentheses, always solve the inside of the parentheses first. This makes sure that any enclosed operations happen before anything else.

For example, in the expression \(6 + 4(3 + 2)\), the first thing to do is evaluate \(3 + 2\) inside the parentheses.

Once solved, you replace the parentheses with the result. This simplifies the expression making it easier to handle the rest of the operations correctly.
Multiplication
Multiplication comes right after solving any operations inside parentheses. According to the order of operations, also known as PEMDAS, multiplication is done before addition.

So, in the expression \(6 + 4 \times 5\), we focus on multiplication first. Here, we multiply 4 by 5, which gives 20. This step simplifies the expression further, making it \(6 + 20\).

Think of multiplication as combining groups. In this example, we are combining 4 groups of 5.
Addition
Addition is one of the last steps in the order of operations. Once you've taken care of parentheses and multiplication, you can perform the addition.

In the example expression \(6 + 20\), we simply add these two numbers to get 26. Addition is all about combining the values together.

This step ensures that you have completed the operations in the correct sequence, leading you to the final result.
PEMDAS
PEMDAS is a helpful acronym for remembering the order of operations. It stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.

Following PEMDAS ensures you're doing each math operation in the right order. Parentheses come first because they group operations that need to be done together.
Next, perform any multiplication or division from left to right. Finally, handle addition and subtraction from left to right.

Using PEMDAS makes sure that everyone solves math problems in the same way, getting the same correct result.

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Most popular questions from this chapter

Evaluate the given expression. Remember to follow the order of operations. $$4+\\{3+5[2+2(3+1)]\\}$$

Explain how you could use the commutative and/or associative properties to make the following computations easier to do. (a) \(-1.7+12.9-8.3\) (b) 10( 7)\((-2.3)\) (c) \(\frac{-10(3.2)}{-1.6}\) (d) \(-30\left(\frac{1.6}{3}\right)(-10)\)

Compute the given expression. Round off your answer to two decimal places where necessary. $$-2(-5.3)$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$5.2-1.4(2.8-0.7)$$

Evaluate the given expression. Remember to follow the order of operations. $$6+(4 \cdot 3)+2$$
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