Problem 71 Evaluate the given expression. R... [FREE SOLUTION]

91影视

Understanding Elementary Algebra with Geometry

Lewis Hirsch, Arthur Goodman

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 71

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

Short Answer

Expert verified

Step by step solution

Simplify Inside the Parentheses

Begin by evaluating the expression inside the parentheses: $4 \cdot 3 + 2$. Perform the multiplication first since it takes precedence over addition.

Multiply Inside the Parentheses

$4 \cdot 3 = 12$

Add Inside the Parentheses

Add 12 and 2, which simplifies to $12 + 2 = 14$. The expression now is: $6 + 14$

Perform the Final Addition

Add the remaining numbers: $6 + 14 = 20$

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Key Concepts

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

Understanding Parentheses

Parentheses are symbols that help group certain parts of an expression. They tell us which part of the expression to solve first.

For example, in the expression $6+(4 \cdot 3+2)$, the calculation inside the parentheses $4 \cdot 3 + 2$ must be completed before anything else.

This grouping helps give the expression a clear and logical order. Think of it as a priority ticket, ensuring some operations are done first, maintaining accuracy in the results.

The Role of Multiplication

When solving expressions, multiplication is performed before addition and subtraction.

In the example \[6 + (4 \cdot 3 + 2)\], within the parentheses, we see multiplication: $4 \cdot 3$.

Multiplication tells us to combine numbers in a certain way, giving higher priority over addition. That's why we simplify $4 \cdot 3 = 12$ first, before doing anything else inside the parentheses.

This rule follows the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Applying Addition

Addition is everywhere in math, making it one of the simplest operations. However, its position in the order of operations means it鈥檚 often done last in an expression.

In the expression \[6 + (4 \cdot 3 + 2)\], after simplifying the multiplication, we add within the parentheses first: $12 + 2 = 14$.

Finally, we add the result outside the parentheses: $6 + 14 = 20$.

This final step wraps up the expression, showing the importance of understanding the role of addition after other operations like multiplication have been completed.

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91影视

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

Short Answer

Step by step solution

Simplify Inside the Parentheses

Multiply Inside the Parentheses

Add Inside the Parentheses

Perform the Final Addition

Key Concepts

Understanding Parentheses

The Role of Multiplication

Applying Addition

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