Problem 125 In the following exercises, simp... [FREE SOLUTION]

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Chapter 1: Problem 125

In the following exercises, simplify using the order of operations. $$ 2[1+3(10-2)] $$

Short Answer

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Step by step solution

Evaluate the expression inside the parentheses

First, simplify the expression inside the parentheses:$10 - 2 = 8$The expression is now: \[2[1 + 3(8)]\]

Perform the multiplication inside the brackets

Next, multiply the number inside the brackets:$3 \times 8 = 24$The expression is now: \[2[1 + 24]\]

Add the numbers inside the brackets

Add the numbers inside the brackets:$1 + 24 = 25$The expression is now: \[2[25]\]

Multiply by the number outside the brackets

Finally, multiply the result by the number outside the brackets:$2 \times 25 = 50$Thus, the simplified expression is: \[50\]

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Key Concepts

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

Parentheses

Understanding how to handle parentheses is crucial in the order of operations. Parentheses are used to group parts of an expression that need to be calculated first. You always start simplifying inside the innermost parentheses and work your way out.
In our example, we start with the expression inside the parentheses: $10 - 2$. This is performed first: $10 - 2 = 8$. Now, the expression updates to: \[2[1 + 3(8)]\].
Here, you can see how completing the operation inside the parentheses takes priority before performing any other operation.

Multiplication

Multiplication comes next in the hierarchy of operations after parentheses. Once you have simplified everything inside the parentheses, you look for any multiplications. In the simplified expression \[2[1 + 3(8)]\], the multiplication $3(8)$ comes next.
You multiply 3 and 8 to get 24: $3 \times 8 = 24$. This updates the expression to: \[2[1 + 24]\].
This step ensures that multiplication is handled before moving on to addition.

Addition

Addition is carried out after handling both parentheses and multiplication. After computing the product inside the brackets in the expression \[2[1 + 24]\], you perform the addition.
Adding 1 and 24 gives you 25: $1 + 24 = 25$. Now, you have: \[2[25]\].
Finally, you finish the expression by multiplying 2 and 25, leading to the simplified answer: $2 \times 25 = 50$. Ensuring you follow operations in the correct sequence prevents any possible mistakes in simplifying expressions.

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91影视

In the following exercises, simplify using the order of operations. $$ 2[1+3(10-2)] $$

Short Answer

Step by step solution

Evaluate the expression inside the parentheses

Perform the multiplication inside the brackets

Add the numbers inside the brackets

Multiply by the number outside the brackets

Key Concepts

Parentheses

Multiplication

Addition

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