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Chapter 2: Problem 72

Find the value of each expression. $$17-(21+13) \div 17$$

Short Answer

Expert verified
The value of the expression is 15.

Step by step solution

01

Solve the Parentheses

Begin by resolving the calculation inside the parentheses. Here, you have to add 21 and 13: \[ 21 + 13 = 34 \]
02

Divide by 17

Take the result from Step 1 and divide it by 17. This will involve performing the division of 34 by 17:\[ 34 \div 17 = 2 \]
03

Subtract from 17

Finally, subtract the result from Step 2 from 17:\[ 17 - 2 = 15 \]

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Key Concepts

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

Parentheses
In mathematics, parentheses are used to group numbers or operations to indicate that the operations within the parentheses should be performed first. This concept is a fundamental part of the order of operations rules, commonly remembered by the acronym PEMDAS.
  • P stands for Parentheses, meaning they are the first operations to solve in any expression.
  • It's crucial to deal with any numbers and operations inside the parentheses before moving on to other parts of the expression.
  • In our exercise, the expression inside the parentheses is \(21 + 13\), which simplifies to \(34\).
Once you solve what鈥檚 inside the parentheses, you can move on to the next operation in the sequence.
Division
After resolving the parentheses, the next operation in the order of operations is division. Division is simply the process of finding out how many times one number is contained within another. In our example problem, we took the solution from the parentheses, \(34\), and divided it by \(17\).
  • When you divide \(34 \div 17\), you are asking how many whole groups of \(17\) can fit into \(34\).
  • In this scenario, \(34\) divides evenly by \(17\), resulting in \(2\).
  • It's important to ensure accuracy in division, as mistakes can lead to incorrect results in the entire expression.
Getting this step correct sets the foundation for the next stage of the calculation.
Addition
Addition is a fundamental mathematical operation where two or more numbers are combined to get a sum. In the context of parentheses, addition happens as an initial step inside the brackets.
  • Our problem involved adding \(21\) and \(13\) inside the parentheses, which totaled \(34\).
  • Always ensure that your arithmetic is correct at this stage as mistakes can affect the end result.
  • Addition, although simple, forms the basis for more complex calculations in math, underlining its importance within this expression and others.
Understanding addition is key to building upon more complicated arithmetic operations.
Subtraction
Subtraction is an arithmetic operation involving the removal of a quantity from another. In this exercise, subtraction comes last after addressing all other operations.
  • You subtract the result of division \(2\) from the initial number \(17\).
  • In our math expression: \(17 - 2\) results in \(15\).
  • Subtraction is essential because it finalizes the solution to the expression, providing the final answer after all operations are completed.
Despite being straightforward, subtraction is crucial in arriving at an accurate solution after following the order of operations.

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Most popular questions from this chapter

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