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Chapter 1: Problem 30

\((19-4) \div(7-2)\)

Short Answer

Expert verified
The result of the calculation is 3.

Step by step solution

01

Calculating Inside Parentheses

Calculate the values inside each pair of parentheses first.\n\nSo, calculate \(19 - 4 = 15\) and \(7 - 2 = 5\).
02

Division

Now divide the two results from step 1.\n\nSo, calculate \(15 \div 5 = 3\).

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Key Concepts

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

Parentheses Evaluation
When solving expressions with parentheses, always start by handling the calculations inside the parentheses. This is because parentheses dictate that operations enclosed within them should be performed first. In the expression \((19-4) \div (7-2)\), focus on evaluating what's inside each set of parentheses.

  • First, calculate \(19 - 4\). This results in \(15\).
  • Next, evaluate \(7 - 2\), which gives \(5\).
Working with parentheses helps simplify expressions step by step and ensures the calculations follow the correct order of operations, which often underpins more complex problems.
Basic Division
Once you've evaluated the parentheses, the next step is to divide the results of these calculations. Basic division involves finding how many times one number fits into another. For the expression, you have:

  • The result from the first parentheses: \(15\)
  • The result from the second parentheses: \(5\)
Perform the division \(15 \div 5\), which equals \(3\). This process highlights the concept that division is about partitioning a number into equal parts, and it's crucial in solving problems efficiently.
Simplifying Expressions
After executing operations like parentheses evaluation and division, the final aim is to simplify the expression to its simplest form. Simplifying involves performing all possible operations to reduce the expression to a single number or a clear result.

For \((19-4) \div (7-2)\), you have evaluated inside the parentheses to get \(15\) and \(5\), and performed the division to reach \(3\). The expression is now simplified because no further operations can be done.

Simplifying helps in understanding the core value of the equation and prepares one for tackling more complex equations later.

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