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Chapter 5: Problem 74

For Exercises \(71-82,\) simplify by using the order of operations. $$11.38-(10.42-7.52)^{2}$$

Short Answer

Expert verified
2.97

Step by step solution

01

Evaluate Inside the Parentheses

First, identify and solve the expression inside the parentheses: 10.42 - 7.52 = 2.9
02

Apply the Exponent

Next, apply the exponent to the result from the parentheses. (2.9)^{2} = 8.41
03

Final Subtraction

Finally, subtract the result from the original number: 11.38 - 8.41 = 2.97

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Key Concepts

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

Simplification
Simplification involves breaking down a complex expression into a more manageable form. This helps to make calculations easier. Ensure that each operation follows the order of operations. Think of it like cleaning up a messy room. You start by organizing smaller sections before tackling the entire space. This way, you don't get overwhelmed with too much to do at once. Simplifying expressions step by step ensures accuracy and understanding. For example, before you subtract or apply an exponent, you simplify any additions or subtractions within parentheses first.
Parentheses
Parentheses come first in the order of operations. They indicate which part of the expression should be evaluated first. Think of them as special instructions showing which calculations to do ahead of others. Always solve the expressions inside parentheses before moving on to other parts of the problem.
In our example, the expression inside the parentheses is \(10.42 - 7.52\). First, identify this part and solve it as a separate, simpler expression. \(10.42 - 7.52 = 2.9\).
This makes understanding easier and ensures the highest accuracy in subsequent steps.
Exponents
Exponents tell you how many times to multiply a number by itself. Always evaluate exponents after handling what鈥檚 inside the parentheses. If the expression contains an exponent, simplify it next. For instance, in the expression \((2.9)^2\), the exponent 2 indicates that you should multiply 2.9 by itself: \((2.9 \times 2.9 = 8.41)\).
Exponents can greatly increase or decrease the value of a number and therefore, their proper evaluation is crucial in simplification. Don't skip or miscalculate this step!
Subtraction
Subtraction comes after evaluating parentheses and exponents. In our problem, after simplifying the parentheses and exponents, the last step is subtraction. Perform this from left to right.
For instance, \(11.38 - 8.41\), means taking away 8.41 from 11.38, leaving you with \(2.97\).
Subtraction is straightforward but should be your final step when following the order of operations.
  • Always ensure your subtraction is accurate.
  • Double-check your result.
  • Use simple subtraction techniques to ensure no mistakes are made.

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Most popular questions from this chapter

For Exercises \(43-48\), write the decimal number representing each word name. The most stolen make of car worldwide is Toyota. For a recent year, there were 4 hundred-thousand Toyota's stolen.

For Exercises \(43-48\), write the decimal number representing each word name. The number of beehives in the United States is 2.6 million. (Source: U.S. Department of Agriculture)

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