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Chapter 5: Problem 38

Simplify. $$ 18.3+2.5 \times 4.2-\left(2.6-0.3^{2}\right) \quad[4.4 \mathrm{c}] $$

Short Answer

Expert verified
26.29

Step by step solution

01

Calculate the exponent

First, handle the exponent inside the parentheses. Calculate \(0.3^{2}\). \(0.3 \times 0.3 = 0.09\).
02

Simplify inside the parentheses

Next, simplify the expression inside the parentheses by subtracting \(0.09\) from \(2.6\). \(2.6 - 0.09 = 2.51\).
03

Perform multiplication

Now, multiply \(2.5 \times 4.2\). \(2.5 \times 4.2 = 10.5\).
04

Combine all parts

Finally, combine all the parts of the expression. Start with \(18.3\), add \(10.5\), then subtract \(2.51\): \(18.3 + 10.5 - 2.51 = 26.29\).

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Key Concepts

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

Understanding Order of Operations
When simplifying expressions, it's crucial to follow the 'order of operations'. This set of rules ensures that everyone solves an expression the same way.

The order of operations can be remembered using the acronym PEMDAS:
  • Parentheses (P)
  • Exponents (E)
  • Multiplication and Division (MD, from left to right)
  • Addition and Subtraction (AS, from left to right)
In our exercise, we start with the parentheses and exponents first. This means we calculate \(0.3^2\) before we handle any other operations inside the parentheses. Once that鈥檚 done, we process any multiplication or division next, followed by addition and subtraction.
Working with Exponents
Exponents represent repeated multiplication of the same number. For example, \(0.3^2\) means \(0.3 \times 0.3\).

In our problem, the term \(0.3^2\) is inside the parentheses, so it's addressed first. We calculate \(0.3 \times 0.3 = 0.09\).

Exponents are important because they drastically change a number's value. Always make sure to handle them early in your simplification process, respecting the order of operations.
Basic Arithmetic in Expression Simplification
Basic arithmetic operations include addition, subtraction, multiplication, and division. They are the foundation for simplifying expressions.

In our exercise, we use these steps:
  • First, calculate \(0.3^2 = 0.09\). This involves a basic multiplication operation.
  • Next, simplify \(2.6 - 0.09 = 2.51\). This is a subtraction operation.
  • Then, perform \(2.5 \times 4.2 = 10.5\). This step involves multiplication.
  • Finally, combine all parts by performing addition and subtraction: \(18.3 + 10.5 - 2.51 = 26.29\).

    Understanding and practicing basic arithmetic ensures you can handle more complex expressions with confidence.

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