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Chapter 5: Problem 5

Simplify. $$\frac{1}{2}(4.8-9.26)$$

Short Answer

Expert verified
-2.23

Step by step solution

01

- Simplify Inside the Parenthesis

First, simplify the expression inside the parenthesis: \(4.8 - 9.26\).
02

- Perform the Subtraction

Calculate \(4.8 - 9.26\). Since \(4.8 < 9.26\), the result will be negative. \(4.8 - 9.26 = -4.46\).
03

- Multiply by \(\frac{1}{2}\)

Now multiply the result by \(\frac{1}{2}\). \(\frac{1}{2} \times -4.46 = -2.23\).

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Key Concepts

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

Parentheses
Parentheses are symbols used in mathematics to group parts of an expression. They tell you to perform the operations inside them first. For example, in the expression \( \frac{1}{2}(4.8 - 9.26) \), you should first solve the calculation inside the parentheses. This is because of the order of operations in math, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)). Here, we first solve the subtraction inside the parenthesis before doing the multiplication. Ensuring we follow the right order is key to simplifying expressions correctly.
Subtraction
Subtraction is one of the basic arithmetic operations where you take away a certain quantity from another. For instance, let's look at the subtraction inside the parentheses: \(4.8 - 9.26\).
  • First, align the numbers by their decimal points.
  • Since 4.8 is less than 9.26, the result will be negative.
  • Subtract each corresponding digit starting from the right side moving to the left.
So, \(4.8 - 9.26 = -4.46\). The result is negative because we are subtracting a bigger number from a smaller number. Being comfortable with subtraction will help you in simplifying many types of expressions.
Multiplication with Fractions
Multiplying fractions might seem tricky at first, but it's quite straightforward. When you multiply a fraction by a number, you are scaling the number by the fraction's value. For example, in our expression \(\frac{1}{2}(4.8 - 9.26)\), we already found that \(4.8 - 9.26 = -4.46\). Now, we need to multiply this by \(\frac{1}{2}\):
  • Multiply the number by the numerator.
  • Then, divide the product by the denominator.
So, \(\frac{1}{2} \times -4.46 = \frac{-4.46}{2} = -2.23\). This final step shows that multiplication with fractions reduces the magnitude of the number according to the fraction.

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