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Chapter 6: Problem 32

For Exercises \(21-36,\) write as a decimal number. $$-5 \frac{4}{5}$$

Short Answer

Expert verified
Answer: The decimal equivalent of the mixed number -5 4/5 is -4.2.

Step by step solution

01

Identify the mixed number given

We are given the mixed number \(-5\frac{4}{5}\). It consists of the whole number part \(-5\) and the fractional part \(\frac{4}{5}\).
02

Convert the fractional part into a decimal number

To convert the fractional part \(\frac{4}{5}\) into a decimal number, divide the numerator (4) by the denominator (5): $$\frac{4}{5} = 4\div5 = 0.8$$
03

Combine the whole number and decimal parts

Now that we have converted the fractional part into a decimal number, we need to combine it with the whole number part to get the final decimal number. We do this by adding the decimal part (0.8) to the whole number part (-5): $$-5 + 0.8 = -4.2$$ The mixed number \(-5\frac{4}{5}\) in decimal form is \(-4.2\).

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Key Concepts

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

Mixed Numbers
A mixed number is a unique mathematical expression. It consists of a whole number accompanied by a fractional part. In simple terms, it's a combination of integers and fractions. For instance, let's look at \(-5\frac{4}{5}\). Here,
  • \(-5\) represents the whole number.
  • \(\frac{4}{5}\) is the fractional part.

Mixed numbers are frequently used in mathematics when you need to express a value that isn't purely a whole number or a sole fraction. Understanding how to work with them is essential in various mathematical operations.
Fractions to Decimals
Converting fractions to decimals is a crucial skill. This process involves dividing the numerator (the top number) by the denominator (the bottom number). Let's use the fraction \(\frac{4}{5}\) from our example.
  • Numerator: 4
  • Denominator: 5

By dividing 4 by 5, we perform the calculation: \(4 \div 5 = 0.8\). The fraction is thus expressed as a decimal number, 0.8. This method transforms a fraction, which may be tricky to visualize, into a simpler decimal format. Decimals are often preferred in situations requiring precision due to their straightforward value representation.
Negative Numbers
Negative numbers are numbers with a value less than zero, signified by a minus sign (\(-\)). They represent quantities below zero and are essential in various contexts, such as financial losses or decreases in mathematics. In our example, the mixed number is \(5\frac{4}{5}\), which converts to \(-4.2\).
  • The minus sign indicates the value is less than zero.
  • Negative values can influence the result in mathematical operations.
  • Adding or subtracting these numbers follows specific rules.

Understanding the role of negative numbers helps students solve problems accurately across many mathematical areas.
Mathematical Operations
Understanding and applying mathematical operations is vital for accurate calculations. In this example, we encountered two primary operations: division and addition. Let's explore their roles:
  • Division: Was used to convert the fractional part \(\frac{4}{5}\) to a decimal (0.8) by dividing 4 by 5.
  • Addition: Involved adding the decimal part (0.8) to the whole number part (\(-5\)), resulting in the final decimal value of -4.2.

By mastering these basic operations, students can tackle more complex mathematical challenges confidently.

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