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Chapter 2: Problem 8

Change the following mixed numbers to improper fractions. $$8 \frac{4}{10}=$$

Short Answer

Expert verified
The improper fraction is \(\frac{84}{10}\).

Step by step solution

01

Understand the Mixed Number

A mixed number consists of a whole number and a fraction. In this case, we have \(8 \frac{4}{10}\), which means there is a whole number 8 and a fraction \(\frac{4}{10}\). The task is to convert this mixed number into an improper fraction.
02

Convert the Whole Number to a Fraction

To convert the whole number 8 to a fraction with the same denominator as the fraction, multiply 8 by 10 (the denominator of \(\frac{4}{10}\)). This gives us \(\frac{80}{10}\).
03

Add the Fractions

Now, add the fraction obtained from the whole number and the given fraction. So, \(\frac{80}{10} + \frac{4}{10}\) is the expression we need to simplify.
04

Simplify the Sum

Add the numerators of the fractions while keeping the denominator the same. This results in \(\frac{80 + 4}{10} = \frac{84}{10}\). Thus, the improper fraction equivalent of the mixed number \(8 \frac{4}{10}\) is \(\frac{84}{10}\).

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Key Concepts

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

Understanding Mixed Numbers
Mixed numbers are figures that combine a whole number with a fraction. They often appear in everyday life, such as when you see one and a half apples or two and three-quarters of an inch. The whole number makes these fractions easy to visualize and work with. For example, with the mixed number \(8 \frac{4}{10}\), 8 is the whole number and \(\frac{4}{10}\) is the fraction.

Converting mixed numbers into improper fractions involves merging these two components into a single fraction. This allows them to be easily used in further mathematical operations. It's essential for tasks like fraction addition or subtraction, where fractions must share the same form to proceed.
Adding Fractions
Fraction addition is the process of combining two or more fractions into a single fraction. For two fractions to be added, they should have the same denominator (the bottom number). This ensures that the fractions are parts of the same whole.
  • Identify the denominators of both fractions. If they are different, find the least common denominator (LCD).
  • Convert the fractions to equivalent fractions with the LCD.
  • Add the numerators (the top numbers) while keeping the denominator the same.
In the context of mixed numbers, as seen in the worked example, the whole number part must be converted to a fraction before addition. Here, once the whole number was rewritten as a fraction, it was added to the existing fractional part, resulting in one single, improper fraction.
Converting Fractions to Decimals
Fractions can also be expressed as decimals, which sometimes makes them easier to interpret. Converting fractions to decimals involves division. Specifically, the numerator (top number) is divided by the denominator (bottom number).

Here are steps to convert \(\frac{84}{10}\) to a decimal:
  • The numerator, 84, is divided by the denominator, 10.
  • Perform the division: 84 divided by 10 equals 8.4
This conversion shakes off any lingering complexity by removing the need to understand parts-in-wholes for everyday calculations, making fractions more approachable for many mathematical applications.

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Most popular questions from this chapter

An order is written for a client to receive 1陆 ounces of a powdered medication dissolved in water. The client drank 戮 ounces of the medication. How much more medication must be given to the client? ______________________________

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