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Chapter 2: Problem 15

Find a decimal equivalent for each fraction or mixed number. \(5 \frac{1}{16}\)

Short Answer

Expert verified
5.0625

Step by step solution

01

- Convert the Mixed Number to an Improper Fraction

First, convert the mixed number into an improper fraction. Multiply the whole number part 5 by the denominator 16 and then add the numerator 1. The improper fraction is \[5 \frac{1}{16} = \frac{5 \times 16 + 1}{16} = \frac{80 + 1}{16} = \frac{81}{16}\]
02

- Perform Division to Find Decimal Equivalent

Now, divide the numerator of the improper fraction by the denominator. Divide 81 by 16 to get the decimal equivalent. \[ \frac{81}{16} = 5.0625 \]

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Key Concepts

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

Improper Fractions
An improper fraction is a fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). Improper fractions can be intimidating, but they're a key concept in mathematics.
This makes improper fractions very useful in various calculations.
To fully grasp improper fractions, consider an example: \[\frac{9}{4}\text{, which is an improper fraction because }9 > 4\].
In summary, an improper fraction might seem complex, but it's just a way to represent a value that is more than one whole.
Mixed Numbers
A mixed number combines a whole number and a fraction, such as \[3 \frac{2}{5}\text{. Mixed numbers are used to represent numbers that are not whole but also aren't best expressed as a simple fraction.}\].
Understanding mixed numbers is crucial, especially when converting them to improper fractions for calculations.
Here鈥檚 how to convert a mixed number to an improper fraction:
  • Multiply the whole number part by the denominator of the fraction.
  • Add the result to the numerator.
  • This sum becomes the new numerator, while the denominator stays the same.

For example, \[5 \frac{1}{16}\text{ can be converted to an improper fraction as }\frac{81}{16}\text{. This makes it easier for further calculations like finding decimal equivalents.}\]
Division of Fractions
Dividing fractions takes place when you need to find a decimal equivalent or simplify calculations. Division of fractions might seem tricky, but it's just a sequence of easy steps.
To perform division involving fractions:
  • Place the numerator inside the division symbol.
  • Place the denominator outside.

For example, to convert \[ \frac{81}{16}\text{ into a decimal, you divide }81 \text{ by } 16 \text{. This results in } 5.0625{.}\]
Understanding these conversions can make many aspects of mathematics easier, from solving equations to understanding measurements.

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Most popular questions from this chapter

Earth Science Elevations are measured from sea level, which is considered to have an elevation of 0 feet. Elevations above sea level are positive, and elevations below sea level are negative. In Exercises \(9-13,\) use this table, which shows the elevation of the lowest point on each continent. $$\begin{array}{|l|c|r|} \hline \text { Continent } & \text { Location of Lowest Point } & \text { Elevation } \\ \hline \text { North America } & \text { Death Valley } & -282 \mathrm{ft} \\ \text { South America } & \text { Valdes Peninsula } & -131 \mathrm{ft} \\ \text { Europe } & \text { Caspian Sea } & -92 \mathrm{ft} \\ \text { Asia } & \text { Dead Sea } & -1,312 \mathrm{ft} \\ \text { Africa } & \text { Lake Assal } & -512 \mathrm{ft} \\ \text { Australia } & \text { Lake Eyre } & -52 \mathrm{ft} \\ \text { Antarctica } & \text { Bentley Subglacial Trench } & -8,327 \mathrm{ft} \\ \hline \end{array}$$ Order the elevations in the table from lowest to highest.

Find the least common multiple of the given numbers. \(5,7,\) and 14

Tell whether the fractions in each pair are equivalent, and explain how you know. \(\frac{4}{12}\) and \(\frac{8}{32}\)

Replace each 0 with \(<,>,\) or \(=\) to make a true statement $$\frac{5}{16} \quad \frac{5}{17}$$

Write each fraction or mixed number as a decimal. \(\frac{3}{5}\)
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