Question

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

Short answer

5.0625

Step-by-step solution

- 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 \[5 \frac{1}{16} = \frac{5 \times 16 + 1}{16} = \frac{80 + 1}{16} = \frac{81}{16}\]

- 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. \[ \frac{81}{16} = 5.0625 \]

Key concepts

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’s 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.