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Chapter 5: Problem 17

Write each fraction or mixed number as a decimal. $$-\frac{16}{5}$$

Short Answer

Expert verified
-3.2

Step by step solution

01

Understand the problem

To convert \(-\frac{16}{5}\) into a decimal, it is necessary to perform the division of the numerator by the denominator.
02

Perform the division

Divide 16 by 5. This results in 3.2. Because the fraction is negative, the decimal form is also negative. So, \(-\frac{16}{5} = -3.2\).

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Key Concepts

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

Negative Fractions
Negative fractions are fractions with a negative sign in front of them.
This can either be written as \(-\frac{a}{b}\) or \(\frac{-a}{b}\).
The negative sign means that the fraction represents a value less than zero.
When you convert a negative fraction to a decimal, keep the negative sign with the final result.
For example, converting \(-\frac{16}{5}\) to a decimal gets us -3.2, not just 3.2.
Division
Division is the process of determining how many times one number, called the divisor, is contained within another number, called the dividend.
In the fraction \(-\frac{16}{5}\), 16 is the dividend and 5 is the divisor.
Performing the division \(\frac{16}{5}\) gives us 3.2.
So, \(-\frac{16}{5} = -3.2\).
When dividing, it's crucial to remember to include the negative sign in your result if the fraction is negative.
Numerator and Denominator
Fractions are composed of a numerator and a denominator.
The numerator is the top number and it represents how many parts of the whole we are taking.
The denominator is the bottom number and it indicates how many parts the whole is divided into.
For example, in the fraction \(-\frac{16}{5}\), 16 is the numerator and 5 is the denominator.
When converting to a decimal, you divide the numerator by the denominator.
Because our fraction is negative, we end up with a negative decimal result.

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