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Chapter 5: Problem 29

Write the improper fraction as a mixed number. $$-\frac{64}{5}$$

Short Answer

Expert verified
Question: Convert the improper fraction $$-\frac{64}{5}$$ to a mixed number. Answer: $$-13\frac{-3}{5}$$.

Step by step solution

01

Divide the numerator by the denominator.

In this case, we need to divide -64 by 5. When dividing, you will get a quotient and a remainder: $$-64 = 5 \times (-13) + (-3)$$ So, the quotient is -13 and the remainder is -3.
02

Write the whole number and proper fraction.

The quotient is the whole number, and the remainder over the denominator is the proper fraction. We can now write the mixed number: $$-13\frac{-3}{5}$$ So the mixed number representation of the improper fraction $$-\frac{64}{5}$$ is $$-13\frac{-3}{5}$$.

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Key Concepts

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

Mixed Numbers
Improper fractions and mixed numbers are two ways to represent numbers that have both whole and fractional parts. A _mixed number_ consists of a whole number and a fraction. This format makes it easier to visualize the value of a number that is larger than a whole.
Mixed numbers give us a more intuitive understanding, especially when dealing with measurements or visualizing everyday situations. For example, the improper fraction \(-\frac{64}{5}\) is the same as the mixed number \(-13\frac{-3}{5}\). This tells us there are 13 full parts and an additional fraction that makes up the total amount.
Numerator and Denominator
In any fraction, the numerator and denominator play key roles. In the fraction \(\frac{a}{b}\), \(a\) is the numerator, representing the number of parts we are interested in. Meanwhile, \(b\), the denominator, indicates the total number of equal parts the whole is divided into.
For example, in our fraction \(-\frac{64}{5}\), \(-64\) is the numerator, representing how many parts we have (in negative, indicating direction or deficit), and \(5\) is the denominator, showing that each whole consists of five parts. Understanding these terms is crucial when dealing with fractions, converting them, and performing arithmetic operations on fractions.
Quotient and Remainder
The division process not only results in a quotient but often leaves a remainder, especially when dividing numbers that don't fit perfectly. The _quotient_ is how many whole times the divisor fits into the dividend, and the remainder is what鈥檚 left after that fitting.
In the given example, when dividing \(-64\) by \(5\), the quotient is \(-13\), and the remainder is \(-3\). So when converting the improper fraction to a mixed number, the quotient becomes the whole number portion, and the remainder forms the fractional part along with the denominator.
Division Process in Fractions
Understanding the division process in fractions is essential for converting improper fractions to mixed numbers. Here鈥檚 a step-by-step process:
  • Divide the numerator by the denominator.
  • The result is your quotient, which is the whole number part of your mixed number.
  • If there is a remainder, it becomes the numerator of the fractional part, with the original denominator remaining unchanged.
For \(-\frac{64}{5}\), performing the division makes it clear: \(-64 \div 5 = -13\) remainder \(-3\). Hence, the conversion results in the mixed number \(-13\frac{-3}{5}\). This process transforms a flat improper fraction into a more digestible format for various practical uses and further arithmetic operations.

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Most popular questions from this chapter

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