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Chapter 4: Problem 75

Convert the improper fraction to a mixed number. $$-\frac{23}{6}$$

Short Answer

Expert verified
-4 \frac{1}{6}

Step by step solution

01

- Divide the Numerator by the Denominator

To convert the improper fraction \(-\frac{23}{6}\), start by dividing the numerator by the denominator. \(-23\) divided by \6\ is approximately \-3.83\. We are interested in the integer part of the result which is \-4\.
02

- Multiply and Subtract

Next, multiply the integer part \(-4\) by the denominator \6\. \-4\ times \6\ equals \-24\. Subtract this from the original numerator to find the remainder: \-23 - (-24) = 1\.
03

- Form the Mixed Number

Now, express the original improper fraction as a mixed number. Combine the integer quotient \(-4\) with the remainder over the original denominator: \-4 \frac{1}{6}\.

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Key Concepts

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

Fraction Division
Understanding fraction division is key when converting improper fractions to mixed numbers. An improper fraction is where the numerator is larger than the denominator. To start, you need to divide the numerator by the denominator. For example, with the fraction \(-\frac{23}{6}\), we divide \(-23\) by \6\. The result of this division is \(-3.83\), but for our purposes, we are focusing on the integer part, which is \(-4\). This step simplifies the process by giving us a whole number to work with.
Mixed Numbers
A mixed number is a combination of a whole number and a fraction. Converting an improper fraction like \(-\frac{23}{6}\) to a mixed number involves separating it into these two parts. After dividing the numerator by the denominator, we use the integer part (in this case \(-4\)) as the whole number. The remaining fraction comes from the remainder of the division. This gives us a clear and easy-to-understand format, such as \(-4 \frac{1}{6}\).
Integer Part
The integer part of the division is crucial in forming the mixed number. This is the whole number portion of your result when you divide the numerator by the denominator. For the fraction \(-\frac{23}{6}\), dividing \(-23\) by \6\ yields an integer part of \(-4\). This step simplifies the improper fraction into its significant components, making it easier to understand and work with in subsequent steps.
Remainder Calculation
The process of finding the remainder is the next step in converting to a mixed number. To do this, multiply the integer part by the denominator and subtract this product from the original numerator. For \(-\frac{23}{6}\), calculate \(-4 \times 6 = -24\). Then, subtract this from the numerator: \(-23 - (-24) = 1\). This remainder, \1\, forms the fractional part of the mixed number. The final mixed number is expressed as \(-4 \frac{1}{6}\), clearly separating the whole number and the remainder.

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Most popular questions from this chapter

Find the LCM. 18 and 24

Multiply or divide the mixed numbers. Write the answer as a mixed number or whole number. $$6 \frac{2}{5} \div(-2)$$

Divide. Write the quotient as a mixed number. $$921 \div 4$$

Add the mixed numbers. $$\begin{array}{r} 2 \frac{1}{11} \\ +5 \frac{3}{11} \\ \hline \end{array}$$

Find the LCM. \(28,10,21,\) and 35
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