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Chapter 4: Problem 31

In the following exercises, rewrite the improper fraction as a mixed number. $$\frac{13}{5}$$

Short Answer

Expert verified
The improper fraction \(\frac{13}{5}\) as a mixed number is \(\frac{13}{5} = 2 \frac{3}{5}\).

Step by step solution

01

Divide the numerator by the denominator

To convert the improper fraction \(\frac{13}{5}\), first divide the numerator (13) by the denominator (5). \[ 13 梅 5 = 2 \text{ R } 3 \]
02

Write the quotient as the whole number

The quotient from the division is 2. This quotient becomes the whole number in the mixed number.
03

Write the remainder as the new numerator

The remainder from the division is 3. This remainder becomes the numerator of the fractional part of the mixed number.
04

Keep the original denominator

The denominator remains the same as the original fraction, which is 5.
05

Combine the whole number and the fraction

Now, combine the whole number with the new fraction. \[ 2 \frac{3}{5} \]

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Key Concepts

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

Mixed Numbers
A mixed number is a number consisting of two parts: a whole number and a fractional part. For example, in the exercise \(\frac{13}{5}\) we converted it to 2 \(\frac{3}{5}\), where 2 is the whole number and \(\frac{3}{5}\) is the fraction.
Mixed numbers are often easier to understand and work with than improper fractions, especially in everyday situations. Whenever you have an improper fraction, you can always change it to a mixed number for simplicity.
Numerator and Denominator
Fractions consist of two main components: the numerator and the denominator. The numerator is the top number of a fraction and represents how many parts we have. The denominator is the bottom number and indicates how many equal parts the whole is divided into.
In the fraction \(\frac{13}{5}\), 13 is the numerator, and 5 is the denominator. When converting an improper fraction, these two components play a crucial role in determining both the quotient (whole number) and the remainder (new numerator).
Division with Remainders
Division with remainders is a fundamental concept when converting improper fractions to mixed numbers. By dividing the numerator by the denominator, we get two key values: the quotient and the remainder.
For example, dividing 13 (numerator) by 5 (denominator) gives us a quotient of 2 and a remainder of 3. \[ 13 梅 5 = 2 \text{ R } 3 \]
The quotient becomes the whole number in the mixed number, while the remainder becomes the numerator of the new fraction.
Fraction Conversion
Fraction conversion involves changing the form of a fraction without altering its value. In the case of improper fractions, we convert them to mixed numbers for easier understanding and usage.
The steps to convert an improper fraction like \(\frac{13}{5}\) include:
  • Dividing the numerator by the denominator.
  • Using the quotient as the whole number.
  • Writing the remainder as the new numerator.
  • Keeping the original denominator the same.

Combining these steps will convert the improper fraction into a mixed number, making it simpler to work with in many scenarios.

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Most popular questions from this chapter

In the following exercises, simplify. $$\left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right)$$

In the following exercises, simplify. $$ \frac{1}{3} \cdot \frac{3}{4} $$

In the following exercises, simplify. $$ \frac{9^{2}-4^{2}}{9-4} $$

In the following exercises, perform the indicated operation. $$ 2 \frac{11}{12}-1 \frac{7}{12} $$

In the following exercises, simplify. $$ -\frac{3}{10}+\left(-\frac{5}{8}\right) $$
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