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Chapter 4: Problem 6

Convert \(\frac{32}{9}\) to a mixed number.

Short Answer

Expert verified
The mixed number is \( 3 \frac{5}{9} \).

Step by step solution

01

Understand the Mixed Number Concept

A mixed number consists of an integer part and a fractional part. To convert an improper fraction like \( \frac{32}{9} \), follow the subsequent steps.
02

Divide the Numerator by the Denominator

Divide 32 by 9 to find the integer part (quotient) and the remainder. \( 32 \div 9 = 3 \) with a remainder of 5.
03

Express the Remainder as a Fraction

Use the remainder to form the fractional part of the mixed number. The mixed number is given as \( Quotient \frac{Remainder}{Denominator} \). Here, it is \( 3 \frac{5}{9} \).

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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 that combines an integer and a fraction. It provides a way to express improper fractions, where the numerator is larger than the denominator, in a more intuitive format. For example, in the exercise converting \( \frac{32}{9} \) to a mixed number, we first need to recognize what a mixed number looks like. A mixed number is written as an integer followed by a proper fraction, like this: \( 3 \frac{5}{9} \). This makes it easier to understand and work with large values. Remember, the integer part shows how many whole units are present, while the fraction represents the leftover part of the division.
long division
Long division is the process used to divide larger numbers. It helps to break down a division problem into a series of easier steps. To convert an improper fraction like \( \frac{32}{9} \) to a mixed number, you use long division:
  • First, divide the numerator (32) by the denominator (9).
  • The result of the division gives you the quotient, which is the integer part of the mixed number.
In our example, dividing 32 by 9 gives you a quotient of 3. This quotient is the integer part of the mixed number.
The remainder of the division is what鈥檚 left after subtracting the product of the quotient and the divisor from the original numerator. For this problem, the remainder is 5 (since 32 - 27 = 5). This remainder forms the numerator of the fractional part of the mixed number.
fractions
Fractions represent parts of a whole. An improper fraction, where the numerator is greater than the denominator, can be converted into a mixed number for simplicity. In converting \( \frac{32}{9} \) to the mixed number \( 3 \frac{5}{9} \), we highlight the concept of both improper and proper fractions:
  • Improper fraction: Numerator (32) is bigger than the denominator (9).
  • Proper fraction: Numerator (5) is smaller than the denominator (9).
After long division, the remainder (here, 5) over the original denominator (9) forms the proper fraction part of the mixed number. Thus, \( \frac{32}{9} \) becomes \( 3 \frac{5}{9} \), efficiently displaying the value as a mix of whole numbers and fractions.

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Most popular questions from this chapter

Add the mixed numbers. $$\begin{array}{r} 5 \frac{2}{7} \\ +4 \frac{3}{7} \\ \hline \end{array}$$

a. What fraction of the alphabet is made up of vowels? (Include the letter \(y\) as a vowel, not a consonant.) b. What fraction of the alphabet is made up of consonants?

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Find the LCM. \(8,10,\) and 12
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