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Chapter 3: Problem 42

Convert to a mixed numeral. $$ \frac{59}{8} $$

Short Answer

Expert verified
The mixed numeral is: \[ 7 \frac{3}{8} \]

Step by step solution

01

Divide the Numerator by the Denominator

Divide 59 by 8. This gives the quotient and the remainder. Perform the division: \[ 59 \div 8 = 7 \qquad \text{(Quotient)} \ 59 - (7 \times 8) = 3 \qquad \text{(Remainder)} \]
02

Write as a Mixed Number

Using the quotient as the whole number part, the remainder as the numerator, and the divisor (8) as the denominator. So, \[ 59 \div 8 \ = \ 7 \frac{3}{8} \]

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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 essential in basic college mathematics. When dividing fractions, we often convert it into a multiplication problem by using the reciprocal of the divisor. However, in this case, we started with an improper fraction and divided the numerator by the denominator. This type of division helps us break down more complex fractions into more manageable pieces. The goal is to find out how many times the denominator can fit into the numerator completely (the quotient), and what remains after that (the remainder). This process is the first step in converting an improper fraction into a mixed numeral.
quotient and remainder
The concepts of quotient and remainder are foundational in arithmetic and algebra. When you divide one number by another, the quotient is the number of times the divisor fits into the numerator. The remainder is what is left over after the division. For instance, in dividing 59 by 8:
  • The quotient is 7, because 8 fits into 59 a total of 7 times.

  • The remainder is 3, because \(59 - (7 * 8) = 3\).
Understanding these terms is crucial for various calculations and for converting improper fractions to mixed numerals.
converting improper fractions
An improper fraction is a fraction where the numerator is larger than the denominator, like \(\frac{59}{8}\). To convert an improper fraction to a mixed numeral, follow these steps:
  • Divide the numerator (59) by the denominator (8). This gives you the quotient (7).

  • Find the remainder by subtracting the product of the quotient and the denominator from the numerator: \(59 - (7 * 8) = 3\).

  • Write the quotient as the whole number part of the mixed numeral.

  • Write the remainder as the numerator of the fractional part, keeping the original denominator.
Therefore, \(\frac{59}{8}\) becomes \(7 \frac{3}{8}\).
basic college mathematics
Basic college mathematics covers a wide range of topics, including arithmetic, algebra, and geometry. Among these, operations with fractions, such as fraction division and converting improper fractions, are fundamental. Mastery of these skills lays the groundwork for more advanced mathematical concepts.

For example, understanding how to convert an improper fraction to a mixed numeral helps in simplifying expressions and solving equations. Practicing problems involving quotients, remainders, and fraction manipulation builds a strong foundation for topics you will encounter in higher-level math courses.

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Most popular questions from this chapter

On Monday, April \(15,\) it rained \(\frac{1}{2}\) in. in the morning and \(\frac{3}{8}\) in. in the afternoon. How much did it rain altogether?

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{7}{100} $$

Add and simplify. $$ \frac{5}{7}+\frac{25}{52}+\frac{7}{4} $$

Simplify. $$ 10 \frac{3}{5}-4 \frac{1}{10}-1 \frac{1}{2} $$

Simplify. $$ \frac{\frac{1}{10}}{10} $$
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