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Chapter 4: Problem 57

Convert the mixed number to an improper fraction. $$-21 \frac{3}{8}$$

Short Answer

Expert verified
The improper fraction is \( \frac{-165}{8} \).

Step by step solution

01

Separate the whole number and the fraction

Identify the whole number part and the fractional part of the mixed number. Here, the whole number is \( -21 \) and the fractional part is \( \frac{3}{8} \). Note the negative sign applies to the entire mixed number.
02

Convert the whole number to a fraction

Express the whole number as a fraction with the same denominator as the fractional part. \( -21 = -21 \frac{8}{8} = \frac{-21 \times 8}{8} = \frac{-168}{8} \).
03

Add the fractional part

Add the fractional part \( \frac{3}{8} \) to the fraction obtained from the whole number. Since both fractions have the same denominator, add their numerators: \[ \frac{-168}{8} + \frac{3}{8} = \frac{-168 + 3}{8} = \frac{-165}{8} \].

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Key Concepts

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

Fractions
A **fraction** is a way of representing a part of a whole. It consists of two parts: a **numerator** (top number) and a **denominator** (bottom number). The numerator represents how many parts we have, while the denominator shows the total number of equal parts in the whole. For example, in the fraction \( \frac{3}{8} \), 3 is the numerator and 8 is the denominator.
Fractions are fundamental in mathematics and are often used in various everyday scenarios, like cooking and dividing objects.
Understanding fractions sets a foundation for learning more complex mathematical concepts.
Improper Fractions
**Improper fractions** are fractions where the numerator is greater than or equal to the denominator. This means the value of the fraction is equal to or greater than one. For instance, \( \frac{9}{4} \) and \( \frac{165}{8} \) are improper fractions.
In the context of converting a mixed number like \(-21 \frac{3}{8}\), we often end up with an improper fraction. The key steps include adjusting the whole number and adding it to the fraction part. This results in an improper fraction: \( \frac{-165}{8} \).
Mixed Numbers
**Mixed numbers** combine a whole number and a fraction. These numbers are a useful way to express values greater than one in a more understandable manner. For example, \(-21 \frac{3}{8}\) is a mixed number consisting of the whole number \(-21\) and the fraction \(\frac{3}{8}\).
To convert mixed numbers to improper fractions, follow these steps:
  • Identify the whole number and fractional parts.
  • Convert the whole number to a fraction with the same denominator as the fractional part.
  • Add the fractional parts together to get an improper fraction.
This method helps in performing operations involving fractions more easily.
Mathematics Education
**Mathematics education** emphasizes understanding and applying fundamental concepts like fractions, mixed numbers, and improper fractions. These basics are critical for solving more advanced problems and real-world applications.
Interactive exercises, like converting mixed numbers to improper fractions, reinforce these concepts. Following step-by-step solutions enables students to grasp the methods and logic behind the procedures.
Effective mathematics education builds confidence and develops problem-solving skills in students, preparing them for higher-level math and everyday situations.

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Most popular questions from this chapter

Simplify the expression. $$\frac{16 a b}{10 a}$$

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How many fourths are in \(1 \frac{3}{4}\) "

Simplify to lowest terms by first reducing the powers of 10. $$-\frac{2000}{1500}$$
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