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Chapter 4: Problem 37

Label the fraction as proper or improper. $$\frac{7}{2}$$

Short Answer

Expert verified
Improper fraction

Step by step solution

01

- Understand the Definitions

A proper fraction is one where the numerator is less than the denominator. An improper fraction is one where the numerator is greater than or equal to the denominator.
02

- Identify the Numerator and Denominator

For the fraction \(\frac{7}{2}\), the numerator is 7 and the denominator is 2.
03

- Compare Numerator and Denominator

Compare the numerator and the denominator. Since 7 (numerator) is greater than 2 (denominator), this fraction is classified as an improper fraction.

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Key Concepts

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

Numerator
The numerator is the number above the fraction line in a fraction. It represents how many parts of a whole we have. For example, in the fraction \(\frac{7}{2}\), the numerator is 7. In simpler terms, if you break the whole into equal parts, the numerator tells you how many of those parts you have.
For instance, if you have a chocolate bar divided into 2 equal parts and you eat 7 pieces, the 7 is your numerator. This helps us understand how much of something we are talking about.
  • Example: In \(\frac{3}{5}\), the numerator is 3.
  • Example: In \(\frac{10}{7}\), the numerator is 10.
The numerator is key in determining if a fraction is proper, improper, or a mixed number.
Denominator
The denominator is the number below the fraction line in a fraction. It indicates into how many equal parts the whole is divided. For the fraction \(\frac{7}{2}\), the denominator is 2. This means we are dividing something into 2 equal parts.
  • Example: In \(\frac{3}{5}\), the denominator is 5, so the whole is split into 5 parts.
  • Example: In \(\frac{10}{7}\), the denominator is 7, thus the whole is divided into 7 parts.
Understanding the denominator helps us know the size of each part of the whole.
Proper Fraction
A proper fraction is one where the numerator is less than the denominator. This means that the fraction represents less than one whole.
For example, in the fraction \(\frac{3}{4}\), the numerator 3 is less than the denominator 4. Therefore, \(\frac{3}{4}\) is a proper fraction.
  • Example: \(\frac{1}{2}\) is a proper fraction because 1 is less than 2.
  • Example: \(\frac{5}{8}\) is a proper fraction because 5 is less than 8.
In contrast, an improper fraction has a numerator that is greater than or equal to the denominator. Therefore, fractions like \(\frac{7}{2}\) are improper since 7 is more than 2.

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Most popular questions from this chapter

Simplify. $$-\left(-\frac{7}{3}\right)$$

Which expressions are equivalent to \(\frac{-9}{10} ?\) \(\begin{array}{cccc}\text { a. } \frac{9}{10} & \text { b. }-\frac{9}{10} & \text { c. } \frac{9}{-10} & \text { d. } \frac{-9}{-10}\end{array}\)

Simplify the fraction to lowest terms. Write the answer as a fraction or a whole number. $$\frac{39}{130}$$

Simplify the expression. $$\frac{5 x^{4}}{15 x^{3}}$$

Label the fraction as proper or improper. $$\frac{2}{3}$$
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