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Chapter 4: Problem 38

Label the fraction as proper or improper. $$\frac{21}{20}$$

Short Answer

Expert verified
Improper fraction.

Step by step solution

01

- Understand Proper and Improper Fractions

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

- Compare the Numerator and Denominator

In the fraction \(\frac{21}{20}\), the numerator is 21 and the denominator is 20. Compare these two numbers.
03

- Determine the Fraction Type

Since 21 (the numerator) is greater than 20 (the denominator), \(\frac{21}{20}\) is 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 of a fraction is the top number in the fraction. It represents how many parts of the whole are being considered. For example, in the fraction \(\frac{3}{4}\), the numerator is 3. This means we are considering 3 parts out of a total of 4 parts. The numerator helps us understand the quantity relative to the whole.
The numerator plays an essential role in defining the type of fraction. If the numerator is less than the denominator, the fraction is proper. If the numerator is greater than or equal to the denominator, the fraction is improper.
Denominator
The denominator of a fraction is the bottom number. It indicates the total number of equal parts that make up the whole. For example, in the fraction \(\frac{5}{8}\), the denominator is 8. This means the whole is divided into 8 equal parts, and the numerator tells us how many of those parts we are considering.
Understanding the denominator is crucial because it shows how the whole is partitioned. When comparing fractions, consistent denominators allow for straightforward comparison of numerators. The larger the denominator, the smaller each part of the whole becomes.
Fraction Comparison
Comparing fractions involves looking at their numerators and denominators to determine their sizes relative to each other. Here are some key points to consider:
  • If two fractions have the same denominator, compare their numerators directly. The fraction with the larger numerator is the larger fraction.
  • If two fractions have different denominators, you can find a common denominator and then compare the numerators.
  • Improper fractions can be converted to mixed numbers to better understand their size.

Let's look at the exercise example, \(\frac{21}{20}\). We compare the numerator 21 and the denominator 20. Since 21 is greater than 20, \(\frac{21}{20}\) is an improper fraction. Knowing how to compare fractions helps in identifying whether they are proper or improper and improves our overall number sense.

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Most popular questions from this chapter

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

For Exercises 65鈥�76, convert the improper fraction to a mixed number. $$\frac{37}{8}$$

Simplify to lowest terms by first reducing the powers of 10. $$\frac{720}{800}$$

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

Convert the improper fraction to a mixed number. $$-\frac{27}{10}$$
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