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Chapter 4: Problem 34

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

Short Answer

Expert verified
Proper fraction

Step by step solution

01

Identify the numerator and denominator

The given fraction is \(\frac{2}{3}\). Identify the numerator and denominator. Here, 2 is the numerator and 3 is the denominator.
02

Compare numerator and denominator

Compare the numerator and the denominator. 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.
03

Determine the type of fraction

In this case, 2 (numerator) is less than 3 (denominator). Therefore, the fraction \(\frac{2}{3}\) is a proper fraction.

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Key Concepts

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

Numerator
In a fraction, the numerator is the top number. It indicates how many parts of the whole are being considered. For instance, in the fraction \( \frac{2}{3} \), the numerator is 2. This means you have 2 parts out of a total of 3. The numerator plays a vital role in determining whether a fraction is proper or improper. If it is smaller than the denominator, the fraction is proper. If it equals or exceeds the denominator, the fraction is improper.
An easy way to remember this is to think of the numerator as the 'counter' of parts.
Denominator
The denominator is the bottom number of a fraction. It shows the total number of equal parts that make up the whole. In the fraction \( \frac{2}{3} \), the denominator is 3, which means the whole is divided into 3 equal parts. Like the foundation of a building, the denominator supports the whole fraction by indicating the size of each part.
By comparing the numerator and denominator, you can determine the type of fraction. If the denominator is larger than the numerator, the fraction is proper. Conversely, a numerator equal to or larger than the denominator results in an improper fraction.
Fraction Comparison
To determine whether a fraction is proper or improper, you need to compare the numerator to the denominator.

Here鈥檚 a step-by-step approach:
  • First, identify the numerator and denominator.

  • Next, compare the two numbers. If the numerator is smaller than the denominator, the fraction is proper. If the numerator is equal to or larger than the denominator, the fraction is improper.

Using the example \( \frac{2}{3} \):
  • The numerator is 2, and the denominator is 3.
  • Since 2 is smaller than 3, \( \frac{2}{3} \) is a proper fraction.
Proper and improper fractions are essential for understanding more complex math concepts like mixed numbers and decimal conversions.

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Most popular questions from this chapter

Convert the mixed number to an improper fraction. $$-15 \frac{1}{2}$$

Simplify to lowest terms by first reducing the powers of 10. $$\frac{120}{160}$$

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

Convert the mixed number to an improper fraction. $$6 \frac{1}{3}$$

Divide. Write the quotient as a mixed number. $$695 \div 34$$
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