To determine whether the fraction [tex]\(\frac{4}{5}\)[/tex] is a proper fraction, an improper fraction, a mixed number, or a decimal fraction, we need to understand the definitions of these terms and analyze the given fraction based on these definitions.
1. Proper Fraction:
- A fraction is considered proper if the numerator (the top number) is less than the denominator (the bottom number).
2. Improper Fraction:
- A fraction is considered improper if the numerator is greater than or equal to the denominator.
3. Mixed Number:
- A mixed number is a combination of a whole number and a proper fraction.
4. Decimal Fraction:
- A decimal fraction is a fraction where the denominator is a power of 10 (e.g., 10, 100, 1000).
Now, let's analyze the given fraction, [tex]\(\frac{4}{5}\)[/tex]:
- The numerator is 4.
- The denominator is 5.
First, we check if it is a proper fraction:
- Since the numerator (4) is less than the denominator (5), [tex]\(\frac{4}{5}\)[/tex] is indeed a proper fraction.
Next, let's check if it is an improper fraction:
- For a fraction to be improper, the numerator must be greater than or equal to the denominator. Here, 4 is not greater than or equal to 5, so [tex]\(\frac{4}{5}\)[/tex] is not an improper fraction.
Furthermore, let's see if it is a mixed number:
- A mixed number involves a whole number part and a proper fraction part. Since 4 is less than 5, it doesn't fit the criteria for a mixed number.
Lastly, consider if it is a decimal fraction:
- The denominator of [tex]\(\frac{4}{5}\)[/tex] is 5, which is not a power of 10. So, it is not a decimal fraction.
Given the definitions and our analysis, [tex]\(\frac{4}{5}\)[/tex] is best categorized as a proper fraction.
Hence, the answer is:
- a proper fraction
