Which statement about improper fractions is true?

Which statement about improper fractions is true?

• A. An improper fraction has a numerator equal to the denominator.
• B. A proper fraction has a numerator greater than the denominator.
• C. An improper fraction has a numerator greater than the denominator.
• D. A mixed number cannot be expressed as an improper fraction.

Answer: (C)

Understanding improper fractions starts with the relationship between the numerator and the denominator. An improper fraction is one in which the numerator is larger than the denominator, so the value is greater than one. For example, 9/4 or 7/3 are improper because more parts are shaded than the whole, meaning more than one whole is being counted. This is why the statement about improper fractions being defined by a numerator greater than the denominator is true. In contrast, a proper fraction has a numerator smaller than the denominator, like 2/5, which represents less than one. The idea that a mixed number cannot be expressed as an improper fraction is false because every mixed number can be rewritten as an improper fraction (for instance, 2 1/3 equals 7/3). Also, saying an improper fraction has a numerator equal to the denominator would describe a value of 1, which is not the general property used here.

Understanding improper fractions starts with the relationship between the numerator and the denominator. An improper fraction is one in which the numerator is larger than the denominator, so the value is greater than one. For example, 9/4 or 7/3 are improper because more parts are shaded than the whole, meaning more than one whole is being counted. This is why the statement about improper fractions being defined by a numerator greater than the denominator is true. In contrast, a proper fraction has a numerator smaller than the denominator, like 2/5, which represents less than one. The idea that a mixed number cannot be expressed as an improper fraction is false because every mixed number can be rewritten as an improper fraction (for instance, 2 1/3 equals 7/3). Also, saying an improper fraction has a numerator equal to the denominator would describe a value of 1, which is not the general property used here.