Which statement defines a proper fraction?

Which statement defines a proper fraction?

• A. Numerator greater than denominator
• B. Numerator less than denominator
• C. Denominator is zero
• D. Numerator equals denominator

Answer: (B)

A proper fraction is one whose value is less than 1 when written as a real number. In simple fractions, that happens exactly when the numerator is smaller than the denominator (and the denominator isn’t zero). So the statement “numerator less than denominator” correctly defines a proper fraction, since it yields a value between 0 and 1, like 3/8. If the numerator is larger than the denominator, the fraction is greater than 1 (improper). If the denominator is zero, the expression is undefined. If the numerator equals the denominator, the value is 1, which is not a proper fraction.

A proper fraction is one whose value is less than 1 when written as a real number. In simple fractions, that happens exactly when the numerator is smaller than the denominator (and the denominator isn’t zero). So the statement “numerator less than denominator” correctly defines a proper fraction, since it yields a value between 0 and 1, like 3/8. If the numerator is larger than the denominator, the fraction is greater than 1 (improper). If the denominator is zero, the expression is undefined. If the numerator equals the denominator, the value is 1, which is not a proper fraction.