Enter an improper fraction to quickly convert it to a mixed number.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator, typically represented as \( \frac{a}{b} \), where \( a \geq b \). For example, \( \frac{5}{3} \) and \( \frac{7}{4} \) are improper fractions because the numerator is larger than the denominator.
A mixed number, also known as a mixed fraction, consists of an integer part and a proper fraction part, typically written as \( c \frac{d}{e} \), where \( c \) is the integer part and \( \frac{d}{e} \) is the proper fraction (with \( d < e \)). For example, \( 1 \frac{2}{3} \) and \( 2 \frac{1}{4} \) are mixed numbers.
To convert an improper fraction to a mixed number, follow these steps:
Solution:
1. Calculate the integer part:
\( c = \left\lfloor \frac{9}{4} \right\rfloor = 2 \)
2. Calculate the proper fraction part:
\( d = 9 - 2 \times 4 = 1 \)
3. Write the mixed number:
\( 2 \frac{1}{4} \)
Result: The improper fraction \( \frac{9}{4} \) converts to the mixed number \( 2 \frac{1}{4} \).
Solution:
1. Calculate the integer part:
\( c = \left\lfloor \frac{11}{3} \right\rfloor = 3 \)
2. Calculate the proper fraction part:
\( d = 11 - 3 \times 3 = 2 \)
3. Write the mixed number:
\( 3 \frac{2}{3} \)
Result: The improper fraction \( \frac{11}{3} \) converts to the mixed number \( 3 \frac{2}{3} \).
Solution:
1. Calculate the integer part:
\( c = \left\lfloor \frac{7}{2} \right\rfloor = 3 \)
2. Calculate the proper fraction part:
\( d = 7 - 3 \times 2 = 1 \)
3. Write the mixed number:
\( 3 \frac{1}{2} \)
Result: The improper fraction \( \frac{7}{2} \) converts to the mixed number \( 3 \frac{1}{2} \).