Improper Fraction to Mixed Number Calculator

Enter an improper fraction to quickly convert it to a mixed number.

Convert Improper Fractions into Mixed Numbers

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Result

What is an Improper Fraction?

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.

What is a Mixed Number?

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.

How to Convert an Improper Fraction to a Mixed Number?

To convert an improper fraction to a mixed number, follow these steps:

  1. Identify the improper fraction form: An improper fraction is usually written as \( \frac{a}{b} \), where \( a \geq b \).
  2. Calculate the integer part: Divide the numerator \( a \) by the denominator \( b \) to get the integer part \( c \): \( c = \left\lfloor \frac{a}{b} \right\rfloor \)
  3. Calculate the proper fraction part: Subtract the integer part \( c \) multiplied by the denominator \( b \) from the numerator \( a \) to get the new numerator \( d \): \( d = a - c \times b \)
  4. Write the mixed number: Combine the integer part and the proper fraction part to form the mixed number: \( c \frac{d}{b} \)

Examples

Example 1: Convert the improper fraction \( \frac{9}{4} \) to a mixed number.

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 \( 2 \frac{1}{4} \).

Example 2: Convert the improper fraction \( \frac{11}{3} \) to a mixed number.

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 \( 3 \frac{2}{3} \).

Example 3: Convert the improper fraction \( \frac{7}{2} \) to a mixed number.

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 \( 3 \frac{1}{2} \).