Mixed Number to Improper Fraction Calculator

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

Convert Mixed Numbers to Improper Fractions

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Result

What is a Mixed Number?

A mixed number, also known as a mixed fraction, is a number composed of an integer part and a proper fraction part. It is usually written in the form \( c \frac{d}{e} \), where \( c \) is the integer part, and \( \frac{d}{e} \) is the proper fraction (with \( d < e \)). For example, \( 1 \frac{2}{3} \) and \( 3 \frac{1}{4} \) are both mixed numbers.

What is an Improper Fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, typically written 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 or equal to the denominator.

How to Convert a Mixed Number to an Improper Fraction?

Follow these steps to convert a mixed number to an improper fraction:

1. Identify the mixed number form

A mixed number is typically written as \( c \frac{d}{e} \).

2. Calculate the numerator of the improper fraction

Multiply the integer part \( c \) by the denominator \( e \), then add the numerator \( d \) of the proper fraction: \( a = c \times e + d \)

3. Write the improper fraction

Combine the calculated numerator \( a \) and the original denominator \( e \) to form the improper fraction: \( \frac{a}{e} \)

Examples

Example 1: Convert the mixed number \( 2 \frac{1}{3} \) to an improper fraction.

Solution:

1. Calculate the numerator:

\( a = 2 \times 3 + 1 = 6 + 1 = 7 \)

2. rite the improper fraction:

\( \frac{7}{3} \)

Result: The mixed number \( 2 \frac{1}{3} \) converts to the improper fraction \( \frac{7}{3} \).

Example 2: Convert the mixed number \( 3 \frac{2}{5} \) to an improper fraction.

Solution:

1. Calculate the numerator:

\( a = 3 \times 5 + 2 = 15 + 2 = 17 \)

2. Write the improper fraction:

\( \frac{17}{5} \)

Result: The mixed number \( 3 \frac{2}{5} \) converts to the improper fraction \( \frac{17}{5} \).

Example 3: Convert the mixed number \( 1 \frac{3}{4} \) to an improper fraction.

Solution:

1. Calculate the numerator:

\( a = 1 \times 4 + 3 = 4 + 3 = 7 \)

2. Write the improper fraction:

\( \frac{7}{4} \)

Result: The mixed number \( 1 \frac{3}{4} \) converts to the improper fraction \( \frac{7}{4} \).

Example 4: Convert the mixed number \( 4 \frac{5}{6} \) to an improper fraction.

Solution:

1. Calculate the numerator:

\( a = 4 \times 6 + 5 = 24 + 5 = 29 \)

2. Write the improper fraction:

\( \frac{29}{6} \)

Result: The mixed number \( 4 \frac{5}{6} \) converts to the improper fraction \( \frac{29}{6} \).