Mixed Fraction Calculator

About Mixed Fraction Calculator

A mixed number combines a whole number with a fraction. Convert by multiplying whole × denominator + numerator.

How to use this calculator

1. Enter the mixed number or improper fraction you want to convert.
2. If you start with a mixed number, identify the whole number, numerator, and denominator.
3. If you start with an improper fraction, divide the numerator by the denominator to find the whole number and remainder.
4. Read the result and, if needed, use the step-by-step explanation to see how the conversion was done.

The formula explained

The formula \(a\frac{b}{c} = \frac{ac+b}{c}\) turns a mixed number into an improper fraction. It works by converting the whole part into pieces of size \(\frac{1}{c}\), then adding the extra fractional pieces.

• a = the whole number in the mixed fraction
• b = the numerator of the fractional part
• c = the denominator of the fractional part

Step by step method

1. Multiply the whole number by the denominator.
2. Add the numerator to that product.
3. Put the result over the same denominator, then simplify if possible.

Worked example

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

1. Multiply the whole number and denominator: \(3 \times 5 = 15\).
2. Add the numerator: \(15 + 2 = 17\).
3. Write the result over the original denominator: \(\frac{17}{5}\).

Tips and common mistakes

• Always keep the original denominator when converting a mixed number to an improper fraction.
• When converting back from an improper fraction, divide carefully, because the remainder becomes the new numerator.

Frequently asked questions