Mixed Number Calculator

What is a mixed number?

A mixed number is made of a whole number and a proper fraction, for example \(2 \dfrac{1}{3}\). It represents a value greater than one, but written in a way that highlights how many “wholes” and how many “extra parts” you have.

The same value can also be written as an improper fraction, where the numerator is at least as big as the denominator. For instance, \[ 2 \dfrac{1}{3} = \dfrac{7}{3}. \]

How to convert a mixed number to an improper fraction

Suppose you have a mixed number \(a \dfrac{b}{c}\) where \(a\) is the whole number, \(b\) is the numerator and \(c\) is the denominator. (We assume \(c \ne 0\).)

1. Multiply the whole number by the denominator: \(a \times c\).
2. Add the numerator: \(a \times c + b\).
3. Keep the same denominator \(c\).

Example: \[ 2 \dfrac{1}{3} = \dfrac{2 \cdot 3 + 1}{3} = \dfrac{6 + 1}{3} = \dfrac{7}{3}. \]

For a negative mixed number, such as \(-2 \dfrac{1}{3}\), the whole value is negative: \[ -2 \dfrac{1}{3} = -\dfrac{7}{3}. \]

How to convert an improper fraction to a mixed number

Now start with an improper fraction \(\dfrac{n}{d}\) where \(|n| \ge d\) and \(d \ne 0\).

1. Divide \(n\) by \(d\): \(n = qd + r\) where \(q\) is the quotient and \(r\) is the remainder.
2. The whole part is \(q\).
3. The fractional part is \(\dfrac{r}{d}\).

Example: \[ \dfrac{11}{4} = 2 \dfrac{3}{4} \quad \text{because } 11 = 2 \cdot 4 + 3. \]

Simplifying a mixed number or fraction

A fraction \(\dfrac{n}{d}\) is in simplest form if the numerator and denominator have no common factor greater than 1. To simplify:

1. Find the greatest common divisor (GCD) of \(n\) and \(d\).
2. Divide both numerator and denominator by the GCD.

Our calculator does this automatically for you when the “simplify result” option is checked.

Examples you can try

• Mixed to improper: \(3 \dfrac{2}{5}\). \(3 \cdot 5 + 2 = 17\), so \(3 \dfrac{2}{5} = \dfrac{17}{5}\).
• Improper to mixed: \(\dfrac{22}{7}\). \(22 = 3 \cdot 7 + 1\), so \(\dfrac{22}{7} = 3 \dfrac{1}{7}\).
• Negative mixed number: \(-4 \dfrac{3}{8}\). First convert \(4 \dfrac{3}{8} = \dfrac{35}{8}\), then add the minus sign: \(-4 \dfrac{3}{8} = -\dfrac{35}{8}\).

FAQ: using the mixed number calculator correctly

What is a mixed number?

It is a number made of a whole part and a proper fraction, like \(2 \dfrac{1}{3}\). Mixed numbers are common in primary and middle school maths, cooking recipes and everyday measurements.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, and write the result over the original denominator: \(a \dfrac{b}{c} = \dfrac{a \cdot c + b}{c}\). The calculator applies this rule and simplifies the fraction if you ask it to.

How do I convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number, and the remainder over the denominator is the fractional part. For example, \(11/4 = 2 3/4\) because \(11 = 2 \cdot 4 + 3\).

Can I use this mixed number calculator for graded work?

You can definitely use it to check your work and understand each step. For exams and assignments, always follow your teacher’s instructions and show your own step-by-step reasoning, even if you used a calculator to verify the answer.