Practice or solve mixed fractions (mixed numbers) problems with the mixed fraction calculator. A mixed fraction is a whole number and a proper fraction combined. By using this online mixed fraction calculator you can easily add, subtract, multiply and divide mixed fractions. Fill in your two mixed numbers below and choose your action (add, subtract, multiply or divide). The mixed fraction calculator automatically simpifies improper fractions and reduces the result to the lowest terms and it also shows you the work and steps of the calculation.
Mixed number calculator (with steps)
Simple fraction calculatorMixed fraction calculator
Work and steps of the calculation
The mixed fraction calculator has not yet performed a calculation. Enter two mixed numbers above and choose whether you want to add, subtract, multiply or divide the mixed numbers. The result will be automatically simplified (reduced) by the mixed fraction calculator and the work and steps of the calculation will be shown here.
Regardless of the type of calculation you want to make with mixed numbers, you should always rewrite the whole numbers as a fraction first. The whole numbers must be rewritten as an improper fraction with the same denominator as the fraction part. Second, add the numerator of the improper fraction to the numerator of the fraction part, resulting in a new improper fraction. When both mixed numbers have been rewritten as improper fractions, you can add, subtract, multiply or divide the fractions.
Example mixed number to improper fraction
To perform a calculation with a mixed number, the first thing you need to do is to convert your mixed fraction(s) to (an) improper fraction(s). Below we show you an example of how to rewrite a mixed fraction into an improper fraction.
3
2
5
1
Rewrite the whole number part as an improper fraction with the same denominator as the fraction part.
Multiply the whole number (3) by a fraction whose numerator and denominator are the same (so the actual value is 1) and have the value of the denominator of the fraction part (5). The whole number is now rewritten as an improper fraction with the same denominator as the fraction part.
3
=
3
x
5
5
=
3 x 5
5
=
15
5
2
Add the improper fraction and fraction part.
Because the denominators are the same now, we can add the numerators.
15
5
+
2
5
=
15 + 2
5
=
17
5
3
In summary
3
2
5
=
3 x 5
5
+
2
5
=
15
5
+
2
5
=
17
5
Once the mixed fraction is rewritten as an improper fraction, we can use it to perform calculations with other fractions.
What is a mixed fraction?
A mixed fraction is a number that consists of a whole number and a fraction. For example, 3 ½, "3" is the whole number part and "½" is the fraction part.
This notation is a convenient way to express improper fractions (where the numerator is greater than the denominator). To convert an improper fraction to a mixed fraction, first divide the numerator by the denominator. The whole number part is then the result of this division, while the remainder (the difference between the numerator and the obtained whole number multiplied by the denominator) forms the fraction part.
Mixed fractions are often used to describe practical situations, such as measuring time, length, or weight. They provide a simple and understandable way to represent parts of a whole.
The value of a mixed fraction is always greater than 1 or less than -1. Examples of mixed fractions are:
1
2
3
-2
4
7
3
5
8
Improper fractions vs mixed fractions
An improper fraction is a type of fraction in which the numerator (the top number) is greater than or equal to the denominator (the bottom number). In other words, the numerator is either larger or equal to the denominator, which means that the fraction represents an absolute value that is greater than or equal to 1. Examples of improper fractions:
5
3
-
7
4
12
12
To convert an improper fraction to a mixed fraction, first divide the numerator by the denominator. The whole number part is then the result of this division, while the remainder (the difference between the numerator and the obtained whole number multiplied by the denominator) forms the fraction part.
To convert a mixed fraction to an improper fraction, rewrite the whole number part as a fraction with the same denominator as the fraction part. Multiply the whole number by the denominator of the fraction. This will give you the numerator of the improper fraction.
Mixed fraction to improper fraction in mathematical terms:
a
b
c
=
ac + b
c
For most calculations with mixed fractions, it is necessary to convert the mixed fraction to an improper fraction.
The mixed fraction calculator shows he entire work and steps of the calculation, including the conversion of an improper fraction into a mixed fraction. If you only want to simplify an improper fraction to a mixed fraction, you can use the simplify fraction calculator.
| Improper | Mixed |
|---|---|
5 3 | 1 2 3 |
- 7 4 | -1 3 4 |
12 12 | 1 |
