Mixed number calculator

This calculator performs basic and advanced operations with mixed numbers, fractions, integers, and decimals. Mixed numbers are also called mixed fractions. A mixed number is a whole number and a proper fraction combined, i.e. one and three-quarters. The calculator evaluates the expression or solves the equation with step-by-step calculation progress information. Solve problems with two or more mixed numbers fractions in one expression.

The result:

8 1/6 + 2 5/6 = 11/1 = 11

The result spelled out in words is eleven.

Calculation steps

Conversion a mixed number 8 1/6 to a improper fraction: 8 1/6 = 8 1/6 = 8 · 6 + 1/6 = 48 + 1/6 = 49/6

To find a new numerator:
a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6
b) Add the answer from the previous step 48 to the numerator 1. New numerator is 48 + 1 = 49
c) Write a previous answer (new numerator 49) over the denominator 6.

Eight and one sixth is forty-nine sixths.
Conversion a mixed number 2 5/6 to a improper fraction: 2 5/6 = 2 5/6 = 2 · 6 + 5/6 = 12 + 5/6 = 17/6

To find a new numerator:
a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6
b) Add the answer from the previous step 12 to the numerator 5. New numerator is 12 + 5 = 17
c) Write a previous answer (new numerator 17) over the denominator 6.

Two and five sixths is seventeen sixths.
Add: 49/6 + 17/6 = 49 + 17/6 = 66/6 = 6 · 11/6 · 1 = 11
Both fractions have the same denominator, which is then the common denominator in the adding them. In the following intermediate step, cancel by a common factor of 6 gives 11/1.
In other words, forty-nine sixths plus seventeen sixths equals eleven.

What is a mixed number?

A mixed number is an integer and fraction

a \frac{b}{c}

whose value equals the sum of that integer and fraction. For example, we write two and four-fifths as

2 \frac{4}{5}

. Its value is

2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{1 0}{5} + \frac{4}{5} = \frac{1 4}{5}

. The mixed number is the exception - the missing operand between a whole number and a fraction is not multiplication but an addition:

2 \frac{4}{5} \neq = 2 \cdot \frac{4}{5}

. A negative mixed number - the minus sign also applies to the fractional

- 2 \frac{4}{5} = - (2 \frac{4}{5}) = - (2 + \frac{4}{5}) = - \frac{1 4}{5}

. A mixed number is sometimes called a mixed fraction. Usually, a mixed number contains a natural number and a proper fraction, and its value is an improper fraction, that is, one where the numerator is greater than the denominator.

How do I imagine a mixed number?

We can imagine mixed numbers in the example of cakes. We have three cakes, and we have divided each into five parts. We thus obtained 3 * 5 = 15 pieces of cake. One piece when we ate, there were 14 pieces left, which is

2 \frac{4}{5}

of cake. When we eat two pieces,

2 \frac{3}{5}

of the cake remains.

Examples:

• sum of two mixed numbers: 1 3/4 + 2 3/8
• addition of three mixed numbers: 1 3/8 + 6 11/13 + 5 7/8
• addition of two mixed numbers: 2 1/2 + 4 2/3
• subtracting two mixed numbers: 7 1/2 - 5 3/4
• multiplication of mixed numbers: 3 3/4 * 2 2/5
• comparing mixed numbers: 3 1/4 2 1/3
• What is 3/4 as a mixed number: 3/4
• subtracting mixed number and fraction: 1 3/5 - 5/6
• sum mixed number and an improper fraction: 1 3/5 + 11/5