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:

9 5/2 + 6 7/10 = 91/5 = 18 1/5 = 18.2

The result spelled out in words is eighteen and one fifth (or ninety-one fifths).

Calculation steps

Conversion a mixed number 9 5/2 to a improper fraction: 9 5/2 = 9 5/2 = 9 · 2 + 5/2 = 18 + 5/2 = 23/2

To find a new numerator:
a) Multiply the whole number 9 by the denominator 2. Whole number 9 equally 9 * 2/2 = 18/2
b) Add the answer from the previous step 18 to the numerator 5. New numerator is 18 + 5 = 23
c) Write a previous answer (new numerator 23) over the denominator 2.

Nine and five halves is twenty-three halves.
Conversion a mixed number 6 7/10 to a improper fraction: 6 7/10 = 6 7/10 = 6 · 10 + 7/10 = 60 + 7/10 = 67/10

To find a new numerator:
a) Multiply the whole number 6 by the denominator 10. Whole number 6 equally 6 * 10/10 = 60/10
b) Add the answer from the previous step 60 to the numerator 7. New numerator is 60 + 7 = 67
c) Write a previous answer (new numerator 67) over the denominator 10.

Six and seven tenths is sixty-seven tenths.
Add: 23/2 + 67/10 = 23 · 5/2 · 5 + 67/10 = 115/10 + 67/10 = 115 + 67/10 = 182/10 = 2 · 91/2 · 5 = 91/5
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 10) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 10 = 20. In the following intermediate step, cancel by a common factor of 2 gives 91/5.
In other words, twenty-three halves plus sixty-seven tenths equals ninety-one fifths.

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