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:

23 1/2/3 3/4 = 94/15 = 6 4/15 ≅ 6.2666667

The result spelled out in words is six and four fifteenths (or ninety-four fifteenths).

Calculation steps

Conversion a mixed number 23 1/2 to a improper fraction: 23 1/2 = 23 1/2 = 23 · 2 + 1/2 = 46 + 1/2 = 47/2

To find a new numerator:
a) Multiply the whole number 23 by the denominator 2. Whole number 23 equally 23 * 2/2 = 46/2
b) Add the answer from the previous step 46 to the numerator 1. New numerator is 46 + 1 = 47
c) Write a previous answer (new numerator 47) over the denominator 2.

Twenty-three and a half is forty-seven halves.
Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

To find a new numerator:
a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
b) Add the answer from the previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters.
Divide: 47/2 : 15/4 = 47/2 · 4/15 = 47 · 4/2 · 15 = 188/30 = 2 · 94 /2 · 15 = 94/15
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 15/4 is 4/15) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 2 gives 94/15.
In other words, forty-seven halves divided by fifteen quarters equals ninety-four fifteenths.

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