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:

19 1/2 + 5 5/8 + 6 1/4 = 251/8 = 31 3/8 = 31.375

The result spelled out in words is thirty-one and three eighths (or two hundred fifty-one eighths).

Calculation steps

Conversion a mixed number 19 1/2 to a improper fraction: 19 1/2 = 19 1/2 = 19 · 2 + 1/2 = 38 + 1/2 = 39/2

To find a new numerator:
a) Multiply the whole number 19 by the denominator 2. Whole number 19 equally 19 * 2/2 = 38/2
b) Add the answer from the previous step 38 to the numerator 1. New numerator is 38 + 1 = 39
c) Write a previous answer (new numerator 39) over the denominator 2.

Nineteen and a half is thirty-nine halves.
Conversion a mixed number 5 5/8 to a improper fraction: 5 5/8 = 5 5/8 = 5 · 8 + 5/8 = 40 + 5/8 = 45/8

To find a new numerator:
a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
b) Add the answer from the previous step 40 to the numerator 5. New numerator is 40 + 5 = 45
c) Write a previous answer (new numerator 45) over the denominator 8.

Five and five eighths is forty-five eighths.
Add: 39/2 + 45/8 = 39 · 4/2 · 4 + 45/8 = 156/8 + 45/8 = 156 + 45/8 = 201/8
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, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 8 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-nine halves plus forty-five eighths equals two hundred one eighths.
Conversion a mixed number 6 1/4 to a improper fraction: 6 1/4 = 6 1/4 = 6 · 4 + 1/4 = 24 + 1/4 = 25/4

To find a new numerator:
a) Multiply the whole number 6 by the denominator 4. Whole number 6 equally 6 * 4/4 = 24/4
b) Add the answer from the previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
c) Write a previous answer (new numerator 25) over the denominator 4.

Six and one quarter is twenty-five quarters.
Add: the result of step No. 3 + 25/4 = 201/8 + 25/4 = 201/8 + 25 · 2/4 · 2 = 201/8 + 50/8 = 201 + 50/8 = 251/8
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(8, 4) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 4 = 32. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, two hundred one eighths plus twenty-five quarters equals two hundred fifty-one eighths.

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