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:

19.685/2 = 3937/400 = 9 337/400 = 9.8425

The result spelled out in words is nine and three hundred thirty-seven four-hundredths (or three thousand nine hundred thirty-seven four-hundredths).

Calculation steps

Conversion a decimal number to a fraction: 19.685 = 19685/1000 = 3937/200

a) Write down the decimal 19.685 divided by 1: 19.685 = 19.685/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
19.685/1 = 196.85/10 = 1968.5/100 = 19685/1000
Note: 19685/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
19685/1000 = 3937 * 5/200 * 5 = 3937 * 5/200 * 5 = 3937/200
Divide: 19.685 / 2 = 3937/200 · 1/2 = 3937 · 1/200 · 2 = 3937/400
The second operand is an integer. It is equivalent to the fraction 2/1. 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 2/1 is 1/2) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, three thousand nine hundred thirty-seven two-hundredths divided by two equals three thousand nine hundred thirty-seven four-hundredths.

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