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:

7 1/2 - 5 3/4 = 7/4 = 1 3/4 = 1.75

The result spelled out in words is one and three quarters (or seven quarters).

Calculation steps

Conversion a mixed number 7 1/2 to a improper fraction: 7 1/2 = 7 1/2 = 7 · 2 + 1/2 = 14 + 1/2 = 15/2

To find a new numerator:
a) Multiply the whole number 7 by the denominator 2. Whole number 7 equally 7 * 2/2 = 14/2
b) Add the answer from the previous step 14 to the numerator 1. New numerator is 14 + 1 = 15
c) Write a previous answer (new numerator 15) over the denominator 2.

Seven and a half is fifteen halves.
Conversion a mixed number 5 3/4 to a improper fraction: 5 3/4 = 5 3/4 = 5 · 4 + 3/4 = 20 + 3/4 = 23/4

To find a new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4
b) Add the answer from the previous step 20 to the numerator 3. New numerator is 20 + 3 = 23
c) Write a previous answer (new numerator 23) over the denominator 4.

Five and three quarters is twenty-three quarters.
Subtract: 15/2 - 23/4 = 15 · 2/2 · 2 - 23/4 = 30/4 - 23/4 = 30 - 23/4 = 7/4
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 4) = 4. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 4 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, fifteen halves minus twenty-three quarters equals seven quarters.

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